The Failure of Risk Management

WHY IT'S BROKEN AND HOW TO FIX IT

Second Edition

DOUGLAS W. HUBBARD

This second edition first published 2020

© 2020 by Douglas W. Hubbard. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

Edition History

John Wiley & Sons, Inc. (1e, 2009)

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Library of Congress Cataloging-in-Publication Data

Names: Hubbard, Douglas W., 1962– author.

Title: The failure of risk management : why it's broken and how to fix it / Douglas W. Hubbard.

Description: Second edition. | Hoboken, New Jersey : Wiley, 2020. | Includes index.

Identifiers: LCCN 2019051494 (print) | LCCN 2019051495 (ebook) | ISBN 9781119522034 (hardback) | ISBN 9781119522027 (adobe pdf) | ISBN 9781119522041 (epub)

Subjects: LCSH: Risk management.

Classification: LCC HD61 .H76 2020 (print) | LCC HD61 (ebook) | DDC 658.15/5—dc23

LC record available at https://lccn.loc.gov/2019051494

LC ebook record available at https://lccn.loc.gov/2019051495

Cover Design: Wiley

Cover Image: © RomoloTavani/iStock.com

I dedicate this book to my entire support staff: my wife, Janet, and our children, Evan, Madeleine, and Steven, and to the Armed Forces of the United States of America.

About the Author

Mr. Hubbard's career in quantitatively based management consulting began in 1988 with Coopers & Lybrand. He founded Hubbard Decision Research in 1999 and he developed the applied information economics (AIE) method to solve complex, risky decisions. He has used AIE in many fields, including cybersecurity, aerospace, biotech, environmental policy, commercial real estate, tech startups, entertainment, and military logistics, to name a few. His AIE methodology has received critical praise from respected research firms such as Gartner, Forrester, and others.

He is the author of the following books (all published with Wiley between 2007 and 2016):

How to Measure Anything: Finding the Value of Intangibles in Business (one of the all-time, best-selling books in business math)

The Failure of Risk Management: Why It's Broken and How to Fix It

Pulse: The New Science of Harnessing Internet Buzz to Track Threats and Opportunities

How to Measure Anything in Cybersecurity Risk (coauthored with Richard Seiersen)

His books have sold over 140,000 copies in eight languages and are used as textbooks in dozens of university courses including at the graduate level. Two of his books are required reading for the Society of Actuaries exam prep, and he is the only author with more than one on the list. In addition to his books, Mr. Hubbard has published articles in Nature, The American Statistician, IBM Journal of R&D, CIO Magazine, and more.

Preface

A lot has happened in the decade since the first edition of this book, both in the world of risk management and in my own work. Since then, I've written two more editions of my first book, How to Measure Anything: Finding the Value of Intangibles in Business as well as writing Pulse: The New Science of Harnessing Internet Buzz to Track Threats and Opportunities and How to Measure Anything in Cybersecurity Risk. By 2017 this book (along with How to Measure Anything) was placed on the required reading list for the Society of Actuaries Exam Prep.

Regarding the broader topic of risk management, there were several more examples of risk management gone wrong since the first edition. The Fukushima Daiichi nuclear power plant disaster in Japan, the Deepwater Horizon oil spill in the Gulf of Mexico, and multiple large cyberattacks that compromised hundreds of millions of personal records. But I won't dwell on these anecdotes or the events that occurred prior to the first edition. This book should be just as relevant after the next big natural disaster, major product safety recall, or catastrophic industrial accident. Better yet, I hope readers see this book as a resource they need before those events occur. Risk management that simply reacts to yesterday's news is not risk management at all.

I addressed risk in my first book, How to Measure Anything: Finding the Value of Intangibles in Business. Risk struck me as one of those items that is consistently perceived as an intangible by management. True, risk is intangible in one sense. A risk that something could occur—the probability of some future event—is not tangible in the same way as progress on a construction project or the output of a power plant. But it is every bit as measurable. Two entire chapters in the first book focused just on the measurement of uncertainty and risks.

Unfortunately, risk management based on actual measurements of risks is not the predominant approach in most industries. I see solutions for managing the risks of some very important problems that are in fact no better than astrology. And this is not a controversial position I'm taking. The flaws in these methods are widely known to the researchers who study them. The message has simply not been communicated to the larger audience of managers.

All of my books—not just the two that explicitly mention risk in the title—are really about making or supporting critical decisions where there is a lot of uncertainty and a cost to being wrong. In other words, I write about risky decisions. I was drawn to this topic after watching consultants come up with a lot of questionable schemes for assessing risks, measuring performance, and prioritizing portfolios with no apparent foundation in statistics or decision science. Arbitrary scoring schemes and other qualitative methods have virtually taken over some aspects of formalized decision-making processes in management. In other areas, some methods that do have a sound, scientific, and mathematical basis are consistently misunderstood and misapplied.

I just didn't see enough attention brought to this topic. Of all the good, solid academic research and texts on risk analysis, risk management, and decision science, none seem to be directly addressing the problem of the apparently unchecked spread of pseudoscience in this field. In finance, Nassim Taleb's popular books, Fooled by Randomness and The Black Swan have pointed out the existence of serious problems. But in those cases, there was not much practical advice for risk managers and very little information about assessing risks outside of finance. There is a need to point out these problems to a wide audience for a variety of different risks.

Writing on this topic would be challenging for several reasons, not the least of which is the fact that any honest and useful treatment of risk management steps on some toes. That hasn't changed since the first edition. Proponents of widely used methods—some of which have been codified in international standards—have felt threatened by some of the positions I am taking in this book. Therefore, I've taken care that each of the key claims I make about the weaknesses of some methods is supported by the thorough research of others and are not just my own opinion. The research is overwhelmingly conclusive—much of what has been done in risk management, when measured objectively, has added no value to the issue of managing risks. It may actually have made things worse.

The biggest challenge would be reaching a broad audience. Although the solution to better risk management is, for most, better quantitative analysis, a specialized mathematical text on the analysis and management of risks would not reach a wide-enough audience. The numerous technical texts already published haven't seemed to penetrate the management market, and I have no reason to believe that mine would fare any better. The approach I take here is to provide my readers with just enough technical information so that they can make a 180-degree turn in risk management. They can stop using the equivalent of astrology in risk management and at least start down the path of the better methods. For risk managers, mastering those methods will become part of a longer career and a study that goes beyond this book. This is more like a first book in astronomy for recovering astrologers—we have to debunk the old and introduce the new.

Douglas W. Hubbard

February 2020

Acknowledgments

Many people helped me with this book in many ways. Some I have interviewed for this book, some have provided their own research (even some prior to publication), and others have spent time reviewing my manuscript and offering many suggestions for improvement. In particular, I would like to thank Dr. Sam Savage of Stanford University, who has been extraordinarily helpful on all these counts.

Reed Augliere | Jim Dyer | Harry Markowitz
David Bearden | Jim Franklin | Jason Mewis
Christopher “Kip” Bohn | Andrew Freeman | Bill Panning
Andrew Braden | Vic Fricas | Sam Savage
David Budescu | Dan Garrow | John Schuyler
Bob Clemen | John Hester | Yook Seng Kong
Ray Covert | Steve Hoye | Thompson Terry
Dennis William Cox | David Hubbard | David Vose
Tony Cox | Karen Jenni | Stephen Wolfram
Diana Del Bel Belluz | Rick Julien | Peter Alan Smith
Jim DeLoach | Daniel Kahneman | Jack Jones
Robin Dillon-Merrill | Allen Kubitz | Steve Roemerman
Rob Donat | Fiona MacMillan |

PART ONE
An Introduction to the Crisis

CHAPTER 1
Healthy Skepticism for Risk Management

It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring.

—CARL SAGAN

Everything's fine today, that is our illusion.

—VOLTAIRE

What is your single biggest risk? How do you know? These are critical questions for any organization regardless of industry, size, structure, environment, political pressures, or changes in technology. Any attempt to manage risk in these organizations should involve answering these questions.

We need to ask hard questions about new and rapidly growing trends in management methods, especially when those methods are meant to help direct and protect major investments and inform key public policy. The application of healthy skepticism to risk management methods was long past due when I wrote the first edition of this book more than a decade ago.

The first edition of this book came out on the tail end of the Great Recession in 2008 and 2009. Since then, several major events have resulted in extraordinary losses both financially and in terms of human health and safety. Here are just a few:

Deepwater Horizon offshore oil spill (2010)

Fukushima Daiichi nuclear disaster (2011)

Flint Michigan water system contamination (starting 2012)

Samsung Galaxy Note 7 battery failures (2016)

Multiple large data breaches (Equifax, Anthem, Target, etc.)

Amtrak derailments/collisions (2018)

Events such as these and other natural, geopolitical, technological, and financial disasters in the beginning of the twenty-first century periodically accelerate (maybe only temporarily) interest in risk management among the public, businesses, and lawmakers. This continues to spur the development of several risk management methods.

The methods to determine risks vary greatly among organizations. Some of these methods—used to assess and mitigate risks of all sorts and sizes—are recent additions in the history of risk management and are growing in popularity. Some are well-established and highly regarded. Some take a very soft, qualitative approach and others are rigorously quantitative. If some of these are better, if some are fundamentally flawed, then we should want to know.

Actually, there is very convincing evidence about the effectiveness of different methods and this evidence is not just anecdotal. As we will see in this book, this evidence is based on detailed measurements in large controlled experiments. Some points about what works are even based on mathematical proofs. This will all be reviewed in much detail but, for now, I will skip ahead to the conclusion. Unfortunately, it is not good news.

I will make the case that most of the widely used methods are not based on any proven theories of risk analysis, and there is no real, scientific evidence that they result in a measurable improvement in decisions to manage risks. Where scientific data does exist, the data show that many of these methods fail to account for known sources of error in the analysis of risk or, worse yet, add error of their own.

Most managers would not know what they need to look for to evaluate a risk management method and, more likely than not, can be fooled by a kind of “analysis placebo effect” (more to come on that).¹ Even under the best circumstances, where the effectiveness of the risk management method itself was tracked closely and measured objectively, adequate evidence may not be available for some time.

A more typical circumstance, however, is that the risk management method itself has no performance measures at all, even in the most diligent, metrics-oriented organizations. This widespread inability to make the sometimes-difficult differentiation between methods that work and methods that don't work means that ineffectual methods are likely to spread. Once certain methods are adopted, institutional inertia cements them in place with the assistance of standards and vendors that refer to them as “best practices.” Sometimes they are even codified into law. Like a dangerous virus with a long incubation period, methods are passed from company to company with no early indicators of ill effects until it's too late.

The consequences of flawed but widely adopted methods are inevitably severe for organizations making critical decisions. Decisions regarding not only the financial security of a business but also the entire economy and even human lives are supported in large part by our assessment and management of risks. The reader may already start to see the answer to the first question at the beginning of this chapter, “What is your biggest risk?”

A “COMMON MODE FAILURE”

The year 2017 was remarkable for safety in commercial air travel. There was not a single fatality worldwide from an accident. Air travel had already been the safest form of travel for decades. Even so, luck had some part to play in the 2017 record, but that luck would not last. That same year, a new variation of the Boeing 737 MAX series passenger aircraft was introduced: the 737 MAX 8. Within twelve months of the initial roll out, well over one hundred MAX 8s were in service.

In 2018 and 2019, two crashes with the MAX 8, totaling 339 fatalities, showed that a particular category of failure was still very possible in air travel. Although the details of the two 737 crashes were still emerging as this book was written, it appears that it is an example of a common mode failure. In other words, the two crashes may be linked to the same cause. This is a term familiar to systems risk analysis in some areas of engineering, where several failures can have a common cause. This would be like a weak link in a chain, but where the weak link was part of multiple chains.

I had an indirect connection to another common mode failure in air travel forty years before this book came out. In July 1989, I was the commander of the Army Reserve unit in Sioux City, Iowa. It was the first day of our two-week annual training and I had already left for Fort McCoy, Wisconsin with a small group of support staff. The convoy of the rest of the unit was going to leave that afternoon, about five hours behind us. But just before the main body was ready to leave for annual training, the rest of my unit was deployed for a major local emergency.

United Airlines flight 232 to Philadelphia was being redirected to the small Sioux City airport because of serious mechanical difficulties. It crashed, killing 111 passengers and crew. Fortunately, the large number of emergency workers available and the heroic airmanship of the crew helped make it possible to save 185 onboard. Most of my unit spent the first day of our annual training collecting the dead from the tarmac and the nearby cornfields.

During the flight, the DC-10's tail-mounted engine failed catastrophically, causing the fast-spinning turbine blades to fly out like shrapnel in all directions. The debris from the turbine managed to cut the lines to all three redundant hydraulic systems, making the aircraft nearly uncontrollable. Although the crew was able to guide the aircraft in the direction of the airport by varying the thrust to the two remaining wing-mounted engines, the lack of tail control made a normal landing impossible.

Aviation officials would refer to this as a “one-in-a-billion” event² and the media repeated this claim. But because mathematical misconceptions are much more common than one in a billion, if someone tells you that something that had just occurred had merely a one-in-a-billion chance of occurrence, you should consider the possibility that they calculated the odds incorrectly.

This event, as may be the case with the recent 737 MAX 8 crashes, was an example of a common mode failure because a single source caused multiple failures. If the failures of three hydraulic systems were entirely independent of each other, then the failure of all three hydraulic systems in the DC-10 would be extremely unlikely. But because all three hydraulic systems had lines near the tail engine, a single event could damage all of them. The common mode failure wiped out the benefits of redundancy. Likewise, a single software problem may cause problems on multiple 737 crashes.

Now consider that the cracks in the turbine blades of the DC-10 would have been detected except for what the National Transportation Safety Board (NTSB) called “inadequate consideration given to human factors” in the turbine blade inspection process. Is human error more likely than one in a billion? Absolutely. And human error in large complex software systems like those used on the 737 MAX 8 is almost inevitable and takes significant quality control to avoid. In a way, human error was an even-more-common common mode failure in the system.

But the common mode failure hierarchy could be taken even further. Suppose that the risk management method itself was fundamentally flawed. If that were the case, then perhaps problems in design and inspection procedures, whether it is hydraulics or software, would be very hard to discover and much more likely to materialize. In effect, a flawed risk management is the ultimate common mode failure.

And suppose they are flawed not just in one airline but in most organizations. The effects of disasters like Katrina, the financial crisis of 2008/2009, Deepwater Horizon, Fukashima, or even the 737 MAX 8 could be inadequately planned for simply because the methods used to assess the risk were misguided. Ineffective risk management methods that somehow manage to become standard spread this vulnerability to everything they touch.

The ultimate common mode failure would be a failure of the risk management process itself. A weak risk management approach is effectively the biggest risk in the organization.

The financial crisis occurring while I wrote the first edition of this book was another example of a common mode failure that traces its way back to the failure of risk management of firms such as AIG, Lehman Brothers, Bear Stearns, and the federal agencies appointed to oversee them. Previously loose credit practices and overly leveraged positions combined with an economic downturn to create a cascade of loan defaults, tightening credit among institutions, and further economic downturns. Poor risk management methods are used in government and business to make decisions that not only guide risk decisions involving billions—or trillions—of dollars but also are used to affect decisions that impact on human health and safety.

Fortunately, the cost to fix the problem is almost always a fraction of a percent of the size of what is being risked. For example, a more realistic evaluation of risks in a large IT portfolio worth over a hundred million dollars would not have to cost more than a million—probably a lot less. Unfortunately, the adoption of a more rigorous and scientific management of risk is still not widespread. And for major risks, such as those in the previous list, that is a big problem for corporate profits, the economy, public safety, national security, and you.

A NASA scientist once told me the way that NASA reacts to risk events. If she were driving to work, veered off the road and ran into a tree, NASA management would develop a class to teach everyone how not to run into that specific tree. In a way, that's how most organizations deal with risk events. They may fix that immediate cause but not address whether the original risk analysis allowed that entire category of flaws to happen in the first place.

KEY DEFINITIONS: RISK MANAGEMENT AND SOME RELATED TERMS

There are numerous topics in the broad term of risk management but this term is often used in a much narrower sense than it should be. This is because risk is used too narrowly, management is used too narrowly, or both. And we also need to discuss a few other key terms that will come up a lot and how they fit together with risk management, especially the terms risk assessment, risk analysis, and decision analysis.

If you start looking for definitions of risk, you will find many wordings that add up to the same thing and a few versions that are fundamentally different. For now, I'll skirt some of the deeper philosophical issues about what risk means (yes, there are some, but that will come later) and I'll avoid some of the definitions that seem to be unique to specialized uses. Chapter 6 is devoted to why the definition I am going to propose is preferable to various mutually exclusive alternatives that each have proponents who assume their definition is the “one true” definition.

For now, I'll focus on a definition that, although it contradicts some uses of the term, best represents the one used by well-established, mathematical treatments of the term (e.g., actuarial science), as well as any English dictionary or even how the lay public uses the term.

DEFINITION OF RISK

Long definition: A potential loss, disaster, or other undesirable event measured with probabilities assigned to losses of various magnitudes

Shorter (equivalent) definition: The possibility that something bad could happen

The second definition is more to the point, but the first definition describes a way to quantify a risk. First, we determine a probability that the undesirable event will occur. Then, we need to determine the magnitude of the loss from this event in terms of financial losses, lives lost, and so on.

The undesirable event could be just about anything, including natural disasters, a major product recall, the default of a major debtor, hackers releasing sensitive customer data, political instability surrounding a foreign office, workplace accidents resulting in injuries, or a pandemic flu virus disrupting supply chains. It could also mean personal misfortunes, such as a car accident on the way to work, loss of a job, a heart attack, and so on. Almost anything that could go wrong is a risk.

Because risk management generally applies to a management process in an organization, I'll focus a bit less on personal risks. Of course, my chance of having a heart attack is an important personal risk to assess and I certainly try to manage that risk. But when I'm talking about the failure of risk management—as the title of this book indicates—I'm not really focusing on whether individuals couldn't do a better job of managing personal risks like losing weight to avoid heart attacks. I'm referring to major organizations that have adopted what is ostensibly some sort of formal risk management approach that they use to make critical business and public policy decisions.

Now, let us discuss the second half of the phrase risk management. Again, as with risk, I find multiple, wordy definitions for management, but here is one that seems to represent and combine many good sources.

DEFINITION OF MANAGEMENT

Long definition: The planning, organization, coordination, control, and direction of resources toward defined objective(s)

Shorter, folksier definition: Using what you have to get what you need

There are a couple of qualifications that, although they should be extremely obvious, are worth mentioning when we put risk and management together. Of course, when an executive wants to manage risks, he or she actually wishes to reduce it or at least make sure it is acceptable in pursuit of better opportunities. And because the current amount of risk and its sources are not immediately apparent, an important part of reducing or minimizing risks is figuring out where the risks are. Similar to any other management program, risk management has to make effective use of limited resources. Of course, we must accept that risk is inherent in business and risk reduction is practical only up to a point. Putting all of that together, here is a definition (again, not too different in spirit from the myriad definitions found in other sources).

DEFINITION OF RISK MANAGEMENT

Long definition: The identification, analysis, and prioritization of risks followed by coordinated and economical application of resources to reduce, monitor, and control the probability and/or impact of unfortunate events

Shorter definition: Being smart about taking chances

Risk management methods come in many forms, but the ultimate goal is to minimize risk in some area of the firm relative to the opportunities being sought, given resource constraints. Some of the names of these efforts have become terms of art in virtually all of business. A popular (and, I think, laudable) trend is to put the word enterprise in front of risk management to indicate that it is a comprehensive approach to risk for the firm. Enterprise risk management (ERM) is one of the headings under which many of the trends in risk management appear. I'll call ERM a type of risk management program, because this is often the banner under which risk management is known. I will also distinguish programs from actual methods because ERM could be implemented with entirely different methods, either soft or quantitative.

The following are just a few examples of various programs related to managing different kinds of risks (Note: Some of these can be components of others and the same program can contain a variety of different methods):

Enterprise risk management (ERM)

Project portfolio management (PPM) or Project risk management (PRM)

Portfolio management (as in financial investments)

Disaster recovery and business continuity planning (DR/BCP)

Governance risk and compliance (GRC)

Emergency/crisis management processes

The types of risks managed, just to name a few, include physical security, product liability, information security, various forms of insurance, investment volatility, regulatory compliance, actions of competitors, workplace safety, getting vendors or customers to share risks, political risks in foreign governments, business recovery from natural catastrophes, or any other uncertainty that could result in a significant loss.

As the previous definition indicates, risk management activities include the analysis and mitigation of risks as well as establishing the tolerance for risk and managing the resources for doing all of this. All of these components of risk management are important but the reader will notice that this book will spend a lot of time on evaluating methods of risk analysis. So let me offer both a long and short definition of risk analysis at this point.

DEFINITION OF RISK ANALYSIS

Long definition: The detailed examination of the components of risk, including the evaluation of the probabilities of various events and their ultimate consequences, with the ultimate goal of informing risk management efforts

Shorter definition: How you figure out what your risks are (so you can do something about it)

Note that some risk managers will make a distinction between risk analysis and risk assessment or may use them synonymously. If they are used separately, it is often because the identification of risk is considered separate from the analysis of those risks and together they comprise risk assessment. Personally, I find the analysis and identification of risks to be an iterative, back-and-forth process without a clear border between them. That is, we start with some identification of risk but on analyzing them, we identify more risks. So I may use the terms analysis and assessment a bit more interchangeably.

Now, obviously, if risk analysis methods were flawed, then the risk management would have to be misguided. If the initial analysis of risk is not based on meaningful measures, the risk mitigation methods are bound to address the wrong problems. If risk analysis is a failure, then the best case is that the risk management effort is simply a waste of time and money because decisions are ultimately unimproved. In the worst case, the erroneous conclusions lead the organization down a more dangerous path that it would probably not have otherwise taken. Just consider how flawed risk management may impact an organization or the public in the following situations.

The approval and prioritization of investments and project portfolios in major US companies

The level of protections needed for major security threats, including cybersecurity threats, for business and government

The approval of government programs worth many billions of dollars

The determination of when additional maintenance is required for old bridges or other infrastructure

The evaluation of patient risks in health care

The identification of supply chain risks due to pandemic viruses

The decision to outsource pharmaceutical production overseas

Risks in any of these areas, and many more, could reveal themselves only after a major disaster in a business, government program, or even your personal life. Clearly, mismeasurement of these risks would lead to major problems—as has already happened in some cases.

The specific method used to assess these risks may have been sold as “formal and structured” and perhaps it was even claimed to be “proven.” Surveys of organizations even show a significant percentage of managers who will say the risk management program was “successful” (more on this to come). Perhaps success was claimed for the reason that it helped to “build consensus,” “communicate risks,” or “change the culture.”

Because the methods used did not actually measure these risks in a mathematically and scientifically sound manner, management doesn't even have the basis for determining whether a method works. Sometimes, management or vendors rely on surveys to assess the effectiveness of risk analysis, but they are almost always self-assessments by the surveyed organizations. They are not independent, objective measures of success in reducing risks.

I'm focusing on the analysis component of risk management because, as stated previously, risk management has to be informed in part by risk analysis. And then, how risks are mitigated is informed by the cost of those mitigations and the expected effect those mitigations will have on risks. In other words, even choosing mitigations involves another layer of risk analysis.

This, in no way, should be interpreted as a conflation of risk analysis with risk management. Yes, I will be addressing issues other than what is strictly the analysis of risk as the problem later in this book. But it should be clear that if this link is weak, then that's where the entire process fails. If risk analysis is broken, it is the first and most fundamental common mode failure of risk management.

And just as risk analysis is a subset of risk management, those are subsets of decision analysis in general decision-making. Risks are considered alongside opportunities when making decisions, and decision analysis is a quantitative treatment of that topic. Having risk management without being integrated into decision-making in general is like a store that sells only left-handed gloves.

WHAT FAILURE MEANS

Now that we have defined risk management, we need to discuss what I mean by the failure of risk management. With some exceptions, it may not be very obvious. And that is part of the problem.

First, a couple of points about the anecdotes I just used. I believe airlines and aircraft manufacturers involved in the crashes described before were probably applying what they believed to be a prudent level of risk management. I also believe that many of the other organizations involved in other disasters I listed were not always just ignoring risk management practices. When I refer to the “failure of risk management,” I do not just refer to outright negligence. Deliberately failing to employ the accounting controls that would have avoided Enron's demise, for example, are not the kind of failures I examine the most in this book. I will concentrate more on the failure of sincere efforts to manage risks—as I will presume is the case with many organizations—even though we know the possible lawsuits must argue otherwise. I'm focusing on those organizations that believe they have adopted an effective risk management method and are unaware that they haven't improved their situation one iota.

Second, I used these anecdotes in part to make a point about the limits of anecdotes when it comes to showing the failure or success of risk management. No single event necessarily constitutes a failure of risk management. Nor would a lucky streak of zero disasters have indicated that the risk management was working.

I think this is a departure from some approaches to the discussion of risk management. I have heard some entertaining speakers talk about various anecdotal misfortunes of companies as evidence that risk management failed. I have to admit, these stories are often fascinating, especially where the circumstances are engaging and the outcome was particularly disastrous. But I think the details of the mortgage crisis, 9/11, rogue traders, Hurricane Katrina, major cyberattacks, or Fukushima feed a kind of morbid curiosity more than they inform about risk management. Perhaps the stories made managers feel a little better about the fact they hadn't (yet) made such a terrible blunder.

I will continue to use examples like this because that is part of what it takes to help people connect with the concepts. But we need a better measure of the success or failure of risk management than single anecdotes. In most cases regarding risk management, an anecdote should be used only to illustrate a point, not to prove a point.

So, when I claim that risk management has failed, I'm not necessarily basing that on individual anecdotes of unfortunate things happening. It is possible, after all, that organizations in which a disaster hasn't occurred are just lucky and they may have been doing nothing substantially different from organizations in which disasters have occurred. When I say that risk management has failed, it is for at least one of three reasons, all of which are independent of individual anecdotes:

The effectiveness of risk management itself is almost never measured: The biggest failure of risk management is that there is usually no experimentally verifiable evidence that the methods used improve on the assessment and mitigation of risks, especially for the softer (and much more popular) methods. If the only “evidence” is a subjective perception of success by the very managers who championed the method in the first place, then we have no reason to believe that the risk management method does not have a negative return. For a critical issue like risk management, we should require positive proof that it works—not just accept the lack of proof that it doesn't. Part of the success of any initiative is the measurable evidence of its success. It is a failure of risk management to know nothing of its own risks. It is also an avoidable risk that risk management, contrary to its purpose, fails to avoid.

Some parts that have been measured don't work: The experimental evidence that does exist for some aspects of risk management indicates the existence of some serious errors and biases. Because many risk management methods rely on human judgment, we should consider the research that shows how humans misperceive and systematically underestimate risks. If these problems are not identified and corrected, then they will invalidate any risk management method based even in part on human assessments. Other methods add error through arbitrary scales or the naive use of historical data. Even some of the most quantitatively rigorous methods fail to produce results that compare well with historical observations.

Some parts that do work aren't used: There are methods that are proven to work both in controlled laboratory settings and in the real world, but they are not used in most risk management processes. These are methods that are entirely practical in the real world and, although they may be more elaborate, are easily justified for the magnitude of the decisions risk management will influence.

In total, these failures add up to the fact that we still take unnecessary risks within risk management itself. Now it is time to measure risk management itself in a meaningful way so we can identify more precisely where risk management is broken and how to fix it.

SCOPE AND OBJECTIVES OF THIS BOOK

My objectives with this book are (1) to reach the widest possible audience of managers and analysts, (2) to give them enough information to quit using ineffective methods, and (3) to get them started on better solutions.

The first objective—reaching a wide audience—requires that I don't treat risk management myopically from the point of a given industry. There are many existing risk management texts that I consider important classics, but I see none that map the breadth of the different methods and the problems and advantages of each. There are financial risk analysis texts written specifically for financial analysts and economists. There are engineering and environmental risk texts for engineers and scientists. There are multiple risk management methods written for managers of software projects, computer security, or disaster recovery. Many of these sources seem to talk about risk management as if their methods comprised the entire subject. None seems entirely aware of the others.

The wide audience objective also means that I can't write just about the latest disaster. A reader picking up the first edition of this book in 2009 may think the risk I'm talking about is a financial risk. If I had written this just after the Fukushima Daiichi nuclear disaster of 2011 or more recent events, then risk might have meant something very different. But risk is not selective in that way and the best methods are not specific to one category of risks. Thinking about risks means thinking about events that have not yet occurred, not just last year's news.

Finally, reaching a wide audience requires that I don't just write another esoteric text on quantitative methods for a small community of experts. Of those, there are already some excellent sources that I will not attempt to reproduce. A couple of slightly technical issues will be discussed, but only enough to introduce the important concepts. So, I will spend very little time on well-developed methods in actuarial science or quality control in engineering. The focus will be more on where there are numerous competing methods and the highest levels of management such as ERM.

The last two objectives—to get managers to quit using ineffectual methods and start them on a better path—are also satisfied by a just-technical-enough approach to the problem. This book won't make most managers masters of more quantitative and scientific methods of risk management. I merely want to convince them to make a radical change in direction from the methods they are most likely using now.

To accomplish these objectives, the remainder of this book is divided along the lines implied by the title:

Part One: An Introduction to the Crisis: This first chapter introduced the problem and its seriousness. Chapter 2 outlines the diversity of approaches to assess and mitigate risks and discusses how managers rate their own firms in these areas. Chapter 3 examines how we should evaluate risk management methods. Chapter 4 will show a simple “straw man” that can be the basis for developing a fully quantitative model. (This will also provide a way to imagine an alternative to current risk management methods as we go through a long and detailed criticism of them.)

Part Two: Why It's Broken: After an introduction to four basic schools of thought about risk management, we will discuss the confusing differences in basic terminology among different areas of risk management. Then we will introduce several sources of fundamental errors in popular methods that remain unaddressed. We will list several fallacies that keep some from adopting better methods. Finally, this part of the book will outline some significant problems with even the most quantitative methods being used.

Part Three: How to Fix It: This final part will introduce methods for addressing each of the previously discussed sources of error in risk management methods. We will build on the basic straw man model introduced in chapter 4. We will discuss the basic concepts behind better methods, including how to think about probabilities and how to introduce scientific methods and measurements into risk management. Finally, we will talk about some of the issues involved in creating a culture in organizations and governments that would facilitate and incentivize better risk management.

Throughout this book, I will offer those who require more hands-on examples sample spreadsheets on this book's website at www.howtomeasureanything.com/riskmanagement. Those who prefer the 10,000-foot view can still get a good idea of the issues without feeling dragged down by some technical details, whereas those who prefer to get more information can get specific example calculations. The website will also give all readers access to evolving risks, new ideas and a community of other professionals interested in commenting on those.

See this book's website at www.howtomeasureanything.com/riskmanagement for detailed examples from the book, discussion groups, and up-to-date news on risk management.

NOTES

 1. My use of placebo effect requires a qualification. The placebo effect in medicine is the tendency among patients to experience both subjective and, in some cases, objectively observable improvements in health after receiving treatment that should be inert. This is a purely psychological effect but the improvements could be in objectively measurable ways—such as reducing blood pressure or cholesterol. However, when I refer to a placebo effect, I mean that there literally is no improvement other than the subjective impression of an improvement.

 2. Capt. A. C. Haynes, “United 232: Coping with the ‘One-in-a-Billion’ Loss of All Flight Controls,” Accident Prevention 48, June 1991.

CHAPTER 2
A Summary of the Current State of Risk Management

People who don't take risks generally make about two big mistakes a year. People who do take risks generally make about two big mistakes a year.

—PETER DRUCKER

Before we start changing any system, it's a good idea to get a reading on its current state and to figure out how it got that way. Risk management is a very old idea that has changed dramatically just in the past few decades.

The history of any idea brings its own baggage that often limits our current thinking on the concept and risk management is no exception. Institutions evolve, standards are codified, and professions mature in such a way that it causes all of us to think in more limited ways than we need to. So before we consider the current state, let's see how we got here.

A SHORT AND ENTIRELY-TOO-SUPERFICIAL HISTORY OF RISK

Organizational risk management could be said to have existed at least as early as the first time a king or chieftain decided to fortify walls, make security alliances, or store extra provisions in case of famine. Even more formalized risk management by agreement among parties seems to be a feature of the earliest civilizations. Since ancient Babylon, traders managed the risks of transporting goods great distances by having the buyers provide loans to the sellers that would be repaid with interest only when the goods arrived safely. The Code of Hammurabi by the Babylonian king of that name provided certain compensations or indemnifications for those harmed by bandits or floods. Babylon was also the birthplace of banking, where lenders managed risks starting with the careful selection of debtors.

But throughout most of human history, risk management was an unguided mitigation of risks. Choosing what risks to prepare for was always a matter of gut feel. What differentiates risk management since the start of the Age of Enlightenment is a more systematic approach to assessing the risk. The development of probability theory and statistics in the seventeenth century enabled risk to be quantified in a meaningful way. However, the typical context of these mathematical investigations were well-defined games of chance. These powerful new tools would be adopted only in select industries for select applications and, even then, only slowly.

From the eighteenth century to the beginning of the twentieth century, the quantitative assessment of risk was exemplified in—and largely limited to—insurance and banking. Although the term actuary predates even probability theory, it was not until the mid-nineteenth century that actuaries became an established profession with accreditation requirements and their methods had risen to earn the title of actuarial science.

Later in that period, we see quantitative risk analysis applied to financial markets and perhaps certain government agencies dealing with public health. Still, until the mid-twentieth century, the idea of a retailer or manufacturer using similar methods to assess risk in operations, new products, marketing campaigns, or major acquisitions was not seriously considered. For this reason, the executives in many firms may have treated risk management as synonymous with insurance or making sure the simplest and most obvious precautions are taken (and many still do today). At most, it was effectively a checklist approach in, for example, areas where safety was a key driver (aviation, mining, etc.).

By the 1960s, new methods and tools were being adopted by professionals outside of traditional insurance: engineers and economists. The emergence of computers and the ability to generate thousands of random scenarios with quantitative models made it possible to do the math with uncertain inputs. Engineers in nuclear power and oil and gas were among the first to adopt methods like this outside of insurance. Economists were influenced more by mathematical fields of game theory and decision theory, which provided for the mathematical description of common decision problems, especially decisions under uncertainty. The methods of engineers and economists were both connected to the fundamental ideas of probability theory, and they were largely developed in isolation from actuarial science.

By the end of the twentieth century, a fourth independent set of methods were being used as part of risk management, and these methods had almost no connection to the previous ideas developed by actuaries, economists, or engineers. Struggling to keep track of emerging risks, executives were hungry for a simple way to summarize the risk landscape, without necessarily adopting the more quantitative (and, at the time, more obscure) methods that came before them.

By the 1990s the major consulting firms promoted an early version of a common risk communication tool known as the risk matrix as well as various qualitative risk ranking or risk scoring methods. These were simple to use and simple to communicate. In some cases, pressure to adopt some sort of risk analysis method quickly encouraged the adoption of the simplest method without regard to its effectiveness. Once one approach gains momentum, prudent executives had a growing interest in using a method that everyone else was using. Every shock to the system, such as natural disasters, recessions, terrorism, emerging cybersecurity threats, and more, encouraged wider adoption of whatever simple method was gaining a foothold.

Firms were caught up in a growing “risk culture.” In response to demand for more clarity, several attempts to make so-called formal methodologies for risk assessment and risk management have evolved. Some of these methods are codified in influential standards such as the International Standards Organization (ISO) and the National Institute of Standards & Technology (NIST) in the US. More variations on these have been developed by numerous consulting firms, and many companies created customized approaches based on the same ideas.

If executives needed any more incentive to adopt risk management, new regulations continue to provide the extra push. Since 1988, the Basel I, II, and III Accords created new international standards and requirements for risk management in banking. In the United States, the Sarbanes-Oxley Act of 2002 and the President's Management Agenda (PMA) under Bush in 2001 stated sweeping requirements for risk analysis of all major government programs. All of these regulations required different organizations to adopt risk analysis methods, but without much detail, risk analysis was usually interpreted to be the simpler, qualitative methods. The European Union's General Data Protection Regulation (GDPR) in 2018 provided for the possibility of enormous potential fines for companies who have experienced breaches of personal data of the public. But its requirements for risk assessment specify only qualitative designations such as “high risk.” The Dodd-Frank Wall Street Reform and Consumer Protection Act (2009) specifically required that the Federal Deposit Insurance Commission (FDIC) use a risk matrix.

The need for risk assessment has grown much faster than the awareness of relative performance of solutions. The most popular, newer methods don't necessarily build on the foundation of earlier methods that have stood up to scientific and historical scrutiny. However, even the quantitative risk management methods used in finance revealed cracks under the light of the 2008/2009 financial crisis.

So let's try to map out this rapidly expanding “Wild West” frontier of risk management solutions. Things are moving fast, so this description will probably soon be incomplete. For now, we can examine how risk management is adopted in the modern organization, the risk assessment methods used, and the types of risk mitigation methods used.

CURRENT STATE OF RISK MANAGEMENT IN THE ORGANIZATION

Writing about the “current state” of anything in a book that gets a new edition once a decade may seem like a very low-resolution picture of reality. But the (unfortunate) slow pace of change makes the current state of risk management easier to capture even with such infrequent updates.

To get a finger on the pulse of the current state of risk management, we could rely on the anecdotes of my network of connections in risk management. And I do to some degree. But the best tool we have is structured surveys of various levels of management in organizations. My firm, Hubbard Decision Research (HDR), collaborated with The Netherlands office of the consulting firm KPMG to survey 283 organizations and risk experts from fifty-three countries across many industries. Organizations ranged in size: eighty-four had less than one hundred employees and seventy had more than ten thousand employees. Respondents represented analysts, risk managers, CEOs, and many levels in between. Our focus was to investigate details about how organizations and risk professionals actually assessed and managed risks and what the effect of those efforts were.

In addition to this survey, I have updated a summary of three major sources of surveys mentioned in the first edition of this book. We will look at some surveys conducted between 2007 and 2018 by The Economist Intelligence Unit (EIU),¹ Aon Global Risk Consulting,² and Protiviti.³ And I will throw in some related observations from two other smaller surveys conducted by HDR, which asked risk management–related questions: a 2015 survey of 173 cybersecurity experts and a 2018 survey of eighty project managers. All of the surveys included responses from organizations around the world, from small to Fortune 500 companies in many industries as well as large government agencies. Here is a summary of findings:

Growth in risk management was fast but may have cooled off: In 2007, the Aon survey said 50 percent reported having a formal risk management function and 88 percent said the board was engaged in risk issues. The growth was apparently fast, for a while. The Aon 2017 survey says that 66 percent now have a formal risk function—down slightly from 2015. These numbers don't quite align with the findings of the HDR/KPMG survey, which found that of those who currently have a risk management function, 65 percent say they implemented it since 2007. (That difference could be a difference in the respondent population.) Furthermore, growth in the number of staff in those departments has leveled off according to the Aon survey.

There is support for risk management—mostly: The 2017 EIU report states that lack of support from senior management was a concern of only 21 percent in the previous year and only 15 percent expect it to be a concern in the next year. However, the HDR/KPMG survey finds that a higher proportion (31 percent) believe there is “no recognition by top management in the importance of risk assessment.”

Influence of risk management is not as high as it could be: Regarding influence, the HDR/KPMG survey finds that 67 percent say risk assessment is used to provide “some guidance” or “significant guidance” in “major decisions” whereas the 2017 EIU finds that only 47 percent say the risk function plays a role in strategic decisions.

CURRENT RISKS AND HOW THEY ARE ASSESSED

The Aon, Protiviti, and EIU surveys all asked respondents about their biggest risks. Of course, any survey about the perception regarding the biggest risks are probably transient, but here is the current snapshot.

Exhibit 2.1 summarizes the top five risks in each of these surveys. All three surveys were different but note that there is a bit more agreement between Aon and Protiviti than either of those have with EIU. This may be because EIU was asking specifically about risks in the next twelve months and the other two organizations didn't specify a time frame. Perhaps the EIU respondents felt that these risks were more relevant in the very near term.

These risk-ranking surveys have been taking place for many years and will probably go on for the foreseeable future but we should also ask how organizations determined these risks were their main concerns. On that question, these three surveys did not get into many specifics. That is where the HDR/KPMG surveys tried to fill the gap. Armed with all of this research, here is what we found:

EXHIBIT 2.1 Current Top Risks According to Three Surveys

Protiviti | Aon | EIU
Disruptive technologies | Damage to reputation | Weak demand
Internal resistance to change | Economic slowdown | Market instability within own industry
Cyber threats | Increasing competition | Difficulty raising financing
Regulatory changes | Regulatory changes | Labor (skills shortage, strikes, etc.)
Timely identification and escalation of risks | Cyber threats | Exchange rate fluctuation

Respondents would mostly say their methods are “formal:” The 2017 Aon study found that 60 percent state they have adopted formal or partially formal approaches to risk management. The share that say they have a formalized risk management approach goes up with the size of the firm—96 percent of firms with revenue over $10 billion say they use a formalized approach. About 70 percent overall would claim to have a formal or partially formal approach.

Formal mostly means “qualitative procedure” not quantitative: The HDR/KPMG survey found that what these $10 billion firms mean by formal is mostly (74 percent) a qualitative ranking or scoring method, perhaps using a form of the qualitative risk matrix. This is about the same for companies under that revenue threshold (78 percent). Only 16 percent of firms with revenue over $10 billion (and 20 percent of firms of all sizes) say they use quantitative methods—that is, they use explicit probabilities derived from mathematical and empirical methods using tools such as simulations and tools familiar to actuaries, statisticians, or quantitative risk analysts. Of those who use quantitative methods, the most common is Monte Carlo simulations (85 percent) followed by statistical analysis of historical data (77 percent). Less common are methods such as Bayesian statistics (56 percent) or utility theory (17 percent).

There are obstacles to the adoption of quantitative methods, but adoption is feasible: In the 2007 Protiviti survey, 57 percent said they quantify risks “to the fullest extent possible,” up from 41 percent in 2006. Because, as we noted, only 20 percent of all firms use some form of actual probabilistic methods, it would seem that most respondents in the Protiviti survey would not consider these methods possible. In fact, our survey found that 42 percent said an obstacle to the adoption of quantitative methods was “skepticism about the practicality and effectiveness.” Yet our survey showed that those who use quantitative methods such as simulations and statistical methods come from a variety of industries and company sizes. Even though quantitative methods are common in some industries (finance, insurance, etc.), the users outside of those industries are arguably as diverse as the users of qualitative methods. Apparently, there will be active users of these methods in the same industries and contexts where there are also skeptics.

These surveys agree with my personal experience on some key points. I see that most organizations who say they follow a formal method are merely saying they follow a defined procedure. Whether that defined procedure is based on mathematically and scientifically sound principles—what has been measured to work—is another question altogether. (More on that later.) Exhibit 2.2 provides a summary of what risk assessment methods are used, according to the HDR/KPMG survey.

Each of the categories in exhibit 2.2 contains many specific variations. So, let's dive into each of them in more detail.

EXHIBIT 2.2 Summary of Risk Assessment Methods Used According to the HDR/KPMG Survey

Method | Percentage of Respondents Using
Risk matrix based on a standard (ISO, NIST, etc.) | 14
Internally developed risk matrix | 27
Other qualitative scoring or ranking method | 32
Probabilistic methods (e.g., math based including, simulations, statistical empirical methods, etc.) | 20
Everything else (including expert intuition and various auditing methods) |  7

Expert Intuition, Checklists, and Audits

The most basic of these is part of the “everything else” category in exhibit 2.2—expert intuition. This is a sort of baseline of risk management methods. This is pure gut feel unencumbered by structured rating or evaluation systems of any kind. There are no points, probabilities, scales, or even standardized categories. There are shortcomings to this but there is also lot of value. Experts do know something, especially if we can adjust for various biases and common errors. In order for other methods to be of any value at all, they must show a measurable improvement on gut feel. (In fact, we will show later that unaided expert intuition isn't the worst of them.)

Other approaches that we lumped into the “everything else” category are various forms of audits and checklists. They don't do any structured prioritization of risks based on real measurements. They just make sure you don't forget something important and systematically search for problems. You definitely want your pilot and surgeon to use checklists and to guard against fraud or mistakes; you want your firm's books to be audited. I mention them here because it could be argued that checklists sometimes perform a pure assessment role in risk management. Most organizations will use audits and checklists of some sort even if they don't fall under the sort of issues risk managers may concern themselves with.

The Risk Matrix

The most common risk assessment method is some form of a risk matrix. A total of 41 percent of respondents in the HDR/KPMG survey say they use a risk matrix—14 percent use a risk matrix based on one of the major standards (e.g., NIST, ISO, COSO, etc.) and 27 percent use an internally developed risk matrix. Internally developed risk matrices are most common in firms with revenue over $10 billion, where 39 percent say that is the method they use.

Risk matrices are among the simplest of the risk assessment methods and this is one reason they are popular. Sometimes referred to as heat map or risk map, they also provide the type of visual display often considered necessary for communication to upper management. See exhibit 2.3 for an example of a risk map for both verbal categories and numerical scores.

As the exhibit shows, a risk matrix has two dimensions, usually labeled as likelihood on one axis and an impact on the other. Typically, likelihood and impact are then evaluated on a scale with verbal labels. For example, different levels of likelihood might be called likely, unlikely, extremely unlikely, and so on. Impact might be moderate or critical. Sometimes, the scales are numbered, most commonly on a scale of 1 to 5, where 1 is the lowest value for likelihood or impact and 5 is the highest. Sometimes these scores are multiplied together to get a “risk score” between 1 and 25. The risk matrix is often further divided into zones where total risk, as a function of likelihood and impact, is classified as high-medium-low or red-yellow-green.

EXHIBIT 2.3 Does This Work? One Version of a Risk Map Using Either Numerical or Verbal Scales

There are many variations of risk matrices in many fields. They may differ in the verbal labels used, the point scale, whether the point scales are themselves defined quantitatively, and so on. Chapter 8 will have a lot more on this.

Other Qualitative Methods

The next most common risk assessment method is a qualitative approach other than the risk matrix. These include simply categorizing risks as high, medium, or low without even the step of first assessing likelihood and impact, as with the risk matrix. These also include more elaborate weighted scoring schemes in which the user scores several risk indicators in a situation, multiplies each by a weight, then adds them up. For example, in a safety risk assessment, users might score a particular task based on whether it involves dangerous substances, high temperatures, heavy weights, restricted movement, and so on. Each of these situations would be scored on some scale (e.g., 1 to 5) and multiplied by their weights. The result is a weighted risk score, which is further divided into risk categories (e.g., a total score of 20 to 30 is high and over 30 is critical). This sort of method can sometimes be informed by the previously mentioned checklists and audits.

Mathematical and Scientific Methods

The most sophisticated risk analysts will eventually use some form of probabilistic models in which the odds of various losses and their magnitudes are computed mathematically. It is the basis for modeling risk in the insurance industry and much of the financial industry. It has its own flaws but just as Newton was a starting point for Einstein, it is the best opportunity for continued improvement. It could use subjective inputs, as do the other methods, but it is also well-suited to accept historical data or the results of empirical measurements. This includes the probabilistic risk analysis used in engineering as well as quantitative methods used in finance and insurance. This means that uncertainties are quantified as a probability distribution. A probability distribution is a way of showing the probability of various possible outcomes. For example, there may be a 5 percent chance per year of a major data breach. If the breach occurs, there is a 90 percent chance the impact is somewhere between $1 million and $20 million.

As the previous survey showed, quantitative methods usually involve Monte Carlo simulations. This is simply a way of doing calculations when the inputs themselves are uncertain—that is, expressed as probability distributions. Thousands of random samples are run on a computer to determine the probability distribution of an output (say, the total losses due to cyberattacks) from the inputs (the various possible individual types of cyberattacks and their impacts).

These methods also include various types of statistical analysis of historical data. Although the lack of data is sometimes perceived as a problem in risk analysis (16 percent of HDR/KPMG survey respondents said this was a problem), statistical methods show you need less data than you think, and, if we are resourceful, you have more data than you think. There are a couple of categories of methods that are not strictly based on statistical methods or probabilities, but may get lumped in with mathematical or scientific methods, at least by their proponents. One is deterministic financial analysis. By deterministic I mean that uncertainties are not explicitly stated as probabilities. Readers may be familiar with this as the conventional cost-benefit analysis in a spreadsheet. All the inputs, although they may be only estimates, are stated as exact numbers, but there are sometimes attempts to capture risk analysis. For example, a discount rate is used to adjust future cash flows to reflect the lower value of risky investments. One might also work out best-case and worst-case scenarios for costs and benefits of various decisions.

One final approach that sometimes gets grouped together with mathematical methods in risk management includes expected utility theory, which gives us a way to mathematically make trade-offs between risk and return. These methods combine to create a quantitative method broader than risk analysis: decision analysis. As mentioned in chapter 1, risk analysis is only part of decision analysis. We will be spending a lot more time discussing these approaches.

Other methods under the umbrella of “preference theory” were originally created as derivatives of the previously mentioned expected utility theory, but instead of trading off risk and return, they purport to mathematically assist in the trade-offs of multiple different objectives. Variously named but similar methods include multi-attribute utility theory (MAUT), multi-criteria decision-making (MCDM), and analytic hierarchy process (AHP). They claim more mathematical validity than simple weighted scores but ultimately rely on statements of preferences, not forecasts or estimates, of experts. In the case of AHP, a more sophisticated method is used to determine whether the expert judgments are at least internally consistent. As with the other methods listed so far, these have been used on lots of decision analysis problems that might not strictly be risk assessments, but they are included here because they have been used to evaluate decisions according to their risks.

Whatever the chosen method may be, it should be used to inform specific actions. Many of those actions will involve choices regarding whether and how to mitigate risk in some way. You may decide to invest in new cybersecurity controls, keep tighter control over your supply chain, diversify production processes, increase the number of auditors, require new training, and so on. If they were free you would do them all. If all risk mitigation options were equally costly and equally effective, you could do them in any random order you like. But neither of those is the case. You will have more risks than you can realistically control for and the bang for the buck will vary widely. You will have to prioritize and make choices.

If these methods were used for no more than assessing corporate art for the reception area or where to have the company picnic, then the urgency of this evaluation would not be nearly as high. But, as I have already pointed out, these methods are being used for many of the biggest and riskiest decisions in the corporate world and government. Fortunately, some of these can be modified to produce an approach that can be shown to be a significant improvement on the baseline condition of expert intuition alone. Instead of improving on expert intuition, some apparently add error to expert intuition. Until this gets sorted out, improvements in risk management will not be possible.

NOTES

 1. “Fall Guys: Risk Management in the Front Line,” Economist Intelligence Unit, 2010, https://advisory.kpmg.us/content/dam/advisory/en/pdfs/risk-assurance/risk-management-front-line.pdf; “Best Practice in Risk Management: A Function Comes of Age,” Economist Intelligence Unit, 2007, http://graphics.eiu.com/files/ad_pdfs/eiu_Risk_Management.pdf.

 2. “Global Risk Management Survey 2017,” Aon Corporation, 2017; “Global Enterprise Risk Management Survey,” Aon Corporation, 2010; “Global Risk Management Survey 2007,” Aon Corporation, 2007, https://www.aon.com/getmedia/d95563c6-a3b8-4ff1-bb45-0ed511c78f72/2017-Global-Risk-Management-Survey-Report-rev-120318.aspx.

 3. “Executive Perspectives on Top Risks for 2018,” Protiviti & NC State Poole College of Management, 2018; “2007 U.S. Risk Barometer: Survey of C-Level Executives with the Nation's Largest Companies,” Protiviti, 2007, https://www.protiviti.com/sites/default/files/united_states/insights/nc-state-protiviti-survey-top-risks-2018.pdf.

CHAPTER 3
How Do We Know What Works?

Leaders get out in front and stay there by raising the standards by which they judge themselves—and by which they are willing to be judged.

—FREDRICK SMITH, CEO, FEDEX

The first principle is that you must not fool yourself, and you are the easiest person to fool.

—RICHARD P. FEYNMAN, NOBEL PRIZE–WINNING PHYSICIST

According to some risk management surveys, organizations are very often satisfied with their risk assessment and risk management methods. For example, a survey by the major consulting firm Deloitte in 2012 found that 72 percent of organizations rate themselves as “extremely effective” or “very effective” at managing risks (up slightly from 66 percent in 2010). In other words, a majority believe their risk management is working. But, as the quote by Feynman above tells us, we are easy to fool.

A harder question to answer is, “What is the evidence for the belief that it works?” For any firm that hasn't asked that question before, it should be an immediate priority. If the firm can't answer that question, then it has no reason to believe that efforts to manage risks are working or, for that matter, are even focusing on the right risks. The standard must be some objective measure that could be verified by other stakeholders in the organization or outside auditors.

Most (69 percent according to the HDR/KPMG survey) don't even attempt to measure whether risk management is working. Of those who say they do measure risk, most (63 percent) are merely using a survey of staff with questions such as, “How would you rate the effectiveness of risk management?” It may not be obvious now, but there are ways to measure risk management objectively even though such measurements are uncommon.

This chapter will describe the difficulties in conducting measurements of risk management and some solutions for overcoming them. But first, to highlight the importance of measuring risk management, let's look at one example involving the health and safety of large numbers of people.

ANECDOTE: THE RISK OF OUTSOURCING DRUG MANUFACTURING

In 2007, I was asked to speak at a conference organized by the Consumer Health Products Association (a pharmaceutical industry association). The event organizers were specifically interested in my contrarian views on common risk management methods. After my keynote, I was asked by the event organizers to attend another session on a new risk management method for outsourcing drug manufacturing and provide my comments to the audience. They thought it would be interesting if I could start a conversation by offering an on-the-spot evaluation of the new method.

To control costs, this large pharmaceutical manufacturer was more frequently outsourcing certain batch processes to China. Virtually all of this manufacturer's competition were doing the same. But although the costs were significantly lower, they had a concern that batches from China might have additional quality control issues over and above those of batches manufactured here in the United States. These concerns were entirely justified.

Earlier that year there had already been several widely publicized product safety incidents with goods produced in China. In June, there was a toxin found in toothpaste and lead found in toys produced in China. Then there was tainted pet food that killed as many as 4,000 pets. There was even the disturbing case of “Aqua Dots,” the children's craft-beads that stuck together to make different designs. The coating of these beads could metabolize in the stomach to produce gamma-hydroxybutyrate—the chemical used in date-rape drugs.

So, clearly, assessing the risk of outsourcing was a major area of interest at the conference, and the room was at capacity. The presenter—a very respected chemical engineer—began to describe a risk assessment method based on a subjective weighted score.¹ In it, several “risk indicators” were each scored on a scale of 1 to 5. For example, if the manufacturer already produces a similar but not identical drug, it might get a low risk score of 2 on the indicator called proven technical proficiency. If it was inspected by and got a positive evaluation from the Chinese health agency, but was not yet inspected by the Food and Drug Administration, then it might get a 4 on the formal inspections indicator.

Then these scores were each multiplied by a weight of somewhere between 0.1 and 1.0 and then all of the weighted scores were totaled. The total of the weighted score might be 17.5 for one outsourcing strategy, 21.2 for another, and so on. The team that chose the scores also chose the weights and, again, it was based only on subjective judgments. The team further separated the resulting scores into various stratifications of risk that would, apparently, have some bearing on the decision to use a particular China-based source for a drug. For example, risk scores of over 20 might mean “extremely high risk: Find an alternative”; 10 to 19 might mean “high risk: Proceed only with increased quality assurance”; and so on.

When the presenter had finished, I was expected to provide my two cents on the method. I decided I could neither endorse nor reject the approach outright. To be perfectly fair, neither position could yet be positively justified at that point without knowing a few more details (although there is a good chance it shared the flaws of many weighted scores, which I discuss later). I simply asked, “How do you know it works?” This is the most important question we could ask about a risk analysis and risk management approach. Once I knew the answer to that question, then I could legitimately take a position.

The presenter seemed to struggle with this question, so I then suggested to the presenter that the engineers in this field could be as scientific in their approach to this problem as they are in any other aspect of their profession. I pointed out that, for one, there was no need to start from scratch. If they were developing a new process for pharmaceutical manufacture, I'm sure they would examine existing research in the area. Likewise, there is quite a lot of literature in the general area of assessing risks in a mathematically and scientifically sound manner. It would be helpful to know that they don't have to reinvent any of the fundamental concepts when it comes to measuring risks.

Then I pointed out that in the design of processes in drug production, once they had thoroughly reviewed the literature on a topic, no doubt they would design empirical tests of various components in the process and measure them in a way that would satisfy the peer-reviewed journals and the FDA inspectors alike. Again, this same philosophy can apply to risk.

In fact, a much more sophisticated method is often already used to assess a different risk in the drug industry. Stop-gate analysis (also variously referred to as phase-gate and stage-gate analysis) is used to determine whether a candidate for a new product should advance from formulation to animal testing, then from animal testing to human trials, until finally the company decides whether to go to market. Many drug companies use proven statistical methods at each step in the stop-gate analysis. But, somehow, none of the basic concepts of stop-gate analysis were built on to assess the risks of outsourcing production to China.

I was already fairly sure that they had no objective measure for the effectiveness of this method. If they had known to create such measures, they would probably have been inclined to create a very different approach in the first place. When it came to designing a method for assessing and managing risks, these scientists and engineers developed an approach with no scientific rigor behind it. Although the lack of such rigor would be considered negligent in most of their work, it was acceptable to use a risk assessment method with no scientific backing at all.

Of course, this wasn't deliberate; they just didn't know it could be scientific. They just didn't think of this new risk in the same way as they thought of the substances and processes they use to manufacture drugs in a highly regulated industry. The chemicals they process and the vessels they use are concrete, tangible things and, to the engineers, risk might seem like an abstraction. Even the methods they use in stop-gate analysis might take on an air of concreteness simply because, by now, they have a lot of experience with using it. Perhaps to them, the process of managing an unfamiliar risk seems like an intangible thing that doesn't lend itself to the same methods of validation that a drug manufacturing process would have to undergo for FDA approval. Applying the type of scientific reasoning and testing used on the production of a drug to the risk analysis of producing that same drug in China is a leap they had not considered.

The presenter and the audience felt that the weighted scoring method they described was something close to “best practices” for the industry. When I asked, nobody in the room claimed to have an approach that was any more sophisticated. Most had no risk analysis at all for this problem.

Fortunately for the company that was presenting its risk management solution, it had not yet seen the worst-case scenarios that might result from unsound risk analysis. But with an entire industry approaching the outsourcing problem with either unscientific risk analysis methods or none at all, the worst case was inevitable. Just a few months after the conference, another major drug company using similarly subjective risk management methods on this problem would discover exactly how much was being risked by the outsourcing decisions (and the meager risk analysis applied to it).

Baxter International, Inc. was receiving reports of dangerous adverse reactions to its Chinese-manufactured blood-thinning drug called heparin. To its credit, by mid-January 2008, Baxter had voluntarily recalled some lots of the multidose vials of the drug. By then, the FDA was considering a mandatory recall but had not yet done so because they believed other suppliers might not be able to meet demand for this critical drug. The FDA reasoned that this additional risk to patients requiring heparin therapy would be higher. (I have no idea how much risk analysis went into that decision.)

By February, the FDA had determined that the supply of heparin by other manufacturers was adequate and that Baxter should proceed with the recall of various types of heparin products. At the beginning of the recall in February, the FDA had linked four deaths to the Chinese-manufactured heparin and by March the number had grown to nineteen deaths. By May 2008, the FDA had “clearly linked” a total of eighty-one deaths and 785 severe allergic reactions to the drug.

The risks of outsourcing drug production to China always were high, and the fact that some firms were at least attempting to develop a risk management method—regardless of its effectiveness—indicates that the industry was at least aware of the risk. The FDA is entrusted to inspect the operations of any drug manufacturer selling products in the United States, including foreign-based factories but, by March 2008, the FDA had inspected just 16 of the 566 Chinese drug manufacturers. Most drugs used in the United States are now produced overseas and most of those are from China. The scale of the problem easily justifies the very best risk analysis available.

Obviously, we can't be certain with only this information that the industry's lack of more sophisticated risk management for overseas drug manufacturing was the direct cause of the heparin incident. If the industry had used more sophisticated methods, such as it already uses for stop-gate analysis, we could not be certain that some similar problem would not still have occurred. And, because the entire industry was unsophisticated in this area of risk management, there is certainly no reason to single out Baxter as a particularly bad example. This anecdote, by definition, is merely a single sample of the types of events that can occur and, by itself, is not sufficient to draw scientifically justified conclusions.

For any risk management method used in the pharmaceutical industry or any other industry, we must ask, again, “How do we know it works?” If we can't answer that question, then our most important risk management strategy should be to find a way to answer it and adopt a risk assessment and risk mitigation method that does work.

WHY IT'S HARD TO KNOW WHAT WORKS

One reason why we should be skeptical of the perception of effectiveness of any decision-making method (not just in regards to risk management) is that we may be susceptible to a kind of “analysis placebo” effect. You are probably familiar with how placebos are used in the pharmaceutical industry. To test the effectiveness of a new drug, they don't simply ask whether patients or even the doctors felt a new drug is working. In order to determine that the new drug is really working, patients taking the real drug have to do measurably better than those taking the placebo (which may be a sugar pill). Which patients get the placebo is even hidden from the doctors so that their diagnoses are not biased.

An analysis placebo produces the feeling that some analytical method has improved decisions and estimates even when it has not. Placebo means “to please” and, no doubt, the mere appearance of structure and formality in risk management is pleasing to some. In fact, the analogy to a placebo is going a bit too easy on risk management. In medical research, there can actually be a positive physiological effect from a mere placebo beyond the mere perception of benefit. But when we use the term in the context of risk management we mean there literally is no benefit other than the perception of benefit. Several studies in very different domains show how it is possible for any of us to be susceptible to this effect:

Sports picks: A 2008 study at the University of Chicago tracked probabilities of outcomes of sporting events as assigned by participants given varying amounts of information about the teams without being told the names of teams or players. As the fans were given more information about the teams in a given game, they would increase their confidence that they were picking a winner, even though the actual chance of picking the winner was nearly flat no matter how much information they were given.² In another study, sports fans were asked to collaborate with others to improve predictions. Again, confidence went up after collaboration but actual performance did not. Indeed, the participants rarely even changed their views from before the discussions. The net effect of collaboration was to seek confirmation of what participants had already decided.³

Psychological diagnosis: Another study showed how practicing clinical psychologists became more confident in their diagnoses and prognoses for various risky behaviors by gathering more information about patients, and yet, again, the agreement with observed outcomes of behaviors did not actually improve.⁴

Investments: A psychology researcher at MIT, Paul Andreassen, did several experiments in the 1980s showing that gathering more information about stocks in investment portfolios improved confidence but without any improvement in portfolio returns. In one study, he showed how people tend to overreact to news and assume that the additional information is informative even though, on average, returns were not improved by these actions.⁵

Trivia estimates: Another study investigating the benefits of collaboration asked subjects for estimates of trivia from an almanac. It considered multiple forms of interaction including the Delphi technique, free-form discussion, and other methods of collaboration. Although interaction did not improve estimates over simple averaging of individual estimates, the subjects did feel more satisfied with the results.⁶

Lie detection: A 1999 study measured the ability of subjects to detect lies in controlled tests involving videotaped mock interrogations of “suspects.” The suspects were actors who were incentivized to conceal certain facts in staged crimes to create real nervousness about being discovered. Some of the subjects reviewing the videos received training in lie detection and some did not. The trained subjects were more confident in judgments about detecting lies even though they were worse than untrained subjects at detecting lies.⁷

And these are just a few of many similar studies showing that we can engage in training, information gathering, and collaboration that improves confidence but not actual performance. We have no reason to believe that fundamental psychology observed in many different fields doesn't apply in risk management in business or government. The fact that a placebo exists in some areas means it could exist in other areas unless the data shows otherwise.

The placebo effect might not be as persistent if it were easier to learn from our experience in risk management. But learning is not a given in any environment. Two prolific psychologists, Daniel Kahneman and Gary Klein, once wrote an article about what it takes to learn from experience.

Kahneman and Klein came from what are thought of as opposing views of how judgments are made by experts. Klein, comes from the “naturalistic decision-making” school, where experts in fields such as firefighting are seen as having amazing and intuitive judgments in complex situations. Kahneman represents the “heuristics and biases” research, where all sorts of errors in human judgment are analyzed. They wrote a joint paper in an effort to compare these apparently competing views. But what they found was that in important respects, they did not disagree, so they decided to name the paper, “Conditions for Intuitive Expertise: A Failure to Disagree.”⁸

They found they agreed that developing expert intuition in any field is not an automatic outcome of experience. Experts needed “high-validity” feedback so that the outcomes of estimates and decisions could be learned from. Our feedback should be consistent (we get feedback most, if not all, of the time), quick (we don't have to wait long for it), and unambiguous.

Risk management simply does not provide the type of consistent, immediate, and clear feedback that Kahneman and Klein argue we need as a basis for learning. Risk managers make estimates, decisions, or recommendations without knowing what the effect is for some time, if ever. If risk went down after the implementation of a new policy, how would you know? How long would it take to confirm that the outcome was related to the action taken? How would you determine whether the outcome was just due to luck?

What we will not do to measure the performance of various methods is rely on the proclamations of any expert regardless of his or her claimed level of knowledge or level of vociferousness. So even though I may finally have some credibility in claiming experience after thirty years in quantitative management consulting, I will not rely on any appeals to my authority regarding what works and what does not. I will, instead, resort to using published research from large experiments. Any mention of anecdotes or quotes from “thought leaders” will only be used to illustrate a point, never to prove it.

I don't think it is controversial to insist that reason and evidence are the way to reach reliable conclusions about reality. The best source of evidence is large, random samples, clinical trials, unbiased historical data, and so on. The data should then be assessed with proper mathematical methods to make inferences.

AN ASSESSMENT OF SELF-ASSESSMENTS

The potential existence of an analysis placebo, the difficulty of learning from experience alone in risk management, and the general lack of objective measurements of performance in risk management means that we should be wary of self-assessments in this field. We should bear in mind one particular statement in the previously mentioned article by Daniel Kahneman and Gary Klein:

True experts, it is said, know when they don't know. However, nonexperts (whether or not they think they are) certainly do not know when they don't know. Subjective confidence is therefore an unreliable indication of the validity of intuitive judgments and decisions. (p. 524)

Risk managers are still humans and, not surprisingly, there is a tendency for most of us humans to have at least a slightly inflated opinion of ourselves (friends and family will confirm that I'm no exception). For example, 87 percent of Stanford MBA students rate their academic performance to be in the top half of their class.⁹ Other surveys show that a clear majority of people rate themselves as being more popular,¹⁰ better looking,¹¹ healthier,¹² and better drivers¹³ than at least half of the population.

These are examples of the Dunning-Kruger effect, the tendency for the least competent in a given area to also be the most overconfident in his or her capabilities. I first mentioned this phenomenon in the first edition of this book but it has become more widely recognized (if a bit overused) since then. It comes from the work of Cornell psychologists Justin Kruger and David Dunning. They published their research in the area of self-assessments in the harshly titled article, “Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments.”¹⁴ They show that about two-thirds of the entire population will rate themselves as better than most in reasoning skills, humor, and grammar. Although the last few studies I just mentioned are not focused on management, if you think that C-level management and trained business professionals are more realistic and their confidence is more justified, wait until you read part 2 of the book.

There is no reason to believe risk management avoids the same problems regarding self-assessment. As we saw in the surveys, any attempt to measure risk management at all is rare. Without measurements, self-assessments in the effectiveness of risk management are unreliable given the effect of the analysis placebo, the low validity problem described by Kahneman and Klein, and the Dunning-Kruger effect.

There is an old management adage that says, “You can't manage what you can't measure.” (This is often misattributed to W. E. Deming, but is a truism, nonetheless.) Management guru Peter Drucker considered measurement to be the “fourth basic element in the work of the manager.” Because the key objective of risk management—risk reduction or at least a minimized risk for a given opportunity—may not exactly be obvious to the naked eye, only deliberate measurements could even detect it. The only way organizations could be justified in believing they are “very effective” at risk management is if they have measured it.

Risk professionals from Protiviti and Aon (two of the firms that conducted the surveys in chapter 2) also have their suspicions about the self-assessments in surveys. Jim DeLoach, a Protiviti managing director, states that “the number of organizations saying they were ‘very effective’ at managing risks was much higher than we expected.” Recall that in the Protiviti survey 57 percent of respondents said they quantify risks “to the fullest extent possible” (it was slightly higher, 63 percent, for those that rated themselves “very effective” at risk management). Yet this is not what DeLoach observes first-hand when he examines risk management in various organizations: “Our experience is that most firms aren't quantifying risks … I just have a hard time believing they are quantifying risks as they reported.”

Christopher (Kip) Bohn, an actuary, fellow of the Casualty Actuarial Society, and formerly a director at Aon Global Risk Consulting, is equally cautious about the findings in surveys about how common quantitative methods may be in risk management. Bohn observes, “For most organizations, the state of the art is a qualitative analysis. They do surveys and workshops and get a list of risks on the board. They come up with a ranking system with a frequency and impact, each valued on a scale of, for example, one to five.” This is not exactly what an actuary like Bohn considers to be quantitative analysis of risk.

My own experience also seems to agree more with the personal observations of DeLoach and Bohn than the results of the self-assessment surveys. I treat the results of the HDR/KPMG survey as perhaps an upper bound in the adoption of quantitative methods. Whenever I give a speech about risk management to a large group of managers, I ask those who have a defined approach for managing risks to raise their hands. A lot of hands go up, maybe half on average. I then ask them to keep their hands up only if they measure risks. Many of the hands go down. Then I ask them to keep their hands up only if probabilities are used in their measurements of risks (note how essential this is, given the definition of risk we stated). More hands go down and, maybe, one or two remain up. Then I ask them to keep their hands up if they think their measures of probabilities and losses are in any way based on statistical analysis or methods used in actuarial science. After that, all the hands are down. It's not that the methods I'm proposing are not practical. I have used them routinely on a variety of problems. (I'll argue in more detail later against the myth that such methods aren't practical.)

Of course, some managers have argued that the standards I suggest for evaluating risk management are unfair and they will still argue that their risk management program was a success. When asked for specifics about the evidence of success, I find they will produce an interesting array of defenses for a method they currently use in risk management. However, among these defenses will be quite a few things that do not constitute evidence that a particular method is working. I have reason to believe that these defenses are common, not only because I've heard them frequently but also because many were cited as benefits of risk management in the surveys by Aon, The Economist, and Protiviti.

The following are some common, but invalid, claims given as evidence that a risk management process is successful:

When asked, the managers will say that the other stakeholders involved in the process will claim that the effort was a success. They may even have conducted a formal internal survey. But, as the previous studies show, self-assessments are not reliable. Furthermore, without an independent, objective measure of risk management, the perception of any success may merely be a kind of placebo effect. That is, they might feel better about their situation just by virtue of the fact that they perceive they are doing something about it.

The proponents of the method will point out that the method was “structured.” There are a lot of structured methods that are proven not to work. (Astrology, for example, is structured.)

Often, a “change in culture” is cited as a key benefit of risk management. This, by itself, is not an objective of risk management—even though some of the risk management surveys show that risk managers considered it to be one of the main benefits of the risk management effort. But does the type of change matter? Does it matter if the culture doesn't really lead to reduced risks or measurably better decisions?

The proponents will argue that the method “helped to build consensus.” This is a curiously common response, as if the consensus itself were the goal and not actually better analysis and management of risks. An exercise that builds consensus to go down a completely disastrous path probably ensures only that the organization goes down the wrong path even faster.

The proponents will claim that the underlying theory is mathematically proven. I find that most of the time, when this claim is used, the person claiming this cannot actually produce or explain the mathematical proof, nor can the person he or she heard it from. In many cases, it appears to be something passed on without question. Even if the method is based on a widely recognized theory, such as options theory (for which the creators were awarded the Nobel Prize in 1997) or modern portfolio theory (the Nobel Prize in 1990), it is very common for mathematically sound methods to be misapplied. (And those famous methods themselves have some important shortcomings that all risk managers should know about.)

The vendor of the method will claim that the mere fact that other organizations bought it, and resorted to one or more of the preceding arguments, is proof that it worked. I call this the testimonial proof. But if the previous users of the method evaluated it using criteria no better than those previously listed, then the testimonial is not evidence of effectiveness.

The final and most desperate defense is the claim, “But at least we are doing something.” I'm amazed at how often I hear this, as if it were irrelevant whether the “something” makes things better or worse. Imagine a patient complains of an earache and a doctor, unable to solve the problem, begins to saw off the patient's foot. “At least I am doing something,” the doctor says in defense.

With some exceptions (e.g., insurance, some financial management, etc.), risk management is not an evolved profession with standardized certification requirements and methods originally developed with rigorous scientific testing or mathematical proofs. So we can't be certain that everyone answering the surveys identified in chapter 2 is really using a valid standard to rate his or her success. But even if risk managers had some uniform type of professional quality assurance, surveys of risk managers would still not be a valid measure of risk management effectiveness. That would be like measuring the effectiveness of aspirin by a survey of family practice doctors instead of a clinical trial. What we need are objective measures of the success of risk management.

POTENTIAL OBJECTIVE EVALUATIONS OF RISK MANAGEMENT

If self-assessments don't suffice, then what objective measures are possible for risk management? At its root, the objective measure of risk management should be based on the whether and how much risk was actually reduced or whether risk was acceptable for a given payoff. In order to do that, the risk management method should have an approach for properly assessing the risks. In order to measure the effectiveness of risk management, we have to measure risk itself.

Recall from chapter 1 that risk can be measured by the probability of an event and its severity. If we get to watch an event over a long period of time then we could say something about how frequent the event is and the range of possible impacts. If a large retailer is trying to reduce the risk of loss due to shoplifting (an event that may occur more than a hundred times per month per store), then one inventory before the improved security efforts and another a month after would suffice to detect a change. But a risk manager isn't usually concerned with very high-frequency and low-cost events such as shoplifting.

In a retailer such as Target or Walmart, theft should be so common that it becomes more of a fully anticipated cost than a risk. Similarly, the “risks” of running out of 60W incandescent bulbs or mislabeling a price on a single item are, correctly, not usually the types of risks we think of as foremost in the minds of risk managers. The biggest risks tend to be those things that are more rare but potentially disastrous—perhaps even events that have not yet occurred in this organization.

If it is a rare event (such as many of the more serious risks organizations would hope to model) then we need a very long period of time to observe how frequent and impactful the event may be—given we can survive long enough after observing enough of these events. Suppose, for example, a major initiative is undertaken by the retailer's IT department to make point-of-sale and inventory management systems more reliable. If the chance of these systems being down for an hour or more were reduced from 10 percent per year to 5 percent per year, how would they know just by looking at the first year? And if they did happen to observe one event and the estimated cost of that event was $5 million, how do we use that to estimate the range of possible losses?

Fortunately, there are some methods of determining effectiveness in risk management without just waiting for the events to occur (the very events you are trying to mitigate) just so you can measure their risks. Here are six potential measurement methods that should work even if the risks being managed are rare:

The big experiment

Direct evidence of cause and effect

Component testing

Formal errors

A check of completeness

Answering the right question

The Big Experiment

The most convincing way—and the hardest way—to measure the effectiveness of risk management is with a large-scale experiment over a long period tracking dozens or hundreds of organizations. This is still time-consuming—for example, waiting for the risk event to occur in your own organization—but it has the advantage of looking at a larger population of firms in a formal study. If risk management is supposed to, for example, reduce the risk of events that are so rare that actual results alone would be insufficient to draw conclusions, then we can't just use the short-term history of one organization. Even if improved risk management has a significant effect on reducing losses from various risks, it may take a large number of samples to be confident that the risk management is working.

To build on the previous pharmaceutical outsourcing example, imagine applying a method that pharmaceutical companies would already be very familiar with in the clinical testing of drugs. Suppose that nearly all of the major health products companies (this includes drugs, medical instruments, hospital supplies, etc.) are recruited for a major risk management experiment. Let's say, in total, that a hundred different product lines that will be outsourced to China are given one particular risk management method to use. Another hundred product lines, again from various companies, implement a different risk management method. For a period of five years, each product line uses its new method to assess risks of various outsourcing strategies. Over this period of time, the first group experiences a total of twelve events resulting in adverse health effects traced to problems related to the overseas source. During the same period, the second group has only four such events without showing a substantial increase in manufacturing costs.

Of course, it would seem unethical to subject consumers to an experiment with potentially dangerous health effects just to test different risk management methods. (Patients in drug trials are at least volunteers.) But if you could conduct a study similar to what was just described, the results would be fairly good evidence that one risk management method was much better than the other. If we did the math (which I will describe more later on as well as show an example on the website www.howtomeasureanything.com/riskmanagement) we would find that it would be unlikely for this result to be pure chance if, in fact, the probability of the events were not different. In both groups, there were companies that experienced unfortunate events and those that did not, so we can infer something about the performance of the methods only by looking at the aggregation of all their experiences.

Although this particular study might be unethical, there were some examples of large studies similar to this that investigated business practices. For example, in July 2003, Harvard Business Review published the results of a study involving 160 organizations to measure the effectiveness of more than two hundred popular management tools, such as TQM, ERP, and so on.¹⁵ Then independent external reviews of the degree of implementation of the various management tools were compared to shareholder return over a five-year period. In an article titled “What Really Works,” the researchers concluded, to their surprise, that “most of the management tools and techniques we studied had no direct causal relationship to superior business performance” That would be good to know if your organization was about to make a major investment in one of these methods.

Another study, which was based on older but more relevant data, did look at alternative methods of risk management among insurance companies. There was a detailed analysis of the performance of insurance companies in mid-nineteenth century Great Britain when actuarial science was just emerging. Between 1844 and 1853, insurance companies were starting up and failing at a rate more familiar to Silicon Valley than the insurance industry. During this period 149 insurance companies formed and after that period just fifty-nine survived. The study determined that the insurance companies who were using statistical methods were more likely to stay in business (more on this study later).¹⁶ Actuarial methods that were at first considered a competitive advantage became the norm.

Again, this is the hard way to measure risk management methods. The best case for organizations would be to rely on research done by others instead of conducting their own studies—assuming they find the relevant study. Or, similar to the insurance industry study, the data are all historical and are available if you have the will to dig all of it up. Fortunately, there are alternative methods of measurement.

Direct Evidence of Cause and Effect

Of course, a giant experiment is not usually very practical, at least for individual companies to conduct by themselves. Fortunately, we have some other ways to answer this question without necessarily conducting our own massive controlled experiments. For example, there are some situations in which the risk management method caught what obviously would have been a disaster, such as detecting a bomb in a suitcase, only because of the implementation of a new plastic explosives–sniffing device. Another example would be where an IT security audit uncovered an elaborate embezzling scheme. In those cases, we know it would have been extremely unlikely to have discovered—and addressed—the risk without that particular tool or procedure. Likewise, there are examples of disastrous events that obviously would have been avoidable if some prudent amount of risk management had been taken. For example, if a bank was overexposed on bad debts and reasonable procedures would never have allowed such an overexposure, then we can confidently blame the risk management procedures (or lack thereof) for the problem.

But direct evidence of cause and effect is not as straightforward as it might at first seem. There are times when it appears that a risk management effort averted one risk but exacerbated another that was harder to detect. For example, the FAA currently allows parents traveling with a child under the age of two to purchase only one ticket for the adult who holds the child on his or her lap. Suppose the FAA is considering requiring parents to purchase seats for each child, regardless of age. If we looked at a crash where every separately seated toddler survived, is that evidence that the new policy reduced risk? Actually, no—even if we assume it is clear that particular children are alive because of the new rule. A study already completed by the FAA found that changing the “lap children fly free” rule would increase total fares for the traveling families by an average of $185, causing one-fifth of them to drive instead of fly. When the higher travel fatalities of driving are considered, it turns out that changing the rule would cost more lives than it saves. It appears we still need to check even the apparently obvious instances of cause and effect against some other independent measure of overall risk. The danger of this approach is that it may turn out that even when a cause-effect relationship is clear, it could just be anecdotal evidence. We still need other ways to check our conclusions about the effectiveness of risk management methods.

Component Testing

Lacking large controlled experiments, or obvious instances of cause and effect, we still have ways of evaluating the validity of a risk management method. The component testing approach looks at the gears of risk management instead of the entire machine. If the entire method has not been scientifically tested, we can at least look at how specific components of the method have fared under controlled experiments. Even if the data is from different industries or laboratory settings, consistent findings from several sources should give us some information about the problem.

As a matter of fact, quite a lot of individual components of larger risk management methods have been tested exhaustively. In some cases, it can be conclusively shown that a component adds error to the risk assessment or at least doesn't improve anything. We can also show that other components have strong theoretical backing and have been tested repeatedly with objective, scientific measures. Here are a few examples of component-level research that are already available:

The synthesis of data: One key component of risk management is how we synthesize historical experience. Where we rely on experts to synthesize data and draw conclusions, we should look at research into the relative performance of expert opinion versus statistical models.

Known human errors and biases: If we rely on expert opinion to assess probabilities, we should be interested in reviewing the research on how well experts do at assessing the likelihood of events, their level of inconsistency, and common biases. We should consider research into how hidden or explicit incentives or irrelevant factors affect judgment. We should know how estimates can be improved by accounting for these issues.

Aggregation of estimates: In many cases several experts will be consulted for estimates, and their estimates will be aggregated in some way. We should consider the research about the relative performance of different expert-aggregation methods.

Behavioral research into qualitative scales: If we rely on various scoring or classification methods (e.g., a scale of 1 to 5 or high/medium/low), we should consider the results of empirical research on how these methods are actually used and how much arbitrary features of the scales effect how they are used.

Decomposition: We can look into research about how estimates can be improved by how we break up a problem into pieces and how we assess uncertainty about those pieces.

Errors in quantitative models: If we are using more quantitative models and computer simulations, we should be aware of the most common known errors in such models. We also need to check to see whether the sources of the data in the model are based on methods that have proven track records of making realistic forecasts.

If we are using models such as AHP, MAUT, or similar systems of decision analysis for the assessments of risk, they should meet the same standard of a measurable track record of reliable predictions. We should also be aware of some of the known mathematical flaws introduced by some methods that periodically cause nonsensical results.

Formal Errors

Outright math errors should be the most obvious disqualifiers of a method, and we will find them in some cases. This isn't just a matter of making simplifying assumptions or using shortcut rules of thumb. Those can be useful as long as there is at least empirical evidence that they are helpful. But where we deviate from the math, empirical evidence is even more important. This is especially true when deviations from known mathematics provide no benefits in simplicity compared to perfectly valid mathematical solutions—which is often the main case for taking mathematical shortcuts.

In some cases, it can be shown that mathematically irregular methods may actually lead to dangerously misguided decisions. For example, we shouldn't be adding and multiplying ordinal scales, as is done in many risk assessment methods. We will show later some formal analysis how such procedures lead to misguided conclusions.

A Check of Completeness

Even if we use the best methods, we can't apply them to a risk if we don't even think to identify it as a risk. If a firm thinks of risk management as “enterprise risk management,” then it ought to be considering all the major risks of the enterprise—not just legal, not just investment portfolio, not just product liability, not just worker safety, not just business continuity, not just security, and so on. This criterion is not, however, the same as saying that risk management can succeed only if all possible risks are identified. Even the most prudent organization will exclude risks that nobody could conceivably have considered.

But there are widely known risks that are excluded from some risk management for no other reason than an accident of organizational scope or background of the risk manager. If the scope of risk management in the firm has evolved in such a way that it considers risk only from a legal or a security point of view, then it is systematically ignoring many significant risks. A risk that is not even on the radar can't be managed at all.

The surveys previously mentioned and many “formal methodologies” developed detailed taxonomies of risks to consider, and each taxonomy is different from the others. But completeness in risk management is a matter of degree. The use of a detailed taxonomy is helpful, but it is no guarantee that relevant risks will be identified.

More important, risks should not be excluded simply because they are speaking about risks in completely different languages. For example, cyber risk, financial portfolio risk, safety risk, and project risk do not need to use fundamentally different languages when discussing risk. If project risks are 42, cyber risks are yellow, safety risks are moderate, portfolio risks have a Sharpe Ratio of 1.1, and there is a 5 percent chance a new product will fail to break even, what is the total risk? They can and should be using the same types of metrics so risks across the enterprise can be considered comprehensively.

A risk manager should always assume that the list of considered risks, no matter how extensive, is incomplete. All we can do is increase completeness by continual assessment of risks from several angles and compare them with a common set of metrics. In part 3, we will discuss some angles to consider when developing a taxonomy in the hope that it might help the reader think of previously excluded risks.

Answering the Right Question

The first and simplest test of a risk management method is determining if it answers the relevant question, “Where and how much do we reduce risk and at what cost?” A method that answers this, explicitly and specifically, passes this test. If a method leaves this question open, it does not pass the test—and many will not pass.

For example, simply providing a list of a firm's top ten risks or classifying risks into high, medium, or low doesn't close the loop. Certainly, this is a necessary and early step of any risk management method. I have sometimes heard that such a method is useful if only it helps to start the conversation. Yes, that may be useful, but if it stops there it still leaves the heavy lifting yet to be done. Consider an architectural firm that provides a list of important features of a new building such as “large boardroom,” “nice open entry way with a fountain,” and then walks away without producing detailed plans much less actually constructing the building. Such a list would be a starting point but it is far short of a usable plan, much less detailed blueprints or a finished building.

Relevant risk management should be based on risk assessment that ultimately follows through to explicit recommendations on decisions. Should an organization spend $2 million to reduce its second largest risk x by half, or spend the same amount to eliminate three risks that aren't in the top five biggest risks? Ideally, risk mitigation can be evaluated as a kind of “return on mitigation” so that different mitigation strategies of different costs can be prioritized explicitly. Merely knowing that some risks are high and others are low is not as useful as knowing that a particular mitigation has a 230 percent return on investment (ROI) and another has only a 5 percent ROI or whether the total risks are within our risk tolerance or not.

WHAT WE MAY FIND

We will spend some time on several of the previously mentioned methods of assessing performance, but we will be spending a greater share of our time on component testing. This is due, in part, to the fact that there is so much research on the performance of various components, such as methods of improving subjective estimates, the performance of quantitative methods, using simulations, aggregating expert opinion, and more.

Still, even if risk managers use only component testing in their risk management process, many are likely to find serious shortcomings in their current approach. Many of the components of popular risk management methods have no evidence of whether they work, and some components have shown clear evidence of adding error. Still other components, though not widely used, can be shown to produce convincing improvements compared to the alternatives.

Lacking real evidence of effectiveness, some practitioners will employ some of the previously mentioned defenses. We will address at least some of those arguments in subsequent chapters, and we will show how some of those same arguments could have been used to make the case for the “validity” of astrology, numerology, or crystal healing. When managers can begin to differentiate the astrology from the astronomy, then they can begin to adopt methods that work.

RISK MANAGEMENT SUCCESS-FAILURE SPECTRUM

Best. The firm builds quantitative models to run simulations; all inputs are validated with proven statistical methods, additional empirical measurements are used when optimal, and portfolio analysis of risk and return is used. Always skeptical of any model, the modelers check against reality and continue to improve the risk models with objective measures of risks. Efforts are made to systematically identify all risks in the firm.

Better. Quantitative models are built using at least some proven components; the scope of risk management expands to include more of the risks.

Baseline. Intuition of management drives the assessment and mitigation strategies. No formal risk management is attempted.

Worse (the merely useless). Detailed soft or scoring methods are used, or perhaps misapplied quantitative methods are used, but at least they are not counted on by management. This may be no worse than the baseline, except that they did waste time and money on it.

Worst (the worse than useless). Ineffective methods are used with great confidence even though they add error to the evaluation. Perhaps much effort is spent on seemingly sophisticated methods, but there is still no objective, measurable evidence they improve on intuition. These “sophisticated” methods are far worse than doing nothing or simply wasting money on ineffectual methods. They cause erroneous decisions to be made that would not otherwise have been made.

A firm that conducts an honest evaluation of itself using the prescribed methods will find it falls somewhere along a spectrum of success and failure. Based on the standards I've described for the success of risk management, the reader has probably already figured out that I believe the solution to be based on the more sophisticated, quantitative methods. You may not yet be convinced that such methods are best or that they are even practical. We'll get to that later. For now, let's look at the proposed success/failure spectrum. (See the Risk Management Success-Failure Spectrum box.)

Note that in this spectrum doing nothing about risk management is not actually the worst case. It is in the middle of the list. Those firms invoking the infamous “at least I am doing something” defense of their risk management process are likely to fare worse. Doing nothing is not as bad as things can get for risk management. The worst thing to do is to adopt an unproven method—whether or not it seems sophisticated—and act on it with high confidence.

NOTES

 1. Some of the details of this are modified to protect the confidentiality of the firm that presented the method in this closed session, but the basic approach used was still a subjective weighted score.

 2. C. Tsai, J. Klayman, and R. Hastie, “Effects of Amount of Information on Judgment Accuracy and Confidence,” Organizational Behavior and Human Decision Processes 107, no. 2 (2008): 97–105.

 3. C. Heath and R. Gonzalez, “Interaction with Others Increases Decision Confidence but Not Decision Quality: Evidence against Information Collection Views of Interactive Decision Making,” Organizational Behavior and Human Decision Processes 61, no. 3 (1995): 305–26.

 4. Stuart Oskamp, “Overconfidence in Case-Study Judgments,” Journal of Consulting Psychology 29, no. 3 (1965): 261–65, doi: 10.1037/ h0022125. Reprinted in Judgment under Uncertainty: Heuristics and Biases, ed. Daniel Kahneman, Paul Slovic, and Amos Tversky (Cambridge, UK: Cambridge University Press, 1982).

 5. P. Andreassen, “Judgmental Extrapolation and Market Overreaction: On the Use and Disuse of News,” Journal of Behavioral Decision Making 3, no. 3 (July–September 1990): 153–74.

 6. D. A. Seaver, “Assessing Probability with Multiple Individuals: Group Interaction versus Mathematical Aggregation,” Report No. 78–3 (Los Angeles: Social Science Research Institute, University of Southern California, 1978).

 7. S. Kassin and C. Fong, “I'm Innocent! Effects of Training on Judgments of Truth and Deception in the Interrogation Room,” Law and Human Behavior 23 (1999): 499–516.

 8. D. Kahneman and G. Klein, “Conditions for Intuitive Expertise: A Failure to Disagree,” American Psychologist (September 2009): 515–26.

 9. “It's Academic,” Stanford GSB Reporter (April 24, 2000): 14–15.

10. E. Zuckerman and J. Jost, “What Makes You Think You're So Popular? Self-Evaluation Maintenance and the Subjective Side of the ‘Friendship Paradox,’” Social Psychology Quarterly 64, no. 3 (2001): 207–23.

11. D. M. Messick, S. Bloom, J. P. Boldizar, and C. D. Samuelson, “Why We Are Fairer Than Others,” Journal of Experimental Social Psychology 21 (1985): 480–500.

12. N. D. Weinstein, “Unrealistic Optimism about Future Life Events,” Journal of Personality and Social Psychology 39 (1980): 806–20.

13. O. Svenson, “Are We All Less Risky and More Skillful Than Our Fellow Drivers?” Acta Psychologica 47 (1981): 143–48.

14. D. Dunning and J. Kruger, “Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments,” Journal of Personality and Social Psychology 77, no. 6 (1999): 121–34.

15. N. Nohria, W. Joyce, and B. Roberson, “What Really Works,” Harvard Business Review (July 2003).

16. H. Bühlmann, “The Actuary: The Role and Limitations of the Profession since the Mid-19th Century,” ASTIN Bulletin 27, no. 2 (November 1997): 165–71.

CHAPTER 4
Getting Started: A Simple Straw Man Quantitative Model

Build a little. Test a little. Learn a lot.

—REAR ADMIRAL WAYNE MEYER, AEGIS WEAPON SYSTEM PROGRAM MANAGER

In the next several chapters I will be reviewing what the research says about the performance of popular qualitative methods and certain quantitative, probabilistic methods. Some readers may be a lot more familiar with the former methods and will need at least some kind of reference for the latter. Some may want to start experimenting with a simple quantitative model even before hearing the details about the relative performance of various methods. In either case, it makes sense to introduce a very simple quantitative model early.

Or perhaps some readers may have misconceptions about what qualifies as a quantitative method and may prematurely dismiss them as infeasibly complex requiring a PhD in statistics or actuarial science or requiring unrealistic amounts of data. Nothing could be further from the truth. There is a whole spectrum of quantitative solutions from the very simple to very complex. The concern that anything quantitative must be unmanageable in practice is just another issue we need to address early.

My team at HDR once created quantitative decision models for infrastructure investments in a power utility. They had previously developed their own version of the risk matrix briefly described in chapter 2, and there was resistance to adopting more quantitative models. One concern they had is that they would end up developing an extremely complex and onerous-to-manage quantitative model similar to the ones their colleagues used in risk assessment for nuclear power generation. (Nuclear power, as mentioned in that same chapter 2, was one of the earliest users of Monte Carlo simulations.) Out of the extreme caution we would expect in that industry, the probabilistic risk assessment engineers developed very detailed and sophisticated simulations. They apparently saw the adoption of probabilistic models as an all-or-nothing choice of extreme complexity. In fact, there are many levels of sophistication in quantitative models and even the simplest can have benefits. We will start with one of the simplest.

As an initial straw man quantitative model, I will introduce what I've called the one-for-one substitution model. This is the simplest probabilistic model that is a direct substitution for a risk matrix. For most risk managers, the one-for-one substitution counts as “better” on the “Risk Management Success-Failure Spectrum” mentioned at the end of chapter 3. Once we've introduced that concept, we will gradually introduce additional ideas to further develop this model.

This model is something I introduced in a previous book, How to Measure Anything in Cybersecurity Risk. The idea of introducing that solution early and then building on it later seemed to work well for the readers and the idea is certainly applicable well beyond cybersecurity. I've made just a few changes to generalize it beyond cybersecurity, but if you are familiar with this concept from the previous book, you might skim or skip this section.

In part 3, we will explore more detailed models and more advanced methods. But for now, we will start with a model that merely replaces the common risk matrix with the simplest equivalent in quantitative terms. We will still just capture subjective estimates of likelihood and impact, but probabilistically. Some of the concepts we need to introduce (such as how to provide subjective probabilities) will be developed in more detail later, but this should get you started.

To make the quantitative models as accessible as possible, we will provide a solution native to Excel—no Visual Basic, macros, or add-ins required. Excel has such a large user base and most readers of this book will have some familiarity with Excel even if they don't have a background in programming, statistics, or mathematical modeling. You will not need to develop this model from scratch, either. An entire working example is ready for you to download at www.howtomeasureanything.com/riskmanagement.

When you are done with this chapter, you will have a foundation to build on for the rest of the book. Later, we will incrementally add further improvements. You will learn how to test your subjective assessments of probability and improve on them. You will learn how even a few observations can be used in mathematically sound ways to improve your estimates further. And you will learn how to add more detail to a model if needed.

A SIMPLE ONE-FOR-ONE SUBSTITUTION

We can start down a path for better risk assessment by replacing elements of the method many risk managers are already familiar with—the risk matrix. Again, similar to the risk matrix, we will depend only on the judgment of subject matter experts in the relevant areas of risk. They continue to make a subjective, expert judgment about likelihood and impact, just as analysts now do with the risk matrix. No data are required other than the information that cybersecurity analysts may already use to inform their judgments with a risk matrix. As now, experts can use as much data as they like to inform what ultimately comes down to a subjective judgment.

We only propose that instead of using the scales such as high, medium, low, or 1 to 5, experts learn how to subjectively assess the actual quantities behind those scales—that is, probability and dollar impact. In exhibit 4.1, we summarize how we propose to substitute each element of the common risk matrix with a method that uses explicit probabilities.

The method proposed is, similar to the risk matrix, really just another expression of your current state of uncertainty. It does not yet reflect a proper measurement in the sense that we are using empirical data about the external world. We are merely stating our current uncertainty about it. But now we have expressed this level of uncertainty in a way that enables us to unambiguously communicate risk and update this uncertainty with new information. We will see how each dot on the traditional risk matrix is substituted with one row in the spreadsheet you download.

EXHIBIT 4.1 Simple Substitution of Quantitative versus the Risk Matrix

Instead of …
We Substitute (more to come on each of the substitutes) …

Rating likelihood on a scale of 1 to 5 or low to high Example: “Likelihood of x is a 2” or “likelihood of x is medium.”
Estimate the probability of the event occurring in a given period of time (e.g., 1 year)
“Event x has a 10 percent chance of occurring in the next 12 months.”

Rating impact on a scale of 1 to 5 or “low” to “high” Example: “Impact of x is a 2” or “impact of x is medium.”
Estimate a 90 percent confidence interval for a monetized loss “If event x occurs, there is a 90 percent chance the loss will be between $1 million and $8 million.”

Plotting likelihood and impact scores on a risk matrix
Use the quantitative likelihood and impact to generate a loss exceedance curve—a quantitative approach to expressing risk—using a simple Monte Carlo simulation done in a spreadsheet.

Further dividing the risk matrix into risk categories such as low, medium, high or green, yellow, red and guessing whether you should do something and what you should do
Compare the loss exceedance curve to a risk tolerance curve and prioritize actions based on return on mitigation.

Let's put together the pieces of this approach, starting with how we come up with subjective estimates of probability. Then we will explain how we do the math with those estimates, how we roll them up into a total risk (with a loss exceedance curve), and how we can start to make decisions with this output.

THE EXPERT AS THE INSTRUMENT

In the spirit of the one-for-one substitution we will start with, we will use the same source for an estimate as the current risk matrix—a subject matter expert from the business. Perhaps the person is an expert in supply chains, project management, cybersecurity, product liabilities, or some other area of the organization. They are the same experts you would use to populate the risks listed in any conventional risk matrix or other qualitative risk model. Just as experts already assess likelihood and impact on the conventional risk matrix, they can simply assess these values using meaningful quantities.

We will deal with how to incorporate additional external information in a later step. But simply capturing your current state of uncertainty is an important starting point in any measurement problem. We just need to set up a basic structure with the following steps.

Define a list of risks. There are different options for categorizing risks, but for now let's just say that it is the same list that would have been plotted on the conventional risk matrix. For each dot on your risk matrix, create one row for input on the downloaded spreadsheet. Whatever the name of that risk is, type that name in the “Risk Name” column of the spreadsheet.

Define a specific period of time over which the risk events could materialize. It could be one year, a decade or whatever time frame makes sense - just use it consistently for all the risks.

For each risk, subjectively assign a probability (0 percent to 100 percent) that the stated event will occur in the specified time (e.g., “There is a 10 percent chance a data breach of system x will occur in the next twelve months”). Technically, this is the probability that the event will occur at least once in that time period. (We will consider later how we model events that could happen multiple times in a period.)

For each risk, subjectively assign a range for a monetary loss if such an event occurs as a 90 percent confidence interval. In other words, this is a range wide enough that you are 90 percent certain that the actual loss will be within the stated range (e.g., if there is a data breach in application x, then it is 90 percent likely that there will be a loss equal to somewhere between $1 million and $10 million). Don't try to capture the most extreme outcomes possible. (Note: In a 90 percent confidence interval, there is still a 5 percent chance of being below the lower bound and a 5 percent chance of being above the upper bound.)

Get the estimates from multiple experts if possible, but don't all have a meeting and attempt to reach consensus. Simply provide the list of defined events and let individuals answer separately. If some individuals give very different answers than others, then investigate whether they are simply interpreting the problem differently. For example, if one person says something is 5 percent likely to happen in a year, and another says it is 100 percent likely to happen every day, then they probably interpreted the question differently. (I have personally seen this very result.) But as long as they at least interpret the question similarly, then just average their responses. That is, average all event probabilities to get one probability, and average the lower bounds to produce one lower bound and upper bounds to produce one upper bound.

Once we have recorded the likelihood and 90 confidence interval of losses for each risk in the table, we are ready for the next step: running a simulation to add up the risks.

I need to briefly address some perceived obstacles to using a method like this. Some may object to the idea of subjectively assessing probabilities. Some analysts who had no problem saying likelihood was a 4 on a scale of 1 to 5 or a medium on a verbal scale will argue that there are requirements for quantitative probabilities that make quantification infeasible. Somehow, the problems that were not an issue using more ambiguous methods are major roadblocks when attempting to state meaningful probabilities.

This is a common misunderstanding. There is nothing mathematically invalid about using a subjective input to a calculation. In fact, as we will see, there are problems in statistics that can only be solved by using a probabilistically expressed prior state of uncertainty. And these are actually the very situations most relevant to decision-making in any field, especially risk management. Later, we will discuss the sources supporting this approach, including some very large empirical studies demonstrating its validity. Additionally, we will show how readers can measure and improve their own skills at assessing probabilities using a short series of exercises that can help them continue to improve it over time. We call this calibrated probability assessment, and we will show that there is quite a bit of research backing up the validity of this approach. For now, just recognize that most experts can be trained to subjectively assess probabilities and that this skill is objectively measurable (as ironic as that sounds).

The expert can also be improved by using methods that account for two other sources of error in judgment: the high degree of expert inconsistency and a tendency to make common inference errors when it comes to thinking probabilistically. These improvements will also be addressed in upcoming chapters.

Of course, these sources of error are not dealt with in the typical risk matrix at all. If the primary concern about using probabilistic methods is the lack of data, then you also lack the data to use nonquantitative methods. As we've stated, both the risk matrix and the one-for-one substitution methods are based on the same source of data so far—that is, the opinion of experts in the relevant domain of risk. And we cannot assume that whatever errors you may be introducing to the decision by using quantitative probabilities without being trained are being avoided by using mathematically ambiguous qualitative methods. The lack of data is not alleviated by nonquantitative methods. Ambiguity does not offset uncertainty. We will address more objections to the use of quantitative methods, whether simple or complex, in later chapters.

A QUICK OVERVIEW OF “UNCERTAINTY MATH”

Now that we have recorded the likelihoods and ranges of impacts for a list of potential events, we need a way of summarizing them quantitatively. If we were using exact, deterministic point values—where we pretend to predict all the outcomes exactly—then the math is as simple as adding up the known losses. But because we want to capture and summarize uncertainty, we have to use probabilistic modeling methods to add them up.

So how do we add, subtract, multiply, and divide in a spreadsheet when we have no exact values, only ranges? Fortunately, there is a practical, proven solution, and it can be performed on any modern personal computer—the Monte Carlo simulation briefly mentioned in the short history of risk management in chapter 2. A Monte Carlo simulation uses a computer to generate a large number of scenarios based on probabilities for inputs. For each scenario, a specific value would be randomly generated for each of the unknown variables. Then these specific values would go into a formula to compute an output for that single scenario. This process usually goes on for thousands of scenarios.

For a little more history, we need to go back to the Manhattan Project, America's program to develop the first atomic bomb during World War II. Some mathematicians and scientists working in that project started using simulations of thousands of random trials to help solve certain very hard mathematical problems. Stanislaw Ulam, Nicholas Metropolis, and later John von Neumann had developed a way to use this method on the rudimentary computers available at the time to help solve math problems related to the development of the atomic bomb.¹ They found that randomly running thousands of trials was a way to work out the probabilities of various outcomes when a model has a number of highly uncertain inputs. At the suggestion of Metropolis, Ulam named this computer-based method of generating random scenarios after Monte Carlo, a famous gambling hotspot, in honor of Ulam's uncle, a gambler. Now, with the advantage of greater computing power (easily billions of times greater than what was available on the Manhattan Project, by almost any measure), Monte Carlo simulations assess uncertainties and risks as varied as power generation, supply chain, product development, investment portfolios, cybersecurity, and more.

We are going to use a Monte Carlo simulation to compute an answer to questions such as, “Given all of my stated risks, what is the chance we will lose more than x in the next year?” and “How much does that change if I implement risk mitigation y?” and “What is the return on a given risk mitigation?” A qualitative method such as a risk matrix does not answer these kinds of questions. To answer these questions, we will generate the loss exceedance curve (LEC) briefly shown in exhibit 4.2.

An LEC is a method of visualizing risk in a mathematically unambiguous way. LECs are already used in financial portfolio risk assessment, actuarial science, and what is known as probabilistic risk assessment in nuclear power and other areas of engineering. In these other fields, it is also variously referred to as a probability of exceedance or even complementary cumulative probability function. Exhibit 4.2 shows an example of an LEC.

EXHIBIT 4.2 Example of a Loss Exceedance Curve

To generate an LEC, the spreadsheet you can download from the website will generate ten thousand scenarios using the risks you entered. The spreadsheet simply counts the number of the ten thousand scenarios that had losses exceeding a given amount shown on the horizontal axis of the LEC chart. For example, if there were nine hundred scenarios out of ten thousand that had a total loss exceeding $10 million, then there would be a point on the LEC at $10 million on the horizontal axis and 9 percent on the vertical axis. If there were one hundred scenarios with losses greater than $60 million, then there would be a point at $60 million and 1 percent, and so on. The chart simply shows a series of those points connected in a curve.

To generate the random scenarios, we use what is called a pseudo random number generator, or PRNG. There is a random number–generating function in Excel written as “rand()” that will generate a value between 0 and 1. But we will actually use a different PRNG developed by my staff and me at Hubbard Decision Research. There are two reasons I decided to use my own PRNG instead of Excel's rand() function. First, in statistical tests of randomness the HDR PRNG outperforms Excel's rand(). Very subtle patterns in PRNGs, which can only be detected in sophisticated statistical tests using millions of generated values, are less common in the HDR PRNG than Excel's rand() function. In other words, our method appears to be statistically more random.

Additionally, the HDR PRNG, unlike the Excel rand() function, can be reversed and replayed exactly like fast forward and rewind on a video. It uses a unique identifier for each random scenario and that “trial ID” will always produce the same result. In our spreadsheet, you will see a scroll bar at the top of the spreadsheet. This will enable you to scroll through all the scenarios one by one. If you want to go back to scenario number 9,214, you can do so and get exactly the same result you saw the first time. The Excel rand() function doesn't keep the previous results. If you recalculate a table, the previous values are gone unless you saved them. I find it very useful to exactly re-create specific scenarios in order to validate results.

Using our PRNG, one of these random numbers is generated for each event probability and each impact range for each risk listed for each scenario. In other words, if you have ten risks listed in your one-for-one substitution table, you will have ten risks times two random values per risk (the probability and impact of the event) times ten thousand scenarios (i.e., two hundred thousand individual random values). These ten thousand scenarios are stored using a feature in Excel called a what-if data table. Simply referred to as a data table (confusingly, I think, because many users might think any table of data in Excel is a kind of “data table”), this feature in Excel lets you compute different results in some formula or model by changing one or more values at a time. In this case, we are changing trial ID to generate different results for each random scenario (i.e., trial) in our model. Each row in that table shows a total of all the events in a given scenario.

Note that a data table contains functions written as “{=TABLE(cell address)}.” You cannot directly write this function in the spreadsheet. Excel will create it if you go through the simple process of creating a data table using the what-if features of Excel. (You can review help in Excel to see how to create it in your current version but the downloadable table already has one created for you.)

If you have no experience with Monte Carlo simulations, they're probably easier than you think. My staff and I routinely apply Monte Carlo simulations on a variety of practical business problems. We have seen that many people who initially were uncomfortable with the idea of using Monte Carlo simulations eventually became avid supporters after tinkering with the tools themselves.

Now let's summarize what is going on with our Monte Carlo. I have provided additional details about the Excel formulas in the first appendix and there are also further instructions provided on the downloaded spreadsheet.

For each risk we previously listed in the spreadsheet, we determine if the event occurred. If the event had a 5 percent chance of happening per year, then the simulation uses a formula to make the event occur randomly in 5 percent of the scenarios.

If the event occurs, the simulation will determine the impact. It will use the range provided as a 90 percent confidence interval particular type of distribution called a “lognormal” distribution. Ninety percent of the time the simulation will choose a random value within that interval, 5 percent of the time the simulated value will be above the upper bound, and 5 percent of the time the value will be below the lower bound. This distribution is useful for impacts because of the way it is shaped. It can't produce a zero or negative value, which would not make sense in the cost of the impact of a risk event, but it could potentially produce values well above the upper bound.

The simulation runs ten thousand scenarios for each risk. In each scenario, all the impacts, if there are any, of all the risks are added up and shown in the data table. Each row in the data table shows the total of all the impacts that occurred in a given scenario.

Another table is created that counts up the number of scenarios that have losses exceeding a given amount. This creates a series of points used to draw the loss exceedance curve.

ESTABLISHING RISK TOLERANCE

How much risk can we bear? There is actually a well-developed theory for how to quantify this (more on that later). But in the spirit of keeping this straw man as simple as possible yet still quantitative, we will draw another curve to compare to the LEC. If our LEC is under this “risk tolerance” curve, the risk is acceptable.

Ideally, the risk tolerance curve is gathered in a meeting with a level of management that is in a position to state, as a matter of policy, how much risk the organization is willing to accept. I have gathered risk tolerance curves of several types from many organizations, including risk tolerance for multiple cybersecurity applications.

The required meeting is usually done in about ninety minutes. It involves simply explaining the concept to management and then asking them to establish a few points on the curve. We also need to establish which risk tolerance curve we are capturing (e.g., the per-year risk for an individual system, the per-decade risk for the entire enterprise, etc.). But once we have laid the groundwork, we could simply start with one arbitrary point and ask the following:

Analyst: | Okay, today we are establishing your tolerance for risk. Imagine we add up all the (previously discussed) sources of risk. In total, would you accept a 10 percent chance, per year, of losing more than $5 million due to the listed risks?
Executive: | I prefer not to accept any risk.
Analyst: | Me too, but you accept risk right now in many areas. You could always spend more to reduce risks, but obviously there is a limit.
Executive: | True. I suppose I would be willing to accept a 10 percent chance per year of a $5 million loss or greater from these risks.
Analyst: | How about a 20 percent chance?
Executive: | That feels like pushing it. Let's stick with 10 percent.
Analyst: | Great, 10 percent, then. Now, how much of a chance would you be willing to accept for a much larger loss, like $50 million or more? Would you say even 1 percent?
Executive: | I think I'm more risk averse than that. I might accept a 1 percent chance per year of accepting a loss of $25 million or more …

And so on. After plotting three or four points, we can interpolate the rest and give it to the executive for final approval. There is a small table in the spreadsheet just for entering these points you need to draw the risk tolerance curve.

It is not a technically difficult process, but it is important to know how to respond to some potential questions or objections. Some executives may point out that this exercise feels a little abstract. In that case, give them some real-life examples from their firm or other firms of given losses and how often those happen.

Also, some may prefer to consider such a curve only for a given budget—as in, “That risk is acceptable depending on what it costs to avoid it.” This is also a reasonable concern. You could, if the executive was willing to spend more time, state more risk tolerance at different expenditure levels for risk avoidance.

Executives who want to address that issue should consider taking the concept of risk tolerance beyond the simple “ceiling” for an LEC. This is what the field of decision analysis addresses. We will introduce this version of it later as a way to think about how to trade off risks with potential rewards. For now, however, the simple one-for-one substitution model will use the term risk tolerance here to mean a kind of maximum bearable pain the organization is willing to accept, regardless of reward.

SUPPORTING THE DECISION: A RETURN ON MITIGATION

Ultimately, the point of risk analysis—even with the risk matrix we are replacing—is to support decisions. But the difficulty we had before was making specific resource-allocation choices for specific risk mitigation efforts or controls. What is it worth, after all, to move one high risk to a medium level? Is it $5,000 or $5 million? Or what if we have a budget of $8 million in, for example, supply chain–related risks, and we have eighty lows, thirty mediums, and fifteen highs? And what if we can mitigate more lows for the same money as one medium?

If you have observed (as I have) someone asking a question such as, “If we spent another million dollars, can we move this risk from a red to a yellow?” then you may have felt the dissatisfaction from this approach. Clearly the traditional risk matrix offers little guidance once management actually has to make choices about allocating limited resources. Some might feel they can move from the qualitative to specific decisions based on experience and gut feel, but, as we will show later, this has even more problems.

What organizations need is a “return on control” calculation. That is the monetized value of the reduction in expected losses divided by the cost of the control. To express the return as a percentage return comparable to other returns, it would be conventional to show it as expected value of a risk reduction divided by the cost of the risk reduction, then subtract one from the result, and displayed as a percentage. The minus one is to show return as a percentage of benefits in excess of the costs.

The term expected in the context of quantitative decision methods generally refers to the probability-weighted average of some amount. So expected loss is the average of the Monte Carlo simulation losses. If we applied a control to reduce risks and then we simulated a new set of losses, the average of those losses would be less (by either reducing the chance of any loss, reducing the impact if the loss event occurred, or both). The difference in the loss before and after the control is the reduction in expected losses in the simple formula just given. If the reduction in expected losses was exactly as much as the cost, then this formula would say the return on control was 0 percent. This would be the convention for other forms of investment.

You would also have to identify over what period of time this expected reduction in losses would occur. If the control was just an ongoing expense that could be started and stopped at any time, then this simple formula could just be applied to a year's worth of benefits (loss reduction) and a year's worth of costs. If the control is a one-time investment that could provide benefits over a longer period of time, then follow the financial conventions in your firm for capital investments. You will probably be required then to compute the benefits as a present value of a stream of investments at a given discount rate. Or you may be asked to produce an internal rate of return. We won't spend time on those methods here, but there are fairly simple financial calculations that can, again, be done entirely with simple functions in Excel.

MAKING THE STRAW MAN BETTER

George Box, a statistician famous for his work in quality control, time series forecasts, and many other areas of statistics, once said, “Essentially, all models are wrong, but some are useful.” I add one corollary to this quote: some models are measurably more useful than others. We will increase this usefulness incrementally with additional features though the rest of this book, especially in part 3.

Even with this very simple quantitative model, the component testing methods we discussed in chapter 2 can help us determine if we are really classifying something as better according to the Risk Management Success-Failure Spectrum mentioned in that same chapter. There is existing research that indicates we have improved our assessment of risk just by the act of avoiding the ambiguity of qualitative methods, decomposing uncertain quantities, and even using Monte Carlo simulations. More on that research later.

Now, how much you choose to add to this model to make it even better will be a function of how much detail you are willing to manage and the size of criticality of your risks. If you have very large risks, especially risks existential to the firm or risks involving human safety, you could probably justify a lot more detail. For readers who have had even basic programing, math, or finance courses, they may be able to add more detail without much trouble. But, because everything we are doing in this book was can be handled entirely within Excel, any of these tools would be optional.

We will introduce more about each of these improvements later in the book, but we have demonstrated what a simple one-for-one substitution would look like. Here is a quick summary of some of the ways we will make this model “less wrong” in the chapters ahead:

Improving subjective judgment: Research shows that subjective expert input can be very useful—if we can adjust for issues such as overconfidence and inconsistency. We also know how some methods of eliciting judgments or aggregating the judgments of many experts are better than other methods.

Adding more inputs: We can add a lot more detail by decomposing the likelihood and impact of the event. That is, we can compute the probabilities or impacts of events from other inputs instead of just estimating them directly. For example, the impact of a product recall could involve loss of revenue, legal liabilities, operational costs of the recall, and more.

Considering interconnections: Some events may be correlated. Perhaps some events are necessary conditions for other events and some events may cause possible chain reactions. Now that we have adopted quantitative methods in modeling risks, any of these kinds of relationships can be modeled just by adding more rules to our spreadsheet.

Additional types of distributions: We started out using a simple binary (did the event happen or not) distribution and a lognormal distribution. There are many more to pick from that may better fit the intentions of the subject matter expert estimating them or will better fit the data they are meant to represent.

Using empirical data: Useful statistical inferences can be made even in situations where many people might assume that the data are very limited or otherwise imperfect. Contrary to the common misconception that you need some large number of observations to make any inferences at all, single events can update probabilities if we use a set of methods that are part of what is called Bayesian statistics.

Incorporating decision analysis methods: As discussed earlier in this chapter, there is more to add regarding the concept of risk tolerance. Later, we will introduce additional methods that come from expected utility theory and decision analysis. When risk analysis becomes part of decision analysis and risk management is fully incorporated into management decision-making, then you will need ways of trading off risk and return.

Now that we have introduced what is just about the simplest quantitative method you could use in risk management, let's step back and discuss why there is need for a change at all. In part 2, we will review various conflicting and confusing ideas about risk, research on the performance of experts, problems with popular qualitative methods, and some valid and invalid objections to some quantitative methods. But we will start part 2 by expanding further on the brief history of risk management mentioned in chapter 2 so that we can better see how all these competing methods came about in the first place.

NOTE

 1. Stanislaw Ulam, Adventures of a Mathematician (Berkeley: University of California Press, 1991).

PART TWO
Why It's Broken

CHAPTER 5
The “Four Horsemen” of Risk Management: Some (Mostly) Sincere Attempts to Prevent an Apocalypse

History is a race between education and catastrophe.

—H. G. WELLS

The biggest disasters, like the 2008 financial crisis or the recall of 737 aircraft crashes, generate a search for a cause, and in response to that demand, experts will provide a wide variety of theories. Most of these theories are judgment-laden. Explanations involving conspiracy, greed, and even stupidity are easier to generate and accept than more complex explanations that may be closer to the truth.

A bit of wisdom called Hanlon's razor advises us, “Never attribute to malice that which can be adequately explained by stupidity.”¹ I would add a clumsier but more accurate corollary to this: “Never attribute to malice or stupidity that which can be explained by moderately rational individuals following incentives in a complex system.” People behaving with no central coordination and acting in their own best interest can still create results that appear to some to be clear proof of conspiracy or a plague of ignorance.

With that in mind, we need to understand how very different forces have evolved to create the state of risk management methods as we see them today. Similar to most systems, cultures, and habits, the current state of risk management is a result of gradual pressures and sudden events that happened along the way. Influential individuals with great ideas appear where and when they do more or less randomly. Wartime necessities and new technologies drove other developments that affect risk management today. Institutions with their own motivations arose and would create momentum for certain methods. These institutions had different research objectives and methods than those created by academics, and they had very different perspectives on the same problem. Those who would apply these methods were influenced by associations that were accidental at least as often as designed.

To map out the current state of affairs, I've divided risk management into four general groups according to the types of problems they focus on and the methods they use. There is a lot of overlap in these sets, and I'm sure others could come up with different and equally valid taxonomies. But I think that individuals who think of themselves as risk managers will tend to associate with one of these groups or the methods.

The “Four Horsemen” of Risk Management

Actuaries: These original professional risk managers use a variety of scientific and mathematical methods. Originally they focused on assessing and managing the risks in insurance and pensions, but they have branched out into other areas of risks.

War quants: Engineers and scientists during World War II used simulations and set up most decisions as a particular type of mathematical game. Today, their descendants are users of probabilistic risk analysis, decision analysis, and operations research.

Economists: After World War II, a new set of financial analysis tools were developed to assess and manage risk and return of various instruments and portfolios. Today, financial analysts of various sorts are the primary users of these methods. There is some overlap with the war quants.

Management consultants: Most managers and their advisors use more intuitive approaches to risk management that rely heavily on individual experience. They have also developed detailed “methodologies” for these softer methods, especially after the rising influence of managers addressing information technology. Users and developers of these methods are often business managers themselves or nontechnical business analysts. I'll include auditors of various sorts (safety, accounting, etc.) in this group because certain influential methods they use have a common origin.

Which of these groups are you in? Someone with a management consulting orientation may not have heard of some of the methods used by engineers or actuaries or, if they have, are probably thinking that such methods are impractical. An engineer reading this book may already know that the methods I'm going to discuss are entirely practical but may be unaware that their methods contain systematic errors. A financial analyst or economist may be vaguely aware of some of these solutions from other fields but probably not all of them. Academic researchers (who could have a research focus on any combination of these methods) might not necessarily be following how well methods they research are used in the real world. No matter who you are, there is also a good chance that we will discuss at least some issues outside of your area of focus.

ACTUARIES

Certainly, the oldest profession (in risk management) is practiced in the insurance industry by actuaries. The insurance industry is now often an example of fairly quantitative risk analysis, but there was a period of time—a long one—when insurance existed without what we know today as actuaries.

The word actuary was used as early as the sixteenth century to refer to someone who was a clerk keeping records of accounts. At that time, being an actuary didn't have much to do with probability theory or statistics, which appeared in insurance no earlier than the seventeenth century. Even when these methods did appear, they would not be common—and certainly there would not be standard requirements for another couple of centuries.

Prior to the mid-1800s, having an ownership stake in an insurance company was more like gambling than investing (although shareholders in AIG in 2008 would probably claim this hasn't changed much). And buying an insurance policy was no guarantee that the insurer would be financially able to cover your losses in a legitimate claim. In the days before the general acceptance of (and legal requirement for) actuaries in insurance, using quantitative methods for assessing risk was a kind of competitive advantage, and those who did not use statistical methods paid the price for it. In chapter 2, for example, I mentioned how in the United Kingdom between 1844 and 1853, 149 insurance companies were formed of which fifty-nine survived.² This is far worse than the failure rate of insurers in modern times, even in 2008.

Those that failed tended to be those that did not use mathematically valid premium calculations. Insurance companies have to estimate contingent losses and make sure they have enough reserves on hand to pay out claims if and when they come. The companies that did not calculate this correctly eventually would not be able to pay claims when a disaster occurred or, on the other extreme, would charge too much to stay competitive and keep far too much in reserve at the expense of paying too few dividends to investors (although anxious investors would ensure the latter was almost never the case). According to the International Actuarial Association, one particular insurer—Equitable—survived this period “in good shape and flourished because of the scientific methods it employed.”³

In 1848, in the midst of this turmoil in the quickly growing insurance industry, the Institute of Actuaries in London was formed as a society for the actuarial profession. Actuarial societies in other countries soon followed. Today, when it comes to the question of whether more quantitative methods add value, there is not much of a debate in the insurance industry. It is generally understood that it would be foolish to attempt to compete in the insurance industry without sound actuarial methods (even if going without actuarial methods were legal in most industrialized countries, which it isn't).

But, after events such as the financial crisis of 2008/2009, some might wonder whether actuaries really had any more answers than anyone else. If actuarial science were effective, would the US government have had to take over the insurance giant AIG when it was in danger of becoming insolvent? This is another example of when anecdotes are not that helpful to evaluate risk management approaches, especially when the facts are misunderstood. AIG had taken a large position on instruments called credit default swaps (CDS). A CDS is purchased by mortgage banks to offset the risk of borrowers defaulting on loans. It is called a swap in the financial world because the parties both exchange cash but with different conditions and payment schedules. In the case of a CDS, one party pays cash up front to the other in exchange for a future cash payment on the condition that a borrower defaults on a loan.

This looks like insurance, sounds like insurance, feels like insurance—but, legally, it's not regulated like insurance. The actuaries of AIG, as with any other insurance company, would have to validate the reserves of the firm to ensure it can meet its responsibility to pay claims. But because a CDS is not legally insurance, actuaries are not responsible to review this risk. The part of AIG's business that actuaries did review was not the part that hurt the company. The actuarial profession, unfortunately, is one of a narrow focus. Outside of insurance and pensions, certified, regulated professions are rare in risk management.

The basic idea of the actuarial profession is sound. They are professional risk managers using scientifically and mathematically sound methods, and they are held to high standards of conduct. When an actuary signs a statement claiming that an insurance company can meet its contingent liabilities and is in a position to weather all but the rarest catastrophes, he or she puts his or her license to practice on the line. As with engineers, doctors, or auditors, actuaries are duty-bound to report their best judgment about truth and, if necessary, resign if pressured to do otherwise.

Similar to most venerable institutions, actuarial societies were not always known for keeping up with the latest developments in related fields. The name actuarial science aside, actuaries are not primarily trained to be scientists. Although some actuaries may get involved in original research, most are more like engineers and accountants applying already-established methods. Because they are a necessarily conservative lot, it's understandable that actuaries would be cautious about adopting new ideas. Even a slew of new developments coming out of World War II would take some time to be adopted by actuaries. But now the new and powerful methods developed by wartime necessity are considered standard risk analysis by actuarial science.

In 2009 (shortly after the publication of the first edition of this book), a global association of actuaries created the chartered enterprise risk actuary (CERA) certification. The purpose is to extend the proven methods of actuarial science to topics outside of what is traditionally associated with insurance. CERA-certified actuaries have started showing up in areas such as enterprise risk management and operational risk management, where soft consulting methods used to be more the norm. For reasons explained in detail in the rest of this book, this is a welcome development.

WAR QUANTS: HOW WORLD WAR II CHANGED RISK ANALYSIS FOREVER

When Churchill said, “Never have so many owed so much to so few,” he was talking about the pilots of the Royal Air Force (RAF) defending the citizens of Britain from German bombers. Of course, the RAF deserved every bit of this recognition, but Churchill might as well have been talking about an even smaller group of mathematicians, statisticians, and scientists solving critical problems in the war effort. Mathematicians and scientists have had some influence on business and government operations for centuries, but World War II arguably offered a unique showcase for the power and practicality of such methods. During the war, such thinkers would develop several interesting approaches to problem-solving that would affect business and government operations for decades to come, including the analysis of risk.

One of these groups of wartime mathematicians was the Statistical Research Group (SRG) at Columbia University. The SRG and similar groups among the Allies had been working on complicated problems such as estimating the effectiveness of offensive operations and developing tactics that improved antisubmarine operations.⁴ In military intelligence, such statistical analyses were consistently better than spies at estimating monthly German tank production.⁵ This diverse group of problems and methods was the origin of the field of operations research (OR).

I briefly mentioned in the previous chapter how, later in the war, a group of physicists and mathematicians working on the Manhattan Project developed the Monte Carlo simulation method. They were running into a particularly difficult problem that required a truly revolutionary solution. The problem was how to model fission reactions. Radioactive materials such as uranium or plutonium gradually decay to produce lighter elements and neutrons. When one atom of a heavy element such as uranium splits (i.e., undergoes fission), it releases energy and more neutrons. Those neutrons cause other atoms to split. If this process occurs at a certain sustained, steady rate, it is called critical, and the heat it generates can be harnessed to create electricity for consumption. If the chain reaction rapidly accelerates, it creates a runaway effect called supercriticality. The heat suddenly released from this process creates a rather powerful explosion or at least a meltdown. As you might guess, getting this distinction right is important.

The problem is that lots of factors affect the rate of reaction. How much fissile material there is in a given volume is one factor. Another factor is that the container housing this reaction might be made of material that absorbs neutrons or reflects neutrons, which decelerates or accelerates the reaction. And the geometry of the fuel and the container affect the rate of reaction. Even under ideal conditions, physicists could not calculate exact trajectories of neutrons—they could merely model them as probabilities. Modeling the behavior of this system proved to be impossible with conventional mathematical methods. This was the original reason why the Monte Carlo method was developed—it's a way to do math without exact numbers.

After the war, the Monte Carlo simulation would find other applications in related fields. Norman C. Rasmussen of MIT developed probabilistic risk analysis (PRA) as a basis for managing risks in nuclear power safety. PRA initially used Monte Carlo models to a limited extent⁶ to simulate detailed components of nuclear reactors and the interactions among them. The idea is that if the probability of failures of each of the components of a complex system could be described, the risk of failure of the entire system (e.g., a release of radioactive coolant, a meltdown, etc.) could be computed. This should apply even if that event had never occurred before or even if that particular reactor had not yet been built. PRA using Monte Carlo simulations continued to grow in scope, complexity, and influence in risk management in nuclear safety. It is now considered an indispensable part of the field.

One of the Manhattan Project scientists, John Von Neumann, was helping to develop and promote the idea of Monte Carlo simulations while he was, nearly in parallel, developing what he called game theory, the mathematical description of games of all sorts. In 1944, Von Neumann coauthored a seminal work in the field—Theory of Games and Economic Behavior—with the economist Oscar Morgenstern. One of Von Neumann's fans was the young Abraham Wald, a member of the SRG, who also contributed ideas central to games under uncertainty.

In one important type of game, the player had no competitor but did have to make a decision under uncertainty—in a way, nature was the other player. Unlike competitive games, we don't expect nature to act rationally—just unpredictably. One such decision that can be modeled this way might be whether to invest in a new technology. If a manager invests, and the investment succeeds, then the manager gains some specified reward. But the investment could also be lost with nothing to show for it. However, if the manager rejects the opportunity, the investment itself can't be lost but a big opportunity instead might be missed.

It turns out that quite a few decisions in both business and government can be described as types of one-person games against nature. This evolved into decision theory. After the war, the ideas behind decision theory were being turned into practical tools for business and government. The RAND Corporation, founded just after the war, began applying the theories, Monte Carlo simulations, and a variety of other methods to everything from social welfare policy analysis to cold war nuclear strategies. It also attracted a variety of thinkers who would influence the field of decision-making and risk assessment for the rest of the twentieth century.

In 1968, the term decision analysis (DA) was coined by Ron Howard at Stanford University to refer to practical applications of the theory to real-world problems. As was the focus of game theory and decision theory, Howard's original use of the term decision analysis was prescriptive.⁷ That is, it was meant to specify what decision-makers should do, not necessarily describe what they will do (to some, the term has since expanded to include both).

The introduction of personal computers (PCs) greatly facilitated the practicality of the Monte Carlo method. In the 1990s, companies such as Decisioneering (now owned by Oracle) and Palisade developed software tools that allowed users to run Monte Carlo simulations on PCs. The intellectual descendants of the World War II team continue to promote these tools as both a practical and theoretically sound way to model risks.

One such person, Professor Sam Savage of Stanford University, is an actual descendant of one of the members of the World War II team. Leonard “Jimmie” Savage, his father, was part of the SRG and also the chief statistical consultant to John Von Neumann (this alone is just about the most impressive thing I've ever heard of any statistician). Jimmie Savage went on to author The Foundations of Statistics, which included practical applications of game theory and probabilistic reasoning in general. Sam Savage, the son, is the author of his own Monte Carlo tools and an innovator of modeling methods in his own right. He founded Probabilitymanagment.org, a not-for-profit that I've had the pleasure of being involved with for many years.

This is the culture of risk management for many engineers, scientists, some financial analysts, and others who might have a quantitative background. Risk is something that is modeled quantitatively, often using simulations of systems. Actuaries, too, have adopted Monte Carlo simulations as a standard tool of risk analysis.

This group, similar to actuaries, is generally surprised to learn what passes as risk management as practiced by other people. They are steeped in quantitative methods on a daily basis, they are often subjected to peer reviews by other mathematically oriented people, and their emphasis is on improving their own quantitative models more than studying the nonquantitative methods used by some people. When I describe softer methods to them (i.e., qualitative scoring methods, categorizing risks as medium or high, etc.), they shake their heads and wonder how anyone could believe an approach like that could work. When exposed to some of the more popular methods in risk analysis, they react in a way that I suspect is something similar to how an astrophysicist would react to theories proposed by an astrologer.

I also tend to see the quantitative risk analysts react positively to the question, “How do you know decisions are any better with your modeling approach?” So far, I see much more of a genuine interest in the question and less of a reaction of defensiveness. Although most have not been collecting the data to validate their models, they agree that answering such a question is critical and have generally been helpful in efforts to gather data to answer this question. When I point out known problems with common methods used in Monte Carlo simulations, they seem eager to adopt the improvements. As a group with a scientific orientation, they seem ever wary of the weaknesses of any model and are open to scrutinizing even the most basic assumptions. I believe that it is from actuaries and war quants that we will find the best opportunity for improving risk management.

ECONOMISTS

Prior to the 1990s, Nobel Prizes in economics were generally awarded for explanations of macroeconomic phenomenon such as inflation, production levels, unemployment, money supply, and so on. For most of the history of economics, risk and probabilistic methods were treated superficially. Prior to World War II, arguably one of the key academic accomplishments on that topic in economics was Frank Knight's 1921 book titled Risk, Uncertainty and Profit⁸—a book that never once resorts to using a single equation or calculation about risk, uncertainty, profit, or anything else. By contrast, the economist and mathematician John Maynard Keynes's book of the same year, Treatise on Probability,⁹ was mathematically rigorous and probably had more influence on the subsequent work of the early decision theorists such as Von Neumann and Wald. When it comes to ideas about how basic terms such as risk and uncertainty are used by economists, Knight's more mathematically ambiguous ideas gained more traction.

I will mention again that my attempt at a taxonomy of risk management has overlaps between groups. (I think any taxonomy of this topic would.) There are mathematicians and economists in both the war quant and economist groups but, by an accident of history, they diverged a bit in methods and diverged a lot in the groups they influenced. So, when I speak of the war quants, I will refer more to the methods of operations research and certain engineers. I will group economists more with Knight and how they subsequently influenced the world of financial investments. (More about competing definitions of risk in the next chapter.)

Knight did not pay much attention to optimization problems for individuals—that is, how a person should ideally behave in a given situation—such as the decisions under uncertainty described by Wald and others. It wasn't until just after World War II, with at least indirect influence from the war quants, that economists (Keynes being the earlier exception) started to consider the problems of risk mathematically. And it was not until very recently that economics considered the issues of actually measuring human behavior regarding decisions under uncertainty in a manner more like a science.

Consider how investors have always had to make decisions under uncertainty. Uncertainty about future returns affects how much they value a stock, how they hedge against losses, and how they select investments for a portfolio. But, as incredible as it seems today, the literature on the economic theory of investments was almost silent on the issue of risk until the 1950s. In 1952, twenty-five-year-old Harry Markowitz, a former student of L. J. Savage and new employee of the RAND Corporation, noticed this absence of risk in investment theory.

At RAND, Markowitz would meet George Dantzig, who, similar to Savage, earned his stripes as a war quant (Dantzig was with the US Air Force Office of Statistical Control). The older Dantzig would introduce Markowitz to some powerful OR optimization methods. Dantzig developed a method called linear programming, which would be influential for decades in OR and which gave Markowitz an idea about how to approach portfolio diversification mathematically. The same year that Markowitz started at RAND, his ideas were published in the Journal of Finance.¹⁰

Markowitz explained in his new theory that a portfolio of investments, similar to the investments that comprise it, has its own variance and return. By changing the proportion of various investments in a portfolio, it is possible to generate a wide variety of possible combinations of returns and volatility of returns. Furthermore, because some investments vary somewhat independently of each other, the variability of the portfolio in principle could be less than the variability of any single investment. By analogy, you are uncertain about the role of one die but you would be far less uncertain about the average of one hundred rolls of dice. The effect of diversification together with the flexibility of setting the proportion of each investment in the portfolio enables the investor to optimize the portfolio for a given set of preferences for risk versus return. Markowitz's approach was to use Dantzig's linear programming method to find the optimal combination of investments depending on how much risk the investor was willing to accept for a given return.

When Markowitz presented this solution for his PhD dissertation in 1955, Milton Friedman (who would win the Economics Nobel Prize in 1976) was on his review board. According to Markowitz, Friedman initially argued that Markowitz's modern portfolio theory (MPT) was not part of economics. Friedman might not have been all that serious because Markowitz did successfully pass his orals. But it is true that the issue of optimizing the choice of an individual making decisions with risk was not previously part of economics. Friedman himself developed mathematical models about several economic topics as if the calculations were all deterministic. Clearly, discussing risk in a quantitative, probabilistic sense was a new idea to many economists.

This fits with a general century-long trend within economics to address risk in probabilistic terms and as a problem for individual decision-makers, not just some vague macroeconomic force. At the beginning of the twentieth century, articles in economics literature that discussed risk, rarely mentioned probability. Until the latter part of the twentieth century, most articles in economics journals did not mention the word probability much less do any math with it.

Using the academic research database called JSTOR, I looked for how often the word risk appeared in economic literature and then how often the those articles used the word probability. Exhibit 5.1 shows the percentage of economics articles on the topic of risk that mentioned the concept of probability. Most articles (over 80 percent) about risk didn't even mention probability prior to 1960. But the tendency to treat risk quantitatively (which makes it much more like to have to mention the word probability) increased to a majority by today.

About two decades after Markowitz would first publish MPT, another influential theory would be proposed for using the risk of an investment to price an option. Options are types of derivatives that give the holder the right, but not the obligation, to buy or sell (depending on the type of option) another financial instrument at a fixed price at some future point. The instrument being bought or sold with the option is called the underlying asset and it could be a stock, bond, or commodity. This future point is called the expiration date of the option and the fixed price is called the exercise price. This is different from futures, which obligate both parties to make the trade at the future date at a prearranged price.

EXHIBIT 5.1 Risk and Probability in Economic Literature

A put option gives the holder the right to sell, say, a share of some stock at a certain price on a certain date. A call option gives the holder the right to buy the share at a certain price on a certain date. Depending on the price of the underlying instrument at the expiration date of the option, the holder could make a lot of money—or nothing.

The holder of a call option would use it only if the selling price of the underlying instrument were higher than the exercise price of the option. If the underlying instrument is selling at $100 the day the option expires, and the exercise price is $80, then the owner of the option can buy a $100 share for just $80. The option has a value that would be equal to the difference: $20 each. But if the shares were selling at just $60, then the option would be of no value (the right to buy something at $80 is worth nothing if the going price is $60).

But since the price of the underlying instrument at the expiration date is uncertain—which may be months in the future—it was not always clear how to price an option. A solution to this problem was proposed in 1973 by Robert C. Merton, an economist who first was educated as an applied mathematician, engineer, and scientist before receiving a doctorate in economics from MIT. The idea was developed further by Fischer Black, another applied mathematician, and Myron Scholes (the only one in the group with degrees solely in economics). Merton and Scholes would receive the Nobel Prize in Economics in 1997 for the development of options theory. (Black would probably have shared the prize but he died two years before and it is not awarded posthumously.) The model is now known as the Black-Scholes equation for pricing options.

The next major development in economics introduced the idea of empirical observation. Some would say it would be the first time economics could even legitimately be called a science. MPT and options theory (OT) were about what people should do in ideal situations instead of describing what people actually do. Earlier economics tried to be descriptive but assumed market participants acted rationally. This was called Homo Economus—the economically rational human. But about the 1970s, a group of researchers started to ask how people actually do behave in these situations. These researchers were not economists at all and, for a long time, had no impact on the momentum in the field of economics. However, by the 1990s, the idea of behavioral economics was starting to have an influence on economic thought. The tools developed in this field were even adopted by the most advanced users of PRA.

OT and MPT have at least one important conceptual difference from the PRA done by nuclear power. A PRA is what economists would call a structural model. The components of a system and their relationships are modeled in Monte Carlo simulations. If valve x fails, it causes a loss of backpressure on pump y, causing a drop in flow to vessel z, and so on.

But in the Black-Scholes equation and MPT, there is no attempt to explain an underlying structure to price changes. Various outcomes are simply given probabilities. And, unlike the PRA, if there is no history of a particular system-level event such as a liquidity crisis, there is no way to compute the odds of it. If nuclear engineers ran risk management this way, they would never be able to compute the odds of a meltdown at a particular plant until several similar events occurred in the same reactor design.

Of course, there is some attempt in finance to find correlations among various factors such as the price of a given stock and how it has historically moved with oil prices or the price of another stock. But even correlations are simple linear interpretations of historical movements without the attempt to understand much about the underlying mechanisms. It's like the difference between meteorology and seismology—both systems are extremely complex but at least the former gets to directly observe and model major mechanisms (e.g., storm fronts). Often, the seismologist can merely describe the statistical distribution of earthquakes and can't say much about what goes on deep in the Earth at a given moment. A PRA is more like the former and MPT and OT are more like the latter.

Other methods have evolved from OT and MPT, although none are especially novel improvements on these earlier ideas. Value at risk (VaR), for example, is widely used by many financial institutions as a basis of quantifying risk. VaR is is the loss exceeded at a given probability (e.g., in a given portfolio of investment, the 5 percentile VaR is $10 million).  A VaR is really just a single point on an LEC. Like an LEC, a VaR is a method of communicating risk—although much less information is conveyed with a single point than the entire LEC. Numerous other esoteric methods that I won't bother to list in detail have also grown out of these tools. But if the foundation of the house needs fixing, I'm not going to worry about the curtains just yet.

Even though OT, MPT, and VaR are widely used, they were the target of criticism well before the 2008/2009 financial crisis (but much more so afterward). As this book will explain in more detail later, OT and MPT make some assumptions that do not match observed reality. Major losses are far more common than these models predict. And because they don't attempt to model components of financial markets (e.g., individual banks, periodic major bankruptcies, etc.) the way that a PRA might, these models may fail to account for known interactions that produce common mode failures. Also, we will show how VaR paint a very misleading picture of risk compared to the loss exceedance curve presented in chapter 4.

The financial crisis caused many to think of these financial tools as being the risk management techniques most in need of repair. Certainly, there is plenty of room for improvement. But simply reacting to the most recent event is counter to good risk management. Risk management is about the next crisis. Calls are already being heard for improvements in popular financial tools. The really big problem may be in a far more popular approach to risk management promoted by the best salesmen among the four horsemen: management consultants.

MANAGEMENT CONSULTING: HOW A POWER TIE AND A GOOD PITCH CHANGED RISK MANAGEMENT

In the late 1980s, I started what I considered a dream job for a brand-new MBA, especially one from a small Midwestern university. It was the era of the Big 8 accounting firms, when, long before the demise of Enron and Arthur Andersen, all the major accounting firms had management consulting divisions under the same roof. I was hired to join the management consulting services (MCS) of Coopers & Lybrand and, being in the relatively small Omaha office, we had no specialists. I was able to work on a variety of different problems in lots of organizations.

I tended to define problems we were working on as fundamentally quantitative challenges, which also emphasized my key interests and talents. But that was not the modus operandi for most management consultants I saw. For some of my superiors, I noticed a tendency to see value in what I might now call PowerPoint thinking. We all love our own PowerPoint slides more than our audience probably will. They were based on the “smart art” images in PowerPoint but often light on content. Because these graphics would get tweaked in committee, whatever meaning the chart first had would sometimes get diluted even further. For many management consulting engagements, even some of significant size and scope, the PowerPoint slides together with an oral presentation was the only deliverable.

The other junior-level consultants and I joked about the process as the random deliverable generator (RDG), as if the actual content of the presentation didn't matter as much as the right combination of sexy graphics and buzzwords. Fortunately, Coopers also had pragmatic managers and partners that would keep the RDG from running completely unchecked. But what surprised me the most was how often the RDG actually seemed to generate deliverables (was deliverable even a word before the 1980s?) that satisfied the customers. Possibly, the credibility of the Big 8 name made some clients a little less critical than they otherwise would be.

I suppose some would expect me to be writing about the influence of Peter Drucker or W. E. Deming on management consulting if I claim to have a reasonably complete explanation of the field. But from where I sat, I saw another important trend more influenced by names such as Tom Peters, author of In Search of Excellence, Mike Hammer, author of Reengineering the Corporation, and software engineer James Martin, the author of Information Engineering. They had a flashier pitch and pep talk for an audience of frustrated executives who were looking for a competitive edge. I recall that their books were consistently on required reading lists for us consultants who wanted to show clients that we were literate in what they paid attention to.

Traditionally, the top management consultants were experienced managers themselves with a cadre of MBAs, typically from the best schools in the country. But by the 1980s, a new kind of management consulting related to information technology was changing the industry. It became more common for management consultants not to actually be consulting managers at all. Sometimes they would be software developers and project managers trying (with varying degrees of success) to solve the clients' problems with information technology.

When I started at Coopers & Lybrand, the IBM PC was only a few years old and still not taken seriously by many big organizations. Most critical software applications were on mainframes using COBOL with relational databases. The Big 8 and others in the software development industry were providing services to help organize disparate development efforts in a way that, in theory, would put business needs first. This is where James Martin, a former IBM executive who evangelized developing systems based on a systematic way of documenting business needs, had a major impact.

But innovators such as James Martin gave the Big 8 an even more important idea. Developing software for a client could be risky. If something went wrong, operations could be delayed, the wrong data would be generated, and the client could be seriously injured. Consultants found a way to get the same lucrative business of IT consulting—lots of staff billed at good rates for long periods—without any of the risks and liabilities of software. They could, instead, develop methodologies. Instead of spending that effort developing software, they could spend time developing nearly equally detailed written procedures for some management practice such as, say, running big software projects. The methodology could be licensed and, of course, would often require extensive training and support from the firm that sold it. James Martin had been licensing and supporting his “information engineering” methodology in the same way.

Methodologies such as this were something the Big 8 knew they could sell. If you can't replicate a few superstar consultants, document some structured methodology and have an army of average management consultants implement it. The ideal situation for a consulting firm is a client with whom you can park dozens of junior associates for long periods of time and bill them out at a handsome daily rate befitting the Big 8 name. The business of getting “alignment” between business and computers was just the ticket.

The familiar risk matrix provides exactly this kind of opportunity for the consultants. It was visual and helped everyone feel like they were really analyzing something. The risk matrix is a simple method that could easily have been developed independently more than once, but I did some research into whether there might have been a “patient zero” of the risk matrix. I did find a couple of strong candidates for the origins of the risk matrix and both are related to different types of auditors.

Whether or not individuals in this group had auditor in their title, I'm referring to those whose jobs are hunting for errors, flaws, and irregularities. These include conventional uses of the term in accounting, but also jobs related to regulatory compliance, safety, and so on. Auditors need to be thorough and systematic, with checklist approaches to just about everything they do. But when it comes to risk management, this group was probably isolated from the earlier work by the other three horsemen.

A group involved in a particular type of audit, reliability and safety engineers, used the term criticality matrix as early as the 1970s. Similar to the current risk matrix, the criticality matrix plotted different potential events on a chart with an axis for probability and another axis for the severity of an event. In at least one of the standards that defined this approach, the probability and severity were grouped into ordinal categories.¹¹ The standard that defined the criticality matrix also defined the related procedure for failure modes, effects, and criticality analysis (FMECA).

A similar chart was developed by an auditor—of the financial sort—in the oil and gas industry in the 1980s. Jim DeLoach, the previously mentioned managing director at Protiviti, was witness to the rise of this method while he was at Arthur Andersen in the 1980s and 1990s (just before its demise). He explains how a financial auditor at the oil and gas company Gulf Canada developed what he called a control self-assessment (CSA), which was presented in the same form as a risk matrix. Perhaps this auditor was influenced by engineering safety because FMECA was probably used by that firm. The difference was that the financial auditor applied it much more broadly than the engineering safety assessors applied FMECA.

According to DeLoach, the original author of this method actively promoted it at conferences, and it seemed to catch on with the major consulting firms. “By the mid-1990s,” DeLoach told me, “every major consulting firm got on the train.” They all had developed their own versions of the risk matrix, sometimes a three-by-three version but oftentimes a five-by-five version—that is, with five likelihood categories and five impact categories.

While at Andersen, DeLoach himself was influential in internal audit and control circles and was one of many voices promoting the approach. DeLoach would later renounce the risk matrix altogether in favor of quantitative methods. He was aware of growing research refuting the value of these methods (as we will see in following chapters) and he also became aware that these methods were not informed by more foundational concepts in risk. The standards, textbooks, and other sources published in that field rarely if ever cited the earlier work of actuarial science, probability theory, or decision theory. But the risk matrix had taken hold and is now the most familiar version of risk assessment by far.

For better or worse, management consultants are, hands down, the most effective sales reps among the four horsemen. Making money also means being able to produce consulting on a large scale and keeping expenses low with a large number of consultants and less experienced staff. As a result, a set of strategies has naturally evolved for most successful management consultants in the area of risk management or any other area. (See the following How to Sell Analysis Placebos box.)

HOW TO SELL ANALYSIS PLACEBOS (THAT IS, SNAKE OIL)

Sell the FUD: Fear, uncertainty, and doubt (FUD) help sell just about anything, but especially risk management services. All sales representatives repeat the mantra that buying is ultimately emotional and nothing evokes emotion like FUD. A key technique is being able to discuss the details of the most disastrous events in history. The audience will think they learned something even though they didn't.

Sell structured approaches: Selling a consulting gig that takes a week or two sometimes takes as much effort as one that goes on for a year or more, so if you are going to sell consulting, sell something that takes a lot of time but still justifies a high rate. One way to do that is to say that you follow a structured approach that has a lot of detailed deliverables. These have their own perceived value regardless of whether the method is proven in any scientific way. Most management consulting is in danger of being perceived by prospective customers as insubstantial, and they don't know exactly what they are going to get. Having a structured approach tells clients that they will at least get some defined deliverables and it conveys the sense that it's been done before. The structured approach is, in practice, as authoritative as the experience of individual experts on the team. It is also a differentiator, especially for major consulting firms, because usually only they have the resources to develop such detailed, documented methods.

Sell intuitive approaches—don't worry whether they work: To sell it, management has to understand it. Consultants, similar to everyone else, build self-reinforcing belief systems to defend against attack and reward acceptance of dogma. Dismiss more sophisticated methods as too complex, theoretical, and impractical. Clients will not be able to differentiate a placebo effect from real value in most risk management methods. The following tricks seem to work to produce the sense of value:

Convert everything to a number, no matter how arbitrary. Numbers sound better to management. If you call it a score, it will sound more like golf, and it will be more fun for them.

As long as you have at least one testimonial from one person, you are free to use the word proven as much as you like.

Use lots of “facilitated workshops” to “build consensus.”

Build a giant matrix to map your procedure to other processes and standards. It doesn't really matter what the map is for. The effort will be noticed.

Optional. Develop a software application for it. If you can carry on some calculation behind the scenes that they don't quite understand, it will seem much more like magic and, therefore, more legitimate.

Optional. If you go the software route, generate a spider diagram or bubble chart. It will seem more like serious analysis.

These selling strategies work well regardless of whether the product was developed in complete isolation from more sophisticated risk management methods known to actuaries, engineers, and financial analysts.

The influence of these popular methods cannot be overstated. They are used for major decisions of all sorts and have worked their way into the “best practices” promoted by respected standards organizations. These methods were quickly being adopted by organizations all over the world who wanted to be able to say they were at least following convention. Here are some examples of standards that have much more in common with these consulting methods I have described than any of the previous quantitative methods:

Control Objectives for Information and Related Technology (CobIT). This standard was developed by the Information Systems Audit and Control Association (ISACA) and the IT Governance Institute (ITGI). This includes a scoring method for IT risks.

The Project Management Body of Knowledge (PMBoK). This standard was developed by the Project Management Institute (PMI). Similar to CobIT, it includes a scoring method for evaluating project risk.

The 800-30 Risk Management Guide for Information Technology Systems. This was developed by the National Institute of Standards & Technology (NIST). It advocated another scoring method based on a high, medium, low evaluation of likelihood and impact.

Not only are these not best practices in risk management (because they leave out all of the improvements developed in earlier quantitative methods) but also one might have a hard time believing that some of these organizations even represent the best practices in their own field. For example, PMI's own Organizational Project Management Maturity Model (OPM3) manual says the manual was three years overdue in the making. Presumably, PMI is the premier project management authority for how to get things done on time.

Other standards organizations do not recommend specific methods but explicitly condone softer scoring methods as an adequate solution. The ISO 31000 standard stipulates only that “analysis can be qualitative, semi-quantitative or quantitative, or a combination of these, depending on the circumstances.”¹² It does add, “When possible and appropriate, one should undertake more specific and quantitative analysis of the risks as a following step,” but does not indicate what constitutes “quantitative.” This gives the adopter of this standard plenty of room for interpretation. Because the scoring methods are easier to implement, this virtually ensures that such methods will be the predominant approach taken to comply with the standard.

And don't forget that some of this is making its way into legislation, as first mentioned in chapter 2. Dodd-Frank explicitly requires that the Federal Deposit Insurance Corporation use a risk matrix. The regulation doesn't specifically require it for individual banks, but it probably has some influence on banks who want to show regulators they are making a reasonable effort to manage risks.

The reader probably has determined quite a few pages ago that much of this book is an argument for why probabilistic methods are, in fact, entirely practical and justified for most major decisions once a few improvements are made. At the same time, I'll be arguing for the discontinuation of popular but ineffectual scoring methods regardless of how practical they seem to be.

COMPARING THE HORSEMEN

The four horsemen represent four different, although sometimes related, lineages of risk management methods. They all have different challenges, although some have more than others. Exhibit 5.2 sums up the issues.

Even though there are impressive individuals in other areas, actuarial practice is the only area wherein there are some formal, professional standards and ethics. Actuaries tend to eventually adopt the best quantitative methods from other fields but, as AIG unfortunately proved, the biggest risks are often outside of the actuaries' legal and professional responsibilities.

EXHIBIT 5.2 Summary of the Four Horsemen

The Horsemen | Used by/for | Short Description | Challenges
Actuaries | Historically, insurance and pensions (but branching out into other areas) | Highly regulated and structured certification process; build on established methods, conservative | Early adopters of mathematics to risk but since then tend to be conservatively slow adopters; authority not wide as it could be
War quants | Engineers, a small minority of business analysts, and some financial analysts | Tend to see the risk analysis problem like an engineering problem; detailed systems of components and their interactions are modeled | Where subjective inputs are required, known systemic errors are not adjusted for; empirical analysis is rarely incorporated into modeling
Economists | Financial analysts, some application to nonfinancial investments (projects, equipment investments, etc.) | Focus on statistical analysis of historical data instead of detailed structural models (although there are exceptions) | Still make assumptions known to be false regarding the frequency of extreme market changes; tend to avoid structural models or see them as impossible
Management consultants | Consultants from big and small firms, auditors of many types, almost everyone else not listed in previous categories | Mostly experience based; may have detailed documented procedures for analysis; use scoring schemes. | Methods not validated; errors introduced by subjective inputs and further magnified by the scoring method

The nuclear engineers and others who use PRA and other methods inherited from wartime quantitative analysts also, like actuaries, tend to use mathematically sound methods. However, they are not immune to some errors, and their powerful methods are still considered esoteric and too difficult to use. Methods and tools exist that would overcome this objection, but most risk analysts are not aware of them.

Whereas some financial analysts are extraordinarily gifted mathematicians and scientists themselves, many of the basic assumptions of their financial models seem to go unquestioned. The kinds of common mode failures and cascade effects that caused the 2008/2009 financial crisis perhaps could have been caught by the more detailed modeling approach of a PRA, if anyone had built it (or if they did, they apparently didn't influence management). Instead, the financial models use simple statistical descriptions of markets that ignore these sorts of system failures.

Finally, the management consultants have the softest sell, the easiest sell, and the most successful sell of all the major risk management schools of thought. Unfortunately, they are also the most removed from the science of risk management and may have done far more harm than good.

I should remind the reader at this point of my modification to Hanlon's razor at the beginning of this chapter. We should consider all parties blameless for any shortcomings of the methods that have evolved around them so far, for reasons they had little control over. Most management consultants and auditors, similar to everyone else, are using the methods held up as best practices in their fields. These methods evolved before most consultants started using them. What they use now is a result of nothing more than historical accidents. The question is what they should do now, especially given the critiques of methods later in this book.

MAJOR RISK MANAGEMENT PROBLEMS TO BE ADDRESSED

The remainder of this book is an attempt to analyze the problems faced by one or more of these schools of thought and propose methods to fix them. Six of these challenges are summarized in the next box. The first five points are addressed in the remainder of part 2 of this book (“Why It's Broken”) and map one-to-one to the five following chapters. The last point will be addressed in multiple locations.

SIX CHALLENGES FOR RISK MANAGEMENT

Confusion regarding the concept of risk: Among different specialties in risk management, analysts and managers are using the word risk to mean some very different things. Because part of the solution is better collaboration, we need to get on the same sheet of music.

Completely avoidable human errors in subjective judgments of risk: Most of the methods of risk assessment must rely on at least some subjective inputs by human experts but, without certain precautions, human experts make surprisingly consistent types of errors in judgment about uncertainty and risk. Although research shows that there are methods that can correct for certain systemic errors that people make, very few do so, and the net result is an almost universal understatement of risk.

Pointing out the problems with popular methods: The numerous arbitrary rules and values created in scoring methods not only fail to consider the problems with subjective risks (see previous point) but also they introduce errors of their own and may actually make decisions worse. There is no large, important decision that would not be better served with some other analysis approach.

Misconceptions that block the use of better methods: Even some experienced risk analysts defend the use of ineffectual methods by arguing that better, more sophisticated methods will not work. But each of these arguments is based on fundamental fallacies about the nature of quantitative risk analysis.

Recurring errors in even the most sophisticated models: Most users of the more quantitative approaches do not attempt to measure the reliability of their models by checking against historical data. Quality control is mostly nonexistent in users of popular quantitative modeling tools, and the use of real-world observations is too rare. These are all avoidable problems and should not be considered obstacles to the use of better risk analysis. Some analysts assume that their models take on a level of authority and truth that is never justified. Half-understood models are misapplied in a variety of situations.

Various institutional factors: There are several other factors that affect not only the assessment of risk (which is much of our focus) but also how risks are subsequently managed. For example, the unnecessary isolation of risk analysts from each other—both within the same organization and among organizations—means that important shared risks and relationships will be ignored in overspecialized models. Also, inefficient incentives affect both risk assessment and risk management. Minimizing risk is not a factor in most executive bonus calculations. Human experts are not incentivized to give reliable forecasts and there is little incentive to verify old forecasts against observations. As the surveys in chapter 2 described, a key motivator is compliance and use of so-called best practices. If a ship is sinking, at least the captain can point out that he or she followed established procedures. This is not an irrational motivation from the point of view of the captain (we all seek to reduce the risk of blame), but it may be inadequate in the eyes of the passengers.

NOTES

 1. Attributed to a Robert Hanlon by Arthur Bloch in Murphy's Law Book Two: More Reasons Why Things Go Wrong (Little Rock, AR: Leisure Arts, 1981), but a similar quote was also used by Robert Heinlein in his short story “Logic of Empire,” The Green Hills of Earth (New Rochelle NY: Baen Books, 1951).

 2. H. Bühlmann, “The Actuary: The Role and Limitations of the Profession since the Mid-19th Century,” ASTIN Bulletin 27, no. 2 (November 1997): 165–71.

 3. Ibid.

 4. D. Christopherson and E. C. Baughan, “Reminiscences of Operational Research in World War II by Some of Its Practitioners: II,” Journal of the Operational Research Society 43, no. 6 (June 1992): 569–77.

 5. R. Ruggles and H. Brodie, “An Empirical Approach to Economics Intelligence in World War II,” Journal of the American Statistical Association 42, no. 237 (March 1947): 72–91.

 6. R. A. Knief, Nuclear Engineering: Theory and Technology of Commercial Nuclear Power (Washington, DC: Taylor & Francis, 1992), 391.

 7. R. Howard, “Decision Analysis: Applied Decision Theory,” Proceedings of the Fourth International Conference of Operations Research (Boston: Author, 1966).

 8. F. Knight, Risk, Uncertainty and Profit (Boston: Houghton Mifflin, 1921).

 9. J. M. Keynes, A Treatise on Probability (New York: MacMillan and Co., 1921).

10. H. M. Markowitz, “Portfolio Selection,” Journal of Finance 7, no. 1 (March 1952): 77–91.

11. MIL STD 1629, Procedures for Performing Failure Modes, Effects and Criticality Analysis, (Washington, DC: Department of Defense, 1974).

12. ISO/DIS 31000—Risk Management: Principles and Guidelines on Implementation (Geneva, Switzerland: ISO, 2008/2009).

CHAPTER 6
An Ivory Tower of Babel: Fixing the Confusion about Risk

If you wish to converse with me, define your terms.

—VOLTAIRE

Concepts about risk and even the word risk are sources of considerable confusion even among those who specialize in the topic. There are a lot of well-entrenched and mutually exclusive ideas about risk and risk management, and if we are going to make any progress, we have to work out these differences.

You might think that agreement on what the word risk means should be relatively simple and, for that matter, should have been resolved long ago. If only that were the case. Multiple definitions have evolved in different professions. Some will not even know they are using it differently from others and may incorrectly believe they are clearly communicating with other risk professionals.

We need our vocabulary and concepts on firm footing before we can begin any heavy lifting with risk management. First, let's clear up some confusion about how the word risk is used in different fields. I offered a clear definition of risk in chapter 2, but it is worth restating here. While we're here, let's also clarify the related concept of uncertainty and distinguish between the qualitative and quantitative use of these terms. (Note that this is the same distinction I make in my earlier book, How to Measure Anything: Finding the Value of Intangibles in Business.)

UNCERTAINTY VERSUS RISK AND THE MEASUREMENTS OF EACH

Uncertainty: The lack of complete certainty—that is, the existence of more than one possibility. The “true” outcome, state, result, value is not known.

Measurement of uncertainty: A set of probabilities assigned to a set of possibilities. For example, “There is a 60 percent chance it will rain tomorrow and a 40 percent chance it won't.”

Risk: A state of uncertainty where some of the possibilities involve a loss, injury, catastrophe, or other undesirable outcomes (i.e., something bad could happen).

Measurement of risk: A set of possibilities each with quantified probabilities and quantified losses. For example, “We believe there is a 40 percent chance the proposed oil well will be dry with a loss of $12 million in exploratory drilling costs.”

This specific distinction of the terms not only represents the de facto use of the terms in the insurance industry and certain other types of professions and areas of research but also is closest to how the general public uses the term. And although risk professionals need to be a bit more precise in the use of these terms than the general public, these definitions are otherwise entirely consistent with the definitions offered in all of the major English dictionaries.

But a risk manager needs to know that this specific language is not universally adopted—not even by all risk professionals and academics. Some circles will use a language all their own, and many of them will insist that their definition is the “formal” or the “accepted” definition among experts—unaware that other experts believe the same of other definitions. The lack of a common vocabulary can actually be the root of many disagreements and misconceptions about how to manage risk. So let's review how the definitions of risk and related terms differ and how this confusion can be resolved.

THE FRANK KNIGHT DEFINITION

Frank Knight was an influential economist of the early twentieth century who wrote a text titled Risk, Uncertainty and Profit (1921). The book, which expanded on his 1917 doctoral dissertation, has become what many economists consider a classic. In it, Knight makes a distinction between uncertainty and risk that still influences a large circle of academics and professionals today:

[To differentiate] the measurable uncertainty and an unmeasurable one we may use the term “risk” to designate the former and the term “uncertainty” for the latter.¹

According to Knight, we have uncertainty when we are unable to quantify the probabilities of various outcomes, whereas risk applies to situations where the odds of various possible outcomes can be known. But Knight's definition was and is a significant deviation from both popular use and the practical use of these terms in insurance, statistics, engineering, public health, and virtually every other field that deals with risk.

First, Knight makes no mention of the possibility of loss as being part of the meaning of risk. He states that all we need to specify risk is to quantify probabilities for outcomes—contrary to almost every other use of the term in any field. Whether any of those outcomes are undesirable in some way is irrelevant to Knight's definition. In fact, the same year Knight published his book, the influential economist John Maynard Keynes published A Treatise on Probability, in which he defined risk differently. Within the context of making an investment, Keynes defined risk in terms of the probability of a “sacrifice” that may not be rewarded.² Keynes's definition of risk was not only mathematically well-defined but also consistent with the popular understanding of the word.

Second, Knight's definition of uncertainty seems to be routinely contradicted by other researchers and professionals who speak of “quantifying uncertainty” by applying probabilities to various outcomes. In effect, Knight's definition of risk is what most others would call uncertainty.

Knight starts the preface of his book by stating, “There is little that is fundamentally new in this book.” But his definitions of uncertainty and risk were quite new—in fact, perhaps previously unheard of. Even Knight must have felt that he was breaking new ground because he apparently believed there were no adequate definitions to date that distinguished risk from uncertainty. He wrote in the same text, “Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated.”³

In reality, there was already an extremely consistent, and sometimes mathematically unambiguous, use of these terms in many fields. Even within economics, it was generally understood that uncertainty can be represented quantitatively by probabilities and, similar to Keynes's definition, that risk must include loss. Consider the following quotes from economics journals, one published just after Knight's text and one well before it:

Probability, then, is concerned with professedly uncertain [emphasis added] judgments. Economica, 1922⁴

The word risk has acquired no technical meaning in economics, but signifies here as elsewhere [emphasis added] chance of damage or loss. Quarterly Journal of Economics, 1895⁵

The first quote speaks of probabilities—a term that is widely understood in economics, math, and statistics to be a quantity—as something that applies to uncertainty in judgments. The second quote acknowledges that risk as a chance of loss is generally understood.

The definitions I previously presented for risk and uncertainty were also used consistently in mathematics, especially in regard to games of chance, long before Knight wrote his book. Prior to 1900, many famous mathematicians such as Bayes, Poisson, and Bernoulli discussed uncertainty as being expressed by quantified probabilities. This directly contradicts Knight's use of the word uncertainty as something immeasurable. And there was so much of this work that I could have written an entire book just about the measurement of uncertainty before 1900. Fortunately, I didn't need to, because one was already written: The History of Statistics: The Measurement of Uncertainty before 1900.⁶

One interesting definition of uncertainty that I came across was in the field of the psychology of gambling (where, again, uncertainties are quantified) in the early 1900s. Clemens J. France defined uncertainty as “a state of suspense” in his article, “The Gambling Impulse,” in the American Journal of Psychology in 1902. In 1903, this use of the concept of uncertainty within gambling was common enough that it shows up in the International Journal of Ethics: “Some degree of uncertainty, therefore, and willingness to take the risk are essential for a bet.”⁷

Even shortly after Knight proposed his definitions, other fields carried on quantifying uncertainty and treating risk as the chance of a loss or injury. In 1925, for example, the physicist Werner Heisenberg developed his famous uncertainty principle, which quantified minimum uncertainty of the position and velocity of a particle. The mathematicians who dealt with decisions under uncertainty continued to define uncertainty and risk as we have. And the entire insurance industry carried on doing business as usual apparently without any regard for Knight's proposed alternative definition.

A simple test will demonstrate that Knight's use of the term uncertainty is not the way common sense would tell us to use it. Ask people around you the following three questions:

“If I were to flip a coin, would you be uncertain of the outcome before I flipped it?”

“What is the chance that the outcome will be tails?”

“Assume you are not betting anything on the flip or depending on the flip in any other way. Do you have risk in the coin flip?”

Almost anyone you asked would answer “yes, 50 percent, and no.” Knight's definitions would have to answer “no, 50 percent, and yes” if he were serious about his definitions. Because our answer to question 2 indicates the odds are quantifiable, Knight would have to say a coin flip is not uncertain (he says uncertainty is immeasurable), even though almost anyone would say it is. Also, because the coin flip meets his only criterion for risk (that the odds are quantifiable) then he has to answer yes to question 3, even though the lack of having any stake in the outcome would cause most of the rest of us to say there is no risk.

Although Knight's definitions are quite different from many risk management professionals', his definitions influence the topic even today. I was corresponding with a newly minted PhD who had conducted what she called a prequantitative risk analysis of a major government program. While discussing risk, it became clear that we had a different vocabulary. She was using the term uncertainty as unquantifiable randomness, just as Knight did. She didn't mention Knight specifically but pointed out that, even though it was not the common use, this is how the term is “defined in the literature.” For evidence of this, she cited a definition proposed by the editors of a fairly important anthology of decision science, Judgment and Decision Making: An Interdisciplinary Reader, which defined the terms as Knight did.⁸ I happened to have a copy of this book and in less than five minutes found another article in the same text that discusses how uncertainty is “expressed in terms of probabilities,”⁹ which is consistent with nearly every other source I find.

Knight himself recognized that this was not the common use of these terms. But, for some reason, despite the volume of prior work that quantified both risk and uncertainty, he felt they were not defined properly. Unfortunately, Knight's views held a lot of sway with many economists and noneconomists alike, and it still contributes to confusion in the advancement of risk management. Let's just call it what it is—a blunder. This will brand me a heretic with fans of legendary economists (and there is more of that to come), but it was ill-conceived and didn't clarify anything.

KNIGHT'S INFLUENCE IN FINANCE AND PROJECT MANAGEMENT

According to Knight's definition, risk doesn't necessarily involve a loss. In fact, risk could be a probability of a good thing happening, and this is the common use in some fields. Terms such as upside risk can be heard in the professions of finance and project management.

In the world of finance, words which are often equated with risk are volatility and variance. If a stock price tends to change drastically and frequently, it is considered to be volatile and, therefore, it is risky. This is sometimes associated with Harry Markowitz, the economist who won the Nobel Prize in Economics for modern portfolio theory (MPT). As briefly mentioned in chapter 5, MPT attempts to define how a rational investor would select investments in a portfolio in a way that makes the best overall risk and return for the portfolio.

Markowitz never explicitly promotes such a definition. He merely states that, in most financial articles in general, “if … ‘risk’ [were replaced] by ‘variance of return,’ then little change of apparent meaning would result.” He treats volatility, similar to risk, as something that is acceptable if the return is high enough. In practice, though, analysts who use MPT often equate historical volatility of return to risk.

Although it is true that a stock with historically high volatility of returns is probably also a risky stock, we have to be careful about how this is different from the definitions I proposed previously. First—and this may seem so obvious that it's hardly worth mentioning—volatility of a stock is risky for you only if you own a position on that stock. I usually have a lot of uncertainty about the outcome of the Super Bowl (especially because I don't follow it closely), but unless I were to bet money on it, I have no risk.

Second, even if I have something at stake, volatility doesn't necessarily equate to risk. For example, suppose we played a game where I roll a six-sided die and whatever comes up on the roll I multiply by $100 and pay you that amount. You can, therefore, win anywhere from $100 to $600 on a roll. You only have to pay me $100 to play. Is there uncertainty (i.e., variance or volatility) in the outcome of the roll? Yes; you could net nothing from the game or you could net as much as $500. Do you have risk? No; there is no possible result that ends up as a loss for you.

Of course, games such as that don't usually exist in the market, and that's why it is understandable how volatility might be used as a sort of synonym for risk. In an actively traded market, the price of such a game would be “bid up” until there was at least some chance of a loss. Imagine if I took the same game and, instead of offering it only to you, I offered it to whomever in your office would give me the highest bid for it. It is very likely that someone out of a group of several people would be willing to pay more than $100 for one roll of the die, in which case that person would be accepting a chance of a loss. The market would make any investment with a highly uncertain outcome cost enough that there is a chance of a loss—and therefore a risk for anyone who invests in it.

But what works in the financial markets is not always relevant to managers dealing with investments in the operation of a firm. If you have the opportunity to invest in, say, better insulated windows for your office building, you may easily save substantially more than the investment. Even though energy costs are uncertain, you might determine that, in order for the new windows not to be cost effective, energy costs would have to be a small fraction of what they are now. The difference between this and a stock is that there is no wider market that can compete with you for this investment. You have an exclusive opportunity to make this investment and other investors cannot just bid up the price (although, eventually, the price of the windows may go up with demand).

It is also possible for operational investments with very little variance to be risky when the expected return is so small that even a slight variance would make it undesirable. You would probably reject such an investment, but in the market, the investment would be priced down until it was attractive to someone.

Risk as potentially a good thing as well as a bad thing is also used in the field of project management. Consider the following definition of project risk provided in The Guide to the “Project Management Body of Knowledge” (PMBoK), 2018 edition, published by the Project Management Institute (PMI): “an uncertain event or condition that, if it occurs, has a positive or negative [emphasis added] effect on a project objective.”

Partly due to the influence of PMI, this definition is acknowledged by a large number of people in project management. The PMI was founded in 1969 and by 2018 it had more than five hundred thousand members worldwide. In addition to publishing the PMBoK, it certifies individuals as project management professionals (PMPs). Although PMI attempts to cover projects of all sorts in all fields, there is a large presence of information technology (IT) project managers in its membership.

There are also UK-based organizations that define risk in this way. The Project Risk Analysis & Management Guide (PRAM Guide, 2010) of the UK Association for Project Management (APM) defines risk as “an uncertain event or set of circumstances which, should it occur, will have an effect on achievement of objectives,” and further notes that “consequences can range from positive to negative.” And the British Standards BS6079–1: 2010 Principles and Guidelines for the Management of Projects and BS6079–2: Project Management Vocabulary define risk as a “combination of the probability or frequency of occurrence of a defined threat or opportunity [emphasis added] and the magnitude of the consequences of the occurrence.”

I was discussing this definition of risk with a PMI-certified PMP, and I pointed out that including positive outcomes as part of risk is a significant departure from how the term is used in the decision sciences, insurance, probabilistic risk analysis in engineering, and most other professions that have been dealing with risks for decades. He asked why we wouldn't want to include all possible outcomes as part of risk and not just negative outcomes. I said, “Because there is already a word for that—uncertainty.”

I had another project manager tell me that risk can be a good thing because “sometimes you have to take risk to gain something.” It is true that you often have to accept a risk in order to gain some reward. But, if you could gain the same reward for less risk, you would. This is like saying that expenses—by themselves—are a good thing because you need them for business operations. But, again, if you could maintain or improve operations while reducing spending, you would certainly try. The fact that rewards often require other sacrifices is not the same thing as saying that those sacrifices are themselves desirable. That's why they are called sacrifices—you are willing to endure them to get something else that you want. If it were a good thing, you would want more of it even if all other things were held constant. You accept more costs or more risks, however, only if you think you are getting more of something else.

The fact is that every English dictionary definition you can find—including Merriam-Webster, American Heritage, Oxford English, or even Dictionary.com—defines risk in terms of peril, danger, chance of loss, injury, or harm. Not one mentions risk as including the possibility of a positive outcome alone. Risk as opportunity, in and of itself (as opposed to something one is willing to accept in exchange for opportunity), also contradicts the most established use of the word in the practical world of insurance as well as the theoretical world of decision theory. As we will see, risk aversion as used in decision theory is always in the context of aversion to a probability of a loss, not aversion to a probability of a gain.

Because PMBoK and the other project management standards don't appear to ever cite Knight's work, it isn't clear that PMI was influenced by it. At least we know it wasn't informed by decision science, actuarial science, or probabilistic risk analysis in general. And being confused about the meaning of the word risk isn't the only problem with PMI's approach to risk management. I will be discussing PMI again when I talk about problems with their risk assessment approach.

In summary, potentially varied outcomes imply risk only if some of the outcomes involve losses. Our definition of risk applies equally well regardless of whether the investment is traded on the market or is an operational investment exclusive to the management of a business.

A CONSTRUCTION ENGINEERING DEFINITION

I came across another use of the term risk when I was consulting on risk analysis in the construction engineering industry. It was common for engineers to put ranges on the costs of an engineering project and they would refer to this as the variance model. The price of steel might vary during the course of construction, so they would have to put a range on this value. This was likewise done for the hourly rates of various labor categories or the amount of effort required for each category. The uncertainty about these items would be captured as ranges such as “The hourly cost of this labor next year will be $40 to $60 per hour” or “This structure will take seventy-five to ninety-five days to finish.”

Fair enough; but they didn't consider this a risk of the project. The separate risk model was a list of specific events that may or may not happen, such as “There is a 10 percent chance of an onsite accident that would cause a work stoppage” or “There is a 20 percent chance of a strike among the electricians.” This use of the word risk makes an arbitrary distinction about risk based on whether the source of the uncertainty is a continuous value or a discrete event.

In the definition I propose for risk, the price of steel and labor, which could be much higher than they expected, would be a legitimate source of risk. A construction project has some expected benefit and it is quite possible for increasing costs and delayed schedules to wipe out that benefit and even cause a net loss for the project. Some uncertain outcomes result in a loss and that is all we need to call it a risk. Risk should have nothing to do with whether the uncertainty is a discrete event or a range of values.

RISK AS EXPECTED LOSS

I sometimes come across risk defined as “the chance of an unfortunate event times the cost if such an event occurred.” I've encountered this use of the term in nuclear power, many government agencies, and sometimes IT projects. The product of the probability of some event and the loss of the event are called the expected loss of the event.

Any reader new to the decision sciences should note that when risk analysts or decision scientists use the word expected they mean “probability-weighted average.” An expected loss is the chance of each possible loss times the size of the loss totaled for all losses (this value can be very different from the loss that is the most likely).

This definition was going down the right path before it took an unnecessary turn. It acknowledges the need for measurable uncertainty and loss. But this definition requires an unnecessary assumption about the decision-maker. This definition assumes the decision-maker is “risk neutral” instead of being “risk averse,” as most people are. A risk-neutral person, the value of an uncertain outcome is equal to its expected value, that is, the probability-weighted average of all the outcomes. For example, consider which of the following you would prefer:

A coin flip that pays you $20,000 on heads and costs you $10,000 on tails.

A certain payment to you of $5,000.

To a risk-neutral person, these are identical, because they both have the same expected value: images. However, because most people are not risk neutral, it's too presumptuous to just compute the expected loss and equate that to their risk preference.

How much the manager values a given risk (that is, how much she is willing to pay to avoid it) depends on her risk aversion, and this cannot be determined from simply knowing the odds and the losses involved. Some people might consider the two presented options equivalent if the certain payment were $2,000. Some might even be willing to pay not to have to flip the coin to avoid the chance of a $10,000 loss. But we will get to quantifying risk aversion later.

We can, instead, just leave the risk in its separate components until we apply it to a given risk-averse decision-maker. This treats risk as a sort of vector quantity. Vector quantities are quantities that can be described in only two or more dimensions, and they are common in physics. Quantities that are a single dimension, such as mass or charge, are expressed with one number, such as “mass of 11.3 kilograms” or “charge of .005 coulombs.” But vector quantities, such as velocity or angular momentum, require both a magnitude and a direction to fully describe them.

As with vector quantities in physics, we don't have to collapse the magnitude of the losses and the chance of loss into one number. We can even have a large number of possible outcomes, each with its own probability and loss. If there are many negative outcomes, and they each have a probability and a magnitude of loss, then that entire table of data is the risk (see Exhibit 6.1). Of course, losses and their probabilities often have a continuum of values. If a fire occurs at a major facility, there is a range of possible loss and each point on that range has an associated probability.

Any of the definitions you might find for risk that state that risk is “the probability, chance, and magnitude, amount, severity of a danger, harm, loss, injury” implicitly treat risk as a vector. The quantification of risk is both the probability and the consequence and doesn't require that they be multiplied together.

EXHIBIT 6.1 Example of the Risk of a Project Failure Expressed as a Vector Quantity

Event | Probability | Loss
Total project failure—loss of capital investment | 4% | $5–12 million
Partial failure—incomplete adoption | 7% | $1–4 million 

In order to determine whether one set of probabilities and losses is more undesirable than another, we will still need to compare them on a single quantity. We just don't need to assume risk neutrality. Instead, we need to know how to quantify aversion to risk. In other words, we need to measure our tolerance for risk.

DEFINING RISK TOLERANCE

How much risk are you willing to take? As we just discussed, most firms are risk averse to some degree instead of risk neutral. But exactly how risk averse? This is a very specific question that should get an equally specific answer. There is a mathematically unambiguous way to state this, but, unfortunately, it is often described in terms so ambiguous it becomes virtually useless in real decision-making.

A statement about how much risk an individual or organization is willing to endure may be called a risk tolerance or sometimes risk appetite. Many managers will use these interchangeably and they are often communicated using agreed-on policy statements such as the following:

The company will only tolerate low-to-moderate gross exposure to delivery of operational performance targets including network reliability and capacity and asset condition, disaster recovery and succession planning, breakdown in information systems or information integrity.

I found this example in the white paper of a consulting firm that helps companies come up with these types of policy statements. This is apparently a real risk appetite from one of their clients.

Now, let's consider what this statement is actually telling its target audience. What is “low-to-moderate”? If they have a plan for a $4 million investment that will reduce network outages by half, is it justified? What if that same investment could reduce the chance of “breakdown in information systems” from an annual probability of 6 percent to 2 percent? Statements such as these require so much more interpretation when applied to real-world decisions that they have little practical relevance as a standard policy.

In chapter 4, I described one way to establish—in an unambiguous way—how much risk an organization is willing take. Using the chart for the loss exceedance curve, we described another curve that we want the LEC to be entirely under. We called this the risk tolerance curve. If the LEC is above the risk tolerance curve at any point, then we say we have too much risk. It is a clear-cut rule and leaves no room for interpretation.

Still, there is more we can clarify. We can also quantify how much risk is acceptable depending on a potential reward. The risk tolerance curve on an LEC chart is really just a way of stating the maximum bearable risk, independent of potential reward. That in itself is much more useful than the wordy and ambiguous “risk appetite” example from the white paper, but if we also quantify the trade-off of risk and return, then the risk tolerance can be even more useful.

For example, would your firm pay $220,000 to avoid a 2 percent chance of losing $10 million? You wouldn't if you were risk neutral, because a risk neutral person would consider that risk to be exactly equal to losing $200,000 for certain and would not pay more than that to avoid the risk. But your firm would pay that if it was more like the typical insurance customer.

A way to answer a question like that is to determine a certain monetary equivalent (CME). A CME is an exact and certain amount that someone would consider equivalent to a bet with multiple uncertain outcomes. If we raise the payment until you were just barely indifferent between paying to avoid the risk or not, then the amount you would pay is the CME for that risk, but expressed as a negative value. For example, if you would pay $250,000 to avoid that risk, then the risk has a CME of −$250,000.

The CME can also apply to uncertain rewards. For example, consider a choice between a 20 percent chance of winning $10 million and a certain payment of $1 million. Which would your organization prefer? If you really were risk neutral, then you would value the uncertain reward at exactly $2 million and you would prefer the uncertain gain over a certain payoff of $1 million. But some firms (and most individuals, I think) would prefer the certain amount. Now, if the $1 million cash in hand is preferred, perhaps an even lower certain amount would still be acceptable to the uncertain amount. Again, whatever the point of indifference for a given person or organization would be is the CME for that uncertain reward, but now it would be expressed as a positive amount (because it is a gain, not a loss). If your CME is, say $300,000 in this case, then you are indifferent between being paid $300,000 or taking your chances with a 20 percent chance of winning $1 million.

We could always do this for any combination of uncertain losses and gains, but we don't want to do this on a case-by-case basis. For reasons we will see in the next chapter, our risk tolerance is something that changes frequently and unconsciously. If you had to make such judgments for every bet, you would inevitably act more risk averse on some than others. Fortunately, we can infer what your risk tolerance is by looking at just a few choices. Then the CME can be calculated for any other situations without having to make more subjective judgments.

One way to do this calculation comes from decision analysis (DA), which was first discussed in chapter 5. DA is based on the work of Ron Howard at Stanford and it was inspired by the earlier work of other researchers, such as Oscar Morgenstern and John von Neumann. As previously described, this is a large body of theoretical and applied work that deals with making decisions under a state of uncertainty. A central component is establishing a quantitative tolerance for risk.

The basic idea Morgenstern and von Neumann developed is that we don't think about risk and reward just in terms of probability weighted dollar amounts, but rather probability weighted utility. The reason most of us (other than the risk neutral individuals) don't consider a 20 percent chance of winning $10 million equivalent to $2 million is because utility is nonlinear. In other words, the value you perceive from $10 million (i.e., its utility) is not five times as much as the value you perceive of $2 million. From the point of view of most individuals (not a large firm), $2 million may have a much bigger impact on his or her life than the next $2 million. Another $2 million after that would have even less utility, and so on.

If we can describe a person's (or organization's) utility function then we have a way to work out the CME for any set of uncertain outcomes. Morgenstern and von Neumann showed a rigorous proof for how to do this under certain assumptions for a rational person. Because the person was rational, he or she would have to follow certain commonsense rules about preferences (for example, if you prefer A to B and B to C, then you can't prefer C to A). They found several fascinating, nonintuitive results.

One utility function that meets the basic mathematical requirements is shown below. Now, I will tell you in advance that there are some problems with this approach when modeling the risk tolerance of real decision-makers. But the solutions are still based on modifications of this method. So bear with me while I explain the exponential utility function and how to use it to compute CME. I've written the following function in the form of an Excel spreadsheet. (An example of this can be downloaded at www.howtomeasureanything.com/riskmanagement.)

X is a given reward (so −X would be negative if the reward is positive and −X would be positive it X were a loss). S represents a scale which is unique to a given decision-maker or organization, and it is another way to define risk tolerance. Exhibit 6.2 shows an example of the exponential utility function where S is set equal to $5 million.

It is important to note that the exponential utility function produces a maximum utility of 1 no matter how much the reward is. If S is small the decision-maker reaches “maximum utility” with a smaller reward than if S were larger. A loss, however, has a limitless negative utility. In other words, pleasure maxes out; pain does not.

If we want to work out the CME for a given uncertain utility we can use the following formula. (Again, we are writing this as you would write it in Excel and this example is included in the spreadsheet on the website.)

Here, Pr is the probability of a reward and S and Utility refer to the same quantities mentioned in the previous formula. To apply this to our example of a 20 percent chance of winning $10 million, a firm with an S of $5 million would compute its utility for the gain using the previous utility formula, which gives us a utility of 0.8647. Using the utility of the gain and the probability of the gain in the CME formula we get

EXHIBIT 6.2 The Exponential Utility Function Where S = $5 Million

In other words, the firm would be indifferent between a certain cash payment of $949,348 and a 20 percent chance of winning $10 million. If you, individually, would be indifferent with a much lower certain payoff, that only means your S is much lower. For example, if your CME was $50,000 (the point where you would be indifferent between that certain amount and the uncertain reward) then that just means your S is much lower—just $224,091.

If we used the $5 million value for S for the 2 percent chance of losing $10 million, the CME would be −$601,260. If the company could pay $500,000 for insurance to avoid that risk entirely, it would pay it.

Ron Howard proposed a kind of game to measure S. Imagine we play a game in which the outcome is based on a single coin flip. You could win some amount of money x or lose half of x based on that flip. For example, you could win $200 if the coin flip lands on heads or lose $100 if it lands on tails. Would you take that bet? It is a good bet if you assume you are going to play it a very large number of times. You would definitely come out ahead in the long run. But suppose you could only play it once. If so, how large would you be willing to make x so that the game is still just barely acceptable to you? We can use that as a measure of risk tolerance. For example, if I said I am willing to make x equal to $1,000, then I would be willing to win $1,000 or lose $500 on a single coin flip.

Howard shows how the largest number you would be willing to accept for x can actually be used as a measure of S. Just like the expected value approach described previously, we could reduce risk to a single monetary value, except that we don't have to assume that a decision-maker is risk neutral.

Now, you may have noticed that some consequences of these formulas may produce unrealistic results. First, because utility cannot exceed 1, increasing the reward beyond some point adds no value to the decision-maker. For the case where S = $5 million, the CME of a 20 percent chance of winning $50 million is almost the same as that chance of winning $500 million or $5 billion. No matter how big the reward, the CME of a 20 percent chance of winning it never exceeds $1,115,718 for a decision-maker where S = $5 million.

Also, for large losses, the CME is surprisingly large for even tiny probabilities of a loss. The same decision-maker would pay almost $31 million to avoid a one-in-a-million chance of losing $100 million.

One assumption in the proof of the exponential utility function is that utilities are independent of the previous wealth of the individual or firm. In other words, your preferences for these bets would be the same if you were a billionaire or broke. This assumption is likely one reason why research shows that the risk preferences of individuals deviate from the exponential utility function. The psychologist Daniel Kahneman (whom we will discuss more later) won the 2002 Nobel Prize in Economics for showing empirical evidence of this. Kahneman called his alternative approach to quantifying real risk preferences prospect theory.

For example, suppose decision-makers said they would be indifferent among the three options described in exhibit 6.3. Executives may describe their risk tolerance by identifying three such bets as equally preferable. Unfortunately, no version of the earlier exponential function can make all three of these equally preferable. Does that mean that the decision-maker is irrational? Well, it just means that if there is a model that is rational, it's something other than that particular exponential function.

EXHIBIT 6.3 Example of Three Bets Considered Equivalent by a Decision-Maker

Reward Amount | Probability of Winning
$10 million |  20%
$2 million |  50%
$500,000 | 100%

The trick, therefore, for any solution to the CME is satisfying both the fundamental axioms while meeting the preferences of decision-makers. Plainly irrational preferences can simply be pointed out to the executives. At least in my experience, they quickly come around and adjust accordingly. In other cases, the problems may be less obvious. It may be necessary to accept that rules produce rational results only within a given range of preference but, in practice, this is an entirely reasonable constraint. Even if the model produces nonsensical results (i.e., a decision-maker would prefer investment A to B, B to C, and C to A), that would be okay if such irrational outcomes only appear for unrealistic situations (such as investments much larger than their entire portfolio). The spreadsheet example you can download provides some options.

If we can get executives to converge on an internally consistent, rational set of equivalent bets, we will have a way of computing CME for any combination of risks and rewards. Using CME, we can answer every possible uncertain risk and reward choice for a firm or individual. We can say the risk is worse if there is a 1 percent chance of losing $50 million or a 10 chance of losing $10 million. And we can say whether we would approve of an investment that has a range of possible rewards and losses, each with their own probabilities, and we can say whether it is preferable to any other investment. Even if a bet has a range of many possible outcomes, some involve losses and some involve gains, we can work out the CME. If the CME is negative, we would not only reject the bet but also we would pay to avoid it if necessary. If the CME were positive, we would accept the bet even if we had to pay for the opportunity to take it.

DEFINING PROBABILITY

Does everyone really mean the same thing when they use the word probability? Getting on common footing with this term should be a prerequisite to a common understanding of risk. After all, being able to assess what events are more or less probable should be a key component of risk assessment and, therefore, risk management. What might surprise some risk analysts is that the meaning of this term is somewhat controversial even among statisticians. L. J. Savage once observed the following:

It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel.¹⁰

Perhaps some of the differing definitions of risk are related to differences in the use of the term probability. When people say that some probabilities are “immeasurable,” they are actually presuming a particular meaning of probability. To some writers on this topic, probability is a kind of idealized frequency of a thing. To them, probability means the frequency of an event during which three criteria are met: (1) it is a truly random process, (2) which is “strictly repeatable,” and (3) used an infinite number of trials. This is the definition promoted by a group of statisticians who would call themselves frequentists. This group includes some great statisticians such as R. A. Fisher.

But this is not a universally held notion even among other statisticians and mathematicians of equal status to Fisher. L. J. Savage and many others take the view that probability is a statement about the uncertainty of the observer, not the objective state of some system. You may assign a different probability to something than I would because you have more information than I do; therefore, your state of uncertainty would be different than mine.

A coin flip illustrates the difference between the two approaches. Saying that a coin flip has a 50 percent chance of landing on heads is a statement about the objective state of a physical system. Here, the frequentist view and subjectivist view would agree on the probability. But these views diverge if I already flipped the coin, looked at the result, and kept the result from you. If you were a subjectivist, you would still say there is a 50 percent chance the coin landed heads. I would say it was either 100 percent or 0 percent because I know the outcome exactly. If you were a frequentist and did not see the result, you would not say the probability was 50 percent. You would say it must be either heads or tails but the state is unknown.

In engineering risk analysis, sometimes a distinction is made among these types of uncertainties. “Aleatory” uncertainty is similar to the frequentist's use of probability. It refers to an “objective” state of the system independent of our knowledge of it, such as the known variability in a population of parts. Engineers may know that 10 percent of a given part fails after one hundred hours of use because they've observed failure rates for thousands of parts. But if they didn't have that data, they may put a probability of failure on a part based on “epistemic” uncertainty. That is, they lack perfect knowledge about the objective facts. There are cases where this distinction can be ambiguous but, fortunately, we don't really even need to make that distinction.

I take the side that the frequentist view of probability has little to do with real-world decisions. We just treat all uncertainty as epistemic. Perhaps any uncertainty could be reduced with more detailed study and measurements. If I discovered that there was one particular reason for a part failure that had to do with a slightly different alloy being used for a metal component, then some engineers would argue that was really epistemic uncertainty and not aleatory. Perhaps you can never conclusively prove that some uncertainty isn't ultimately epistemic. The only practical difference is that it may be more economical to reduce some uncertainties than others.

The criteria of truly random, strictly repeatable, and infinite trials make the frequentist definition a pure mathematical abstraction that never matches problems we have in the real world. A frequentist such as Fisher would have said there is no way to put a probability on anything that does not involve random, repeatable samplings over infinite trials. So you could not put a probability on a kind of cyberattack that never happened before.

Actuaries, however, have to deal with making decisions even for risks when there could not be even a hundred trials, much less infinite trials. If insurance companies took the frequentist definition literally, they could rarely if ever legitimately use probability theory.

In the early twentieth century, the actuary Bruno di Finetti proposed a pragmatic, “operational” definition of probability. Insurance companies are nearly risk neutral for each of the large numbers of risks they insure. If they believe that you have a 1 percent chance of making a life insurance claim of $1 million next year, then they consider that nearly equivalent to a liability of exactly $10,000 for certain (a little less, actually, if we consider the interest they could make on the premium before having to pay a claim). Because your family is probably more risk averse about the financial consequences of your death, you would be willing to pay a little more than what the insurance company would value the liability. That's what makes insurance possible. Looking at it another way, if the insurer is indifferent between a certain loss of $10,000 and an uncertain loss of $1 million, then the insurer is for operational purposes treating the probability of the uncertain loss as 1 percent.

Decision psychology gives us another reason to consider the subjectivist view of probability. Later, we will describe another area of research conducted by Daniel Kahneman related to “calibrated probability assessments.” The research of Kahneman and many others show that even experts providing subjective estimates (with training and other adjustments) can produce realistic probabilities. Hubbard Decision Research has also gathered data on more than one thousand people who have participated in our calibration training, which confirms this thought. That is, when they say something is 80 percent probable, it actually happens about 80 percent of the time; when they say 60 percent probable, it happens about 60 percent of the time; and so on. Because this data contain well over 140,000 individual estimates, we have a number of trials that should make even the frequentist pay notice. Over a very large number of trials, it can be shown that subjective estimates can closely match the observed frequencies of events—even when the individual estimates were of one-off events.

In the subjectivist sense of the word probability, a probability is never really immeasurable. Properly trained people can state a probability that best represents their uncertainty about an event. Uncertainty about any event, stated as set of outcomes and their probabilities, can vary from person to person. If you have more or less uncertainty than a colleague for some item, you will state a different probability than he or she would. When it comes to quantifying your own uncertainty, you are the world's leading expert. When you gather more information, your uncertainty will change. This is the practical use of probabilities not only by actuaries but also most real-world decision-makers.

Even with the large amount of empirical evidence supporting the realism of subjective estimates (for trained experts, that is), the frequentist view apparently seems more objectively scientific to some. If a person believes that the subjective view of probability seems unscientific or less rigorous in any way than the frequentists' position, that would be a mistake. In fact, the subjectivist view is often associated with the “Bayesian” school of thought based on what is known as Bayes' theorem.  This is a fundamental concept in probability theory which was developed by Thomas Bayes in the 18th century.  In 1995, the physicist Edwin T. Jaynes, who specialized in the undeniably scientific field of quantum mechanics, argues for the Bayesian view of probability even in physics when he said,

We are now in possession of proven theorems and masses of worked out numerical examples. As a result, the superiority of Bayesian methods is now a thoroughly demonstrated fact in a hundred different areas. ¹¹

ENRICHING THE LEXICON

Let's summarize the risk terminology and add a few more items to our lexicon. We just reviewed several definitions of risk. Many of these were mutually exclusive, contradicted commonsense uses of the language, and they defied even the academic literature available at the time. A risk manager in a large organization with professionals in finance, IT, and perhaps engineering could have easily encountered more than one of these definitions just within his or her own firm. If a risk manager does run into these alternative uses of the word, we have to respond as follows:

Risk has to include some probability of a loss—this excludes Knight's definition.

Risk involves only losses (not gains)—this excludes PMI's definition.

Outside of finance, volatility may not necessarily entail risk—this excludes considering volatility alone as synonymous with risk.

Risk is not just the product of probability and loss. Multiplying them together unnecessarily presumes that the decision-maker is risk neutral. Keep risk as a vector quantity in which probability and magnitude of loss are separate until we compare it to the risk aversion of the decision-maker.

Risk can be made of discrete or continuous losses and associated probabilities. We do not need to make the distinctions sometimes made in construction engineering that risk is only discrete events.

At the beginning of this chapter, I provided definitions of both risk and uncertainty that are perfectly compatible with all these points. They are more consistent with the common use of the terms as well as being sufficient for quantitative analysis.

An enriched professional vocabulary doesn't necessitate shoe-horning disparate concepts into a single word (like PMI did with risk). We have different terms for different concepts, and they seem to me to be less about hair-splitting semantics than about clear-cut, night-and-day differences. Here is a summary and some other terms we just introduced along with a couple of other terms that may come in handy:

Uncertainty: This includes all sorts of uncertainties, whether they are about negative or positive outcomes. This also includes discrete values (such as whether there will be a labor strike during the project) or continuous values (such as what the cost of the project could be if the project is between one and six months behind schedule). Uncertainty can be measured (contrary to Knight's use of the term) by the assignment of probabilities to various outcomes. Although upside risk doesn't make sense in our terminology, the speaker can communicate the same idea by saying upside uncertainty.

Strict uncertainty: This is what many modern decision scientists would call Knight's version of uncertainty. Strict uncertainty is when the possible outcomes are identified but we have no probabilities for each. For the reasons we already stated, this should never have to be the case.

Probability: Probability is a quantitative expression of the state of uncertainty of the decision-maker (or the expert the decision-maker is relying on). As such, a probability is always attainable for any situation. The person providing the probability just has to be trained.

Risk tolerance: Risk tolerance is described with a mathematically explicit calculation that can tell you if a risk is acceptable. It could refer to the “maximum bearable” risk, represented by a curve that the loss exceedance curve should be under. It can also be a CME function that converts different uncertain outcomes to a fixed dollar amount. A bet with a negative CME is undesirable (you would be willing to pay, if necessary, to avoid the bet) and a bet with a positive CME is desirable (you would even pay more for the opportunity to make the bet).

Risk/return analysis: This considers the uncertain downside as well as the uncertain upside of the investment. By explicitly acknowledging that this includes positive outcomes, we don't have to muddy the word risk by shoehorning positive outcomes into it. Part of risk/return analysis is also the consideration of the risk aversion of the decision-maker, and we don't have to assume the decision-maker is risk neutral.

Ignorance: This is worse than strict uncertainty because in the state of ignorance, we don't even know the possible outcomes, much less their probabilities. This is what former US Secretary of Defense Donald Rumsfeld and others would have meant by the term unknown unknowns. In effect, most real-world risk models must have some level of ignorance, but this is no showstopper toward better risk management.

One final note about this terminology is that it has to be considered part of a broader field of decision analysis. Just as risk management must be a subset of management in the organization, risk analysis must be a subset of decision analysis. Decisions cannot be based entirely on risk analysis alone but require an analysis of the potential benefits if managers decide to accept a risk.

NOTES

 1. F. Knight, Risk, Uncertainty and Profit (New York: Houghton-Mifflin, 1921), 19–20.

 2. Keynes described risk as the product of E and q were “E measures the net immediate sacrifice which should be made in the hope of obtaining A; q is the probability that this sacrifice will be made in vain; so that qE is the ‘risk.’” Keynes, A Treastise on Probability (London: MacMillan, 1921), 360.

 3. Knight, Risk, Uncertainty and Profit.

 4. A. Wolf, “Studies in Probability,” Economica 4 (January 1922): 87–97.

 5. J. Haynes, “Risk as an Economic Factor,” Quarterly Journal of Economics 9, no. 4 (July 1895): 409–49.

 6. Stephen Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge, MA: Harvard University Press, 1986).

 7. W. R. Sorley, “Betting and Gambling,” International Journal of Ethics (July 1903).

 8. T. Connolly, H. R. Arkes, and K. R. Hammond, Judgment and Decision Making: An Interdisciplinary Reader, 2nd ed. (New York: Cambridge University Press, 1999).

 9. Baaruch Fischhoff, “What Forecasts (Seem to) Mean,” Judgment and Decision Making: An Interdisciplinary Reader, 2nd ed. (New York: Cambridge University Press, 2000), 362.

10. Leonard J. Savage, The Foundations of Statistics (New York: John Wiley & Sons, 1954), 2.

11. Edwin T. Jaynes, Probability Theory: The Logic of Science (St. Louis, MO: Washington University, 1995), xii.

CHAPTER 7
The Limits of Expert Knowledge: Why We Don't Know What We Think We Know about Uncertainty

Experience is inevitable. Learning is not.

—PAUL J. H. SCHOEMAKER

We are riding the early waves of a 25-year run of a greatly expanding economy that will do much to solve seemingly intractable problems like poverty and to ease tensions throughout the world.

—WIRED (JULY 1997)

Chapter 3 explained the need for component testing in methods for risk management and risk assessment. One critical component we need to test would be the human experts we must rely on for so much of the input. In fact, the simple method introduced in chapter 4—similar to the risk matrix it replaces—will rely heavily on the human expert input. (Empirical methods to improve on expert input will be introduced later.)

Experts may assess a probability quantitatively, as we would do with the chapter 4 model (e.g., “There is a 10 percent chance this project will fail”). If, however, the expert is using a risk matrix, he or she may express this chance on some sort of scale other than explicit probabilities (e.g., “On a scale of 1 to 5, the likelihood of this project failing is a 2”). A risk matrix method may also do without any numbers altogether—ordinal or otherwise—and provide this estimate in some purely verbal form (e.g., “It is unlikely this project will fail”). And whether the risk assessment is lacking any quantities or using advanced quantitative methods, human beings must use their judgment to identify possible risks before they can be included in any assessment.

Yet, although the use of subjective judgment is unavoidable, chapter 3 also explained why we can't just rely on our subjective judgments about the performance of our subjective judgments. What we need is objective assessments of subjective estimates. We need to “calibrate” our experts.

Technicians, scientists, or engineers, for example, using an instrument to measure weight wouldn't want to use the instrument if they didn't know it was calibrated. If they knew a scale was always overstating weight by 5 percent, they would adjust the readings accordingly. For managers and analysts, too, we should apply a measure of some kind to their past performance at estimating risks. We should know whether these instruments consistently overestimate or underestimate risks. We should know whether they are so inconsistent that they give completely different answers even for the identical scenario presented at different times.

Fortunately, this has been extensively researched. We know something about the limitations of the experience experts rely on. In the case of risk management, I believe experience has certain features we should always keep in mind:

Experience is a nonrandom, nonscientific sample of events throughout our lifetime.

Experience is memory-based, and we are very selective regarding what we choose to remember.

What we conclude from our experience (or at least the part we choose to remember of it) can be full of logical errors.

Unless we get reliable feedback on past decisions, there is no reason to believe our experience will tell us much.

No matter how much experience we accumulate, we seem to be very inconsistent in its application.

As a result, it turns out that everyone, including experts in their fields, are not well calibrated when assessing the probabilities of events—a skill we should expect to be critical to proper assessments of risks. The good news is that, even though research shows some profound systemic errors in the subjective assessment of risks, relatively simple techniques have been developed that make managers better estimators of risks. The bad news is that almost none of these methods is widely adopted by risk managers in organizations.

THE RIGHT STUFF: HOW A GROUP OF PSYCHOLOGISTS MIGHT SAVE RISK ANALYSIS

Chapter 3 briefly discussed why we can't assume that experience necessarily converts to improved performance. We described how psychologists Daniel (Danny) Kahneman and Gary Klein found that when the feedback experts receive from their failures is “delayed, sparse, and ambiguous”¹ then learning does not take hold and performance does not improve. Delayed, sparse, and ambiguous feedback sounds a lot like the real world of estimating risks.

Kahneman's work with another researcher provides the foundation of several other important ideas about the judgments of experts. In the 1970s, Kahneman teamed up with Amos Tversky in one of the most productive collaborations ever in the field of judgment and decision-making (JDM) psychology and beyond. Some of the research in this area would have such an impact in economics that, in 2002, Kahneman would become the first psychologist to win the Nobel Prize in Economics—an honor Tversky would certainly have received as well if he had lived long enough to see how far their influence spread.

Kahneman and Tversky were interested in how the human mind deals with uncertainty, risks, and decisions. Their research touched virtually every major topic in this field, and it is difficult to find a research paper in JDM that does not cite them. At one level, the work of Kahneman and Tversky could be described as a catalog of quirks and flaws in human judgment. At another level, it is powerful insight into what drives human behavior that should have implications for all managers. Kahneman describes his interests as being related to the “quality control of decisions,” and it is clear to him that the research shows what doesn't work and what does.

The human mind, obviously, is not a computer. We don't recall events with 100 percent accuracy as if we were accessing a hard drive. And except for a few savants, once we recall those events, we don't do statistical calculations in our heads to determine what those events really mean. Instead, we resort to a set of heuristics. A heuristic is a sort of mental shortcut that in our simpler, hunter-gatherer days probably sufficed for a variety of situations and still does today. A related concept is bias—a tendency to think and behave in a way that interferes with rationality and impartiality. A heuristic, in some cases, may actually be productive, but a bias is generally thought of as undesirable. These heuristics and biases affect both what we manage to recall and how we interpret what we recall.

Some would call a heuristic a kind of rule of thumb, but there is an important difference. Usually, we think of a rule of thumb as a simple rule we consciously apply, such as “Your mortgage on a new home should not be more than three times your annual income” (a rule that was not followed by a lot of people prior to the mortgage crisis of 2008). But, biases and heuristics that have been discovered regarding how people assess risk are generally not consciously considered. Because people are not aware of these heuristics and biases, they can be inferred only by observing how individuals respond in a variety of situations.

Unlike some areas of science, JDM research is not terribly expensive to produce. It usually involves giving large numbers of individuals a variety of problems to solve and evaluating their answers. Often, researchers ask subjects questions about topics in which a rational answer is known and the subjects' responses can be compared with rational responses. Other times, there may not be a single, rational response, but researchers are interested in what conditions affect the subjects' responses and how they make decisions.

Other influential researchers included Paul Slovic, who, sometimes with Kahneman, did important work on how we perceive risks. Sarah Lichtenstein and Baruch Fischhoff conducted a variety of experiments in how we assess our own uncertainty. Robyn Dawes did important work in how some simple systems outperformed human judgment in a variety of tasks. Richard Thaler was an economist who was central to introducing much of Kahneman's work to other economists. It is my belief that nobody who wants to be a risk analyst or risk manager can claim to know much about that topic without knowing something about the work of these thinkers.

Some of this will be unavoidably redundant with my earlier books, especially How to Measure Anything: Finding the Value of Intangibles in Business. There I spoke of methods that researchers have found for assessing risk using subjective inputs and how often subjective estimates of probabilities are far off the mark. But, as I also mention in that book, research tells us that there are solutions to this problem.

MENTAL MATH: WHY WE SHOULDN'T TRUST THE NUMBERS IN OUR HEADS

When a contractor estimates the cost of building a house, he will often make a detailed list of material requirements for each wall, kitchen cabinet, plumbing fixture, and so forth along with the estimated labor of each. Understandably, this would provide an estimate one can have a lot more confidence in than one made without specifying these details.

But, when it comes to risks, managers and experts will routinely assess one risk as very high and another as very low without doing any kind of math. The math regarding probabilities is less intuitive to most people than adding up the cost of a house or the items in a grocery bag. And without deliberate calculations, most people will commit a variety of errors when assessing risks.

First, we have limited ability to recall the relevant experiences we would use to assess a risk. A heuristic that appears to influence our recall of facts is one that Kahneman named the peak end rule: we tend to remember extremes in our experience and not the mundane. As you can imagine, this will have an effect on how we are assessing the odds of various events.

When we believe that weather forecasters are bad at assessing the chance of rain tomorrow, is it because we are actually recalling all the times they said there was only a 5 percent chance of rain and comparing this to the actual number of times it rained on the following day? No, we remember the one time we planned a family reunion at the park when the forecaster said there was only a 5 percent chance of rain, and it rained. Studies show that when a weather forecaster says there is a 5 percent chance of rain, it rains only about 5 percent of the time.² We remember the exceptions instead of computing the actual averages, and this throws off our entire experience with the problem.

Even if we don't have to rely on our faulty memory of events, our heuristics seem to cause us to make logical errors in the assessments of probabilities. Here are just a few myriad items discovered by Kahneman, Tversky, and others:

Misconceptions of chance: If you flip a coin six times, which result is more likely (H = heads, T = tails): HHHTTT or HTHTTH? Actually, they are equally likely. But researchers found that most people assume that because the first series looks “less random” than the second, it must be less likely.³ Kahneman and Tversky cite this as an example of what they call a representativeness bias.⁴ We appear to judge odds based on what we assume to be representative scenarios. The same research shows that when people are asked to simulate random coin flips, they tend to generate far too many short runs of the same result (e.g., two or three heads in a row) and far too few longer runs (four or more heads in a row). We simply tend to confuse patterns and randomness. In World War II, during the blitz on London, it was believed that bombing patterns were not random because some neighborhoods were hit more often than others. Analysis showed that the distribution of multiple hits in areas of a given size was exactly what we would expect a random bombing pattern to generate.⁵

The conjunction fallacy: When people are offered the opportunity to buy air travel insurance just prior to taking a flight, they are apparently willing to pay more for insurance that covers terrorism than insurance that covers any cause of death due to air travel—including terrorism.⁶ Clearly, insurance that covers only terrorism should be worth less than insurance that covers terrorism in addition to several other risks. Perhaps because we can imagine them more clearly, we often see specific events as more likely than broader categories of events.

Irrational belief in small samples: Suppose a US pharmaceutical company gets batches of ingredients from two suppliers in a country known to be notoriously underregulated. The US company knows that if one particular batch processing method is used, only 30 percent of batches will be acceptable. If a more advanced method is used, then 70 percent should be acceptable. For one supplier, we already had twelve batches, of which four were unacceptable. For the newer supplier, we had just four batches but all were acceptable. In which supplier should you be more confident that they are using the modern processing method? When we do the math, we find that both may have exactly the same probability of using the newer process, but most people will apparently believe they should be more confident in the newer supplier. We will discuss some of this math a little later, but you can find a spreadsheet calculation of this outcome under “downloads” at www.howtomeasureanything.com/riskmanagement.

Disregarding variance in small samples: The fact that small samples will have more random variance than large samples tends to be considered less than it should be. Kahneman and Tversky discovered that when subjects are asked to estimate the probability that a randomly selected group of men will have an average height of greater than six feet, subjects gave essentially the same probability whether the group was one thousand men or ten men.⁷ But a little math shows that the average of the group of one thousand randomly selected men should fall within a very narrow range compared to the averages of just ten randomly selected men. In other words, a very small group of men should have a much higher chance of producing a very tall group average or a very short group average.

Insensitivity to prior probabilities: If the doctor told you that a “very reliable” test gave you a positive result for a very rare medical condition, how worried should you be? It depends on how reliable the test is and how rare the condition is. But Kahneman and Tversky found that when people are given specific scenarios, they tend to ignore how rare the condition is in the first place and focus much more on the new information.⁸ Suppose, if a person is known to have the condition, the test will return a positive result 99 percent of the time. Now, suppose the test also gives a negative result 99 percent of the time when we apply it to a person we know does not have the condition. We also know that only one person in ten thousand has this condition. In this case, the vast majority of positive results would be false positives. If ten thousand people were tested at random, there would be about one hundred false positives whereas there should be only about one person with the condition.

These miscalculations and our limited ability to recall the relevant data can affect our estimate of risks every time someone asks, “Which of these events is more likely?” If you are giving a subjective judgment of a risk, you should assume your answer is influenced by one or more of the effects previously listed. Kahneman and Tversky even showed that otherwise statistically sophisticated experts can make the same errors when asked to provide a subjective estimate.⁹ That's the problem with unconscious heuristics and biases in general—if you are not aware of this influence on your thinking, you can't do much about it regardless of your experience and knowledge of statistics in general.

“CATASTROPHIC” OVERCONFIDENCE

Perhaps one of the most pervasive, exhaustively researched, and thoroughly confirmed phenomena discovered by JDM psychologists is that almost everyone is naturally overconfident in his or her predictions. For decades, Kahneman, Tversky, Lichtenstein, Fischhoff, and other researchers have been showing that if we ask people for the chance that some prediction they made will come true, they will systematically state a probability that is too high. In other words, they are not correct as often as they expect to be.

Of all of the phenomena uncovered by JDM researchers, Danny Kahneman believes overconfidence stands out. “They will underestimate real risk systematically,” he told me in a phone call. “The work we did showed the direction of the bias but it is the degree of the bias that is really catastrophic.” Danny Kahneman is not one to throw around a word like catastrophic casually, but it seems justified by the overwhelming results in every study done in this area.

Overconfidence can be measured using a very simple method. Researchers track how often someone is right about an estimate or forecast and compare that to how often they expected to be right. But one or two forecasts are not enough. If someone says she is 90 percent confident in a prediction, and she is wrong on the first try, was she overconfident? Not necessarily. That's why we have to ask a large number of questions to be sure.

After asking a subject a large number of questions, researchers compute what the expected number correct should be. As I mentioned in chapter 6, in the world of decision analysis the word expected usually means “probability-weighted average.” If you make fifty predictions and you are 70 percent confident in each one, then you are expecting to get thirty-five of the predictions right.

Try testing yourself. In exhibit 7.1, state which of the questions are true or false, and then circle the probability that reflects how confident you are in your answer. For example, if you are absolutely certain in your answer, you should say you have a 100 percent chance of getting the answer right. If you have no idea whatsoever, then your chance should be the same as a coin flip (50 percent). Otherwise, it is one of the values between 50 percent and 100 percent. This is a very small sample, of course. But if you perform like most people, you don't need many samples to see the effect of overconfidence.

I wouldn't recommend drawing strong conclusions about your individual performance from a small sample like this, but you get the idea. (You can check the answers at the end of the chapter.) Most people, if asked a large number of such questions, wouldn't do very well. When they say they have a given chance of being right about a forecast, they will be right much less often than that chance would indicate. For example, if a manager says there is a 90 percent chance that some prediction he makes will come true (e.g., “The new store will break even in the first year,” “We will finish this project by January,” or “Sales will increase next quarter”), and he has done so for each of a large number of predictions, we will find that he will be right much less often than 90 percent of the time.

EXHIBIT 7.1 Sample Calibration Test with True/False Trivia Questions

| Statement | Answer (True or False) | Confidence that You Are Correct (Circle One)
1 | The ancient Romans were conquered by the ancient Greeks. |  | 50% 60% 70% 80% 90% 100%
2 | There is no species of three-humped camel. |  | 50% 60% 70% 80% 90% 100%
3 | A gallon of oil weighs less than a gallon of water. |  | 50% 60% 70% 80% 90% 100%
4 | Mars is always further away from Earth than Venus. |  | 50% 60% 70% 80% 90% 100%
5 | The Boston Red Sox won the first World Series. |  | 50% 60% 70% 80% 90% 100%
6 | Napoleon was born on the island of Corsica. |  | 50% 60% 70% 80% 90% 100%
7 | M is one of the three most commonly used letters. |  | 50% 60% 70% 80% 90% 100%
8 | In 2002, the price of the average new desktop computer purchased was under $1,500. |  | 50% 60% 70% 80% 90% 100%
9 | Lyndon B. Johnson was a governor before becoming vice president. |  | 50% 60% 70% 80% 90% 100%
10 | A kilogram is more than a pound. |  | 50% 60% 70% 80% 90% 100%

The good news is that with practice and with some other relatively simple techniques (we'll discuss more later) a person can get fairly good at this. A person who is good at assessing subjective odds in this way is called calibrated. Most of the rest of the world is uncalibrated. In exhibit 7.2, I combined the results of several published calibration studies along with my own client projects into one chart. The authors of the published studies included Sarah Lichtenstein, Baruch Fischhoff, and other researchers. I also included my own client data, which comprises responses from well over one thousand participants gathered over a twenty-year period. In total, I'm combining the results of eleven separate studies, five of which also show the effects of calibration training. The gray areas of the chart represent the differences among the various studies.

EXHIBIT 7.2 Comparison of Uncalibrated and Calibrated Individuals

The results of all of these combined studies are striking. As we would expect, there is some variation among the studies but the results are still very consistent. Here we see that when uncalibrated people say they are 90 percent confident in an answer they gave, the average of the studies show that they are closer to having a 66 percent chance of being right. When they say they are 95 percent sure, they have a 70 percent chance of being right. So, if a procurement officer says he or she is 95 percent confident that the bankruptcy of a vendor won't cause a supply chain disruption, or if an IT security specialist says there is a 90 percent probability there will be no successful hacker attacks this year, overconfidence needs to be considered.

The other finding shown in the chart is encouraging. Calibration training seems to have a significant effect on the ability of individuals to subjectively assess odds. Unfortunately, the vast majority of risk assessment methods practiced make no use of this training.

Calibration may be especially important when dealing with rare, catastrophic risks. When managers say there is a 5 percent chance that an overseas client will default on the payment for a major order, they are saying there is a 95 percent probability that they won't default. Here, a difference of a few percentage points may be critical. A 1 percent chance of default may be acceptable and a 10 percent chance may be far too risky. How fine-tuned a manager's calibration is starts to make a big difference in these situations.

The overconfidence phenomenon also appears when we ask experts about range estimates. Suppose I asked you for an estimate of what the Dow Jones will be at the close of business tomorrow. Of course, you don't know the actual number, but you can put a wide range on it. Let's say you make the range wide enough that you believe there is a 90 percent chance the actual index at the close of trading on the New York Stock Exchange (NYSE) tomorrow will be within your upper and lower bounds. That means you give me two numbers: one that is so low that you think there is only a 5 percent chance the real number will be below it and another number that is so high that you think there is only a 5 percent chance the real number will be above it.

Try another calibration test to see how well you do with ranges. For exhibit 7.3, provide both an upper bound and a lower bound. Remember that the range should be wide enough that you believe there is a 90 percent chance that the answer will be between your bounds. When you are finished, you can check your answers at the end of the chapter.

Again, I have given tests such as this to more than one thousand individuals, and the number grows every month when we conduct more calibration training. Each time, I find that, instead of getting 90 percent of the answers between their upper and lower bounds, most participants get about 30 percent to 60 percent of the answers within their stated upper and lower bounds. Other studies consistently find that even when subjects are asked for 99 percent confidence intervals, they get only about 60 percent of the answers between their upper and lower bounds. That means they were “surprised” about 40 percent of the time when they should have expected answers to be outside of their bounds only about 1 percent of the time.

EXHIBIT 7.3 Sample Calibration Test with 90 Percent Confidence Interval* Questions

| 90% Confidence Interval
| Question | Lower Bound | Upper Bound
1 | In 1938, a British steam locomotive set a new speed record by going how fast (mph)? |  |
2 | In what year did Sir Isaac Newton publish the Universal Laws of Gravitation? |  |
3 | How many inches long is a typical business card? |  |
4 | The internet (then called Arpanet) was established as a military communications system in what year? |  |
5 | What year was William Shakespeare born? |  |
6 | What is the air distance between New York and Los Angeles in miles? |  |
7 | What percentage of a square could be covered by a circle of the same width? |  |
8 | How old was Charlie Chaplin when he died? |  |
9 | How many days does it actually take the Moon to orbit Earth? |  |
10 | The TV show Gilligan's Island first aired on what date? |  |

* Note on Confidence Intervals (CIs): I am using the term confidence interval to mean a range with a stated probability of containing an answer. That is, a 90% CI has a 90% chance of containing the answer within its upper and lower bounds. CI is the same term used in statistics when computing errors around some estimate based on samples from a population. I use the same term for both. Some statisticians—not a clear majority—argue that the 90% CI doesn't really mean there is a 90% probability the answer is within the range. I will argue later that this is a flawed distinction.

Even when the true/false test and the confidence interval test have the same number of questions, the confidence interval test is more informative. This is partly because most people do so much worse on the range tests that even a few questions are sufficient to detect overconfidence. (There is also a statistical reason, because all of these answers must be 90 percent confident, unlike the true/false tests.)

Exhibit 7.4 shows the distribution of initial test scores for 1,165 individuals prior to taking our calibration training at Hubbard Decision Research. The score is the number of stated intervals that contained the correct answer. The vertical bars represent the percentage of tests that got that number of answers within their stated ranges. The dashed line represents the distribution we would expect to see if all 1,165 individuals were calibrated. As the dashed line shows, the most common result if everyone were calibrated is to get a score of 9 out of 10—that is, ten of the answers fell within the stated range. Just by chance, we would expect some to get 8 or 10 but six or less would be rare. Just 1.28 percent of perfectly calibrated individuals would have been unlucky enough to have only six or fewer answers within their stated ranges.

EXHIBIT 7.4 Score Distribution of Actual Ten-Question 90 Percent Confidence Interval Tests Prior to Training Compared to Ideal Calibration

The distribution of actual scores shows that the individuals who took this test were clearly not calibrated. On average, they are getting only 53 percent of the answers within their ranges. In fact, more than a third of individuals got four or fewer answers within their ranges even though we would expect to see not even one individual with a score that low out of a perfectly calibrated group of 1,165 individuals. It is important to realize that the difference here is not that the calibrated group would do better at trivia questions. They are just more realistic at making their ranges appropriately wide enough to represent their uncertainty—not too wide or too narrow.

To review, consider how these findings might affect the estimates needed for the one-for-one substitution model described in chapter 4. We could not be so certain that the unlikely events in our model are so unlikely. We may say that an event is 2 percent likely to occur in the next year, meaning we are 98 percent confident it won't occur. But if our estimate is overconfident, then our 98 percent confidence it won't happen is unjustified. Then we may say the range of impact of that event is $1 million to $5 million if it occurs. But if our ranges are so overconfident as those who took the tests shown in exhibit 7.4, then the range is much too narrow to represent our uncertainty. The lower bound may be lower but the upper bound could be much higher.

As much as we need to rely on experts for knowledge in their particular field, chances are they are not experts in assessing likelihoods, even though they may insist they are. Kahneman refers to this as fractionated expertise. Fractionated expertise is when learning is harder in some areas of expertise than others due to the lack of the previously mentioned clear, quick, and consistent feedback. Assessing probabilities—or getting other people to provide probabilities—turns out to be a special kind of expertise in itself, and we cannot assume it naturally extends from expertise in another field.

Here is a key lesson so far: the detection of overconfidence is only possible if probabilities are used and compared to real performance of correctly estimating outcomes. How would we know whether someone is overconfident when he tells us there is a medium likelihood of a particular event happening? If the event happens 50 percent of the time, did we confirm that it was a medium likelihood? If we look at all the times a project management office said the risk of a project failure was a 2 on a scale of 1 to 5, and twelve out of forty projects with the same risk score failed, was he right? Ambiguous terms such as this can't be evaluated against real-world observations because, as measurements, they are meaningless. Because experts can be trained to provide explicit probabilities, there is no reason to ever use anything else.

THE MIND OF “ACES”: POSSIBLE CAUSES AND CONSEQUENCES OF OVERCONFIDENCE

Unless managers take steps to offset overconfidence in assessments of probabilities, they will consistently underestimate various risks (i.e., they will be more confident than they should be that some disaster won't occur). This may have had some bearing on very-high-profile disasters, such as those of the Space Shuttle Orbiters Challenger and Columbia.

The Nobel Prize–winning physicist, Richard Feynman, was asked to participate in the investigation of the first Space Shuttle accident (involving Challenger). What he found were some risk assessments that seemed at first glance to be obviously optimistic. He noted the following in the Rogers Commission Report on the Space Shuttle Challenger Accident:

It appears that there are enormous differences of opinion as to the probability of a failure with loss of vehicle and of human life. The estimates range from roughly 1 in 100 to 1 in 100,000. The higher figures [1 in 100] come from the working engineers and the very low figures [1 in 100,000] from management. What are the causes and consequences of this lack of agreement? Since 1 part in 100,000 would imply that one could put a Shuttle up each day for 300 years expecting to lose only one, we could properly ask “What is the cause of management's fantastic faith in the machinery?”¹⁰

Feynman believed that if management decisions to launch were based on such an extraordinary confidence in the Shuttle, then these decisions were flawed. As was Feynman's frequent practice, he applied simple tests and reality checks that would cast doubt on these claims.

Perhaps an obvious explanation is the conflict of interest. Are managers really incentivized to be honest with themselves and others about these risks? No doubt, that is a factor, just as it was probably a factor in the assessments of risks taken by bank managers in 2008, whether or not it was consciously considered. However, individuals showed overconfidence even in situations when they had no stake in the outcome (trivia tests, etc.).

JDM research has shown that both the incentives and the amount of effort put into identifying possible surprises will make a difference in overconfidence.¹¹ Some of the sources of overconfidence would affect not only managers who depend on subjective estimates but also those who believe they are using sound analysis of historical data. Managers will fail to consider ways in which human errors affect systems and will fail to consider common mode and cascade system failures.¹²

There may also a tendency to relax our concerns for infrequent but catastrophic events when some time passes without experiencing the event. Robin Dillon-Merrill, a decision and risk analysis professor at Georgetown University, noticed this tendency when she was studying the risk perceptions of NASA engineers prior to the Space Shuttle Columbia accident. The Columbia Accident Investigation Report noted the following:

The shedding of External Tank foam—the physical cause of the Columbia accident—had a long history. Damage caused by debris has occurred on every Space Shuttle flight, and most missions have had insulating foam shed during ascent. This raises an obvious question: Why did NASA continue flying the Shuttle with a known problem that violated design requirements?¹³

Dillon-Merrill considers each time that foam fell off the external tank of the Shuttle, but where the Shuttle still had a successful mission, to be a “near miss.” Her proposal was that near misses are an opportunity to learn that is rarely exploited. She interviewed NASA staff and contractors about how they judged near misses and found two very interesting phenomena that in my opinion have important implications for risk management in general.

Perhaps not surprisingly, she found that near misses and successes were both judged much more favorably than failures. But were these near-miss events being rated more like a failure than a mission success? Did engineers take each near miss as a red flag warning about an impending problem? Incredibly, just the opposite occurred. The study included an experiment where NASA staff and students were asked to choose among various options for hypothetical unmanned space missions. The options included decisions like whether to skip a test due to schedule constraints. Some subjects were given near miss data and some were not. The study found that people with the near-miss information were more likely to choose the riskier alternative.¹⁴

The near miss interpretation paradox: People with near-miss information were more likely to make the riskier choice than people who did not have information about near misses.

It is possible that managers were looking at each near miss and thinking that because nothing had happened yet, perhaps the system was more robust than they thought. Or it might be more subtle than that. Dillon-Merrill found that when people have a known exposure to some relatively unlikely risk, their tolerance for that risk seems to increase even though they may not be changing their estimate of the probability of the risk.

Imagine that you are in an area exposed to hurricane risks. Authorities confirm that there is a 3 percent chance of injury or death each time you do not evacuate when ordered to for a hurricane warning. If you happen to make it through two or three hurricanes without harm, you will become more tolerant of that risk. Note that you are not actually changing your estimate of the probability of the harm (that was provided by authorities); you are simply becoming more numb to the risk as it is.

Now imagine the implications of this for Wall Street. If they have a few good years, everybody will start to become more “risk tolerant” even if they are not changing their underlying forecasts about the probabilities of a financial crisis. Now that the mortgage uncertainty has settled for a decade or so, will all managers, again, start to become more tolerant of risks?

There are other effects to consider when examining the psyche of upper-level decision-makers. Part of overestimating past performance is due to the tendency to underestimate how much we learned in the last big surprise. This is what Slovic and Fischhoff called the I-knew-it-all-along phenomenon. People will exaggerate how “inevitable” the event would have appeared before the event occurred. (News pundits talking about the mortgage crisis certainly make it sound as if it were inevitable, but where were they before the crisis occurred?)

They even remember their previous predictions in such a way that they, as Slovic put it, “exaggerate in hindsight what they knew in foresight.” I hear the I-saw-that-coming claim so often that, if the claims were true, there would be virtually no surprises anywhere in the world. Two lines of dialog in the movie Wall Street revealed Oliver Stone's grasp of this phenomenon. After “Bud” (Charlie Sheen's character) had his initial big successes as a broker, his boss said, “The minute I laid eyes on you, I knew you had what it took.” Later, when Bud was being arrested in the office for the crimes he committed to get those early successes, the same boss said, “The minute I laid eyes on you, I knew you were no good.” Kahneman sums it up:

When they have made a decision, people don't even keep track of having made the decision or forecast. I mean, the thing that is absolutely the most striking is how seldom people change their minds. First, we're not aware of changing our minds even when we do change our minds. And most people, after they change their minds, reconstruct their past opinion—they believe they always thought that.¹⁵

There is one other item about overconfidence that might be more unique to upper management or particularly successful traders. Some managers can point to an impressive track record of successes as evidence that a high level of confidence on virtually all matters is entirely justified on their part. Surely, if a portfolio manager can claim she had above-average market returns for five years, she must have some particularly useful insight into the market. An IT security manager who has presided over a virus-free, hacker-free environment much longer than his peers in other companies must have great skill, right?

Actually, luck can have more to do with success than we might be inclined to think. For example, a statistical analysis of World War I aces showed that Baron von Richthofen (aka The Red Baron) might have been lucky but not necessarily skilled.¹⁶ Two electrical engineering professors, Mikhail Simkin and Vwani Roychowdhury of the University of California at Los Angeles, examined the victories and losses for the 2,894 fighter pilots who flew for Germany. Together, they tallied 6,759 victories and 810 defeats. This is perhaps a suspiciously high win ratio but these numbers include shooting down unarmed scout and delivery planes. The Germans also had a technological advantage in the air during WWI. Furthermore, not all kills could be confirmed and the inflation of these numbers is certainly possible—but there is no reason to assume that the Baron was less prone to exaggeration than others. Simkin and Roychowdhury showed that, given the number of pilots and the win ratio, there was about a 30 percent chance that, by luck alone, one pilot would have gotten eighty kills, the number Manfred von Richthofen is credited for.

This might describe a large number of “successful” executives who write popular books on the special insight they brought to the table, but who then sometimes find they are unable to repeat their success. Given the large number of candidates who spend their careers competing for a small number of upper-management positions, it is likely that some will have a string of successes just by chance alone. No doubt, some of these will be more likely to hold upper-management positions. In the same manner, some will also have a string of successes in a coin-flipping tournament in which there are a large number of initial players. But we know that the winners of this kind of contest are not just better coin-flippers. Sure, there is probably some skill in reaching upper management. But how much of it was more like winning a coin-flipping contest?

INCONSISTENCIES AND ARTIFACTS: WHAT SHOULDN'T MATTER DOES

No matter how much experience we accumulate and no matter how intelligent we are, we seem to be very inconsistent in our estimates and opinions. Often, our estimates of things change for random, unknown reasons. Other times, researchers know what causes a change in our estimates, but it may be for reasons that should not have any logical bearing on what we think.

In 1955, a fifty-two-year-old psychologist building statistical models of how people made estimates found out how large the effects of our inconsistency really are.¹⁷ Egon Brunswik was a deeply troubled but influential professor of psychology at UC Berkley who challenged conventions in psychology. He promoted probabilistic functionalism, the idea that the psychology of organisms cannot be examined independent of uncertainties about their environments. He also developed innovative empirical methods and used the value of statistical descriptions of these thought processes, which included multiple variables. Brunswik would find that the models he created to describe certain human estimations were actually better at the estimates than the humans.

Brunswik's model is not difficult to test in almost any field. Suppose you are a loan officer at a bank and you are given a list of businesses, some information about each of them, and the size of loans they requested. The given information would include a general business category (e.g., manufacturing, retail, service, or other), the previous two years' revenue, the previous two years' profits, and current debt ratio. Suppose that based on that information alone you are asked to determine whether they would most likely default on the loan, be delinquent but not default, or pay back the loan on time.

Using Brunswik's approach, we would then perform what is called a multivariate regression to build a formula that uses the same data to approximate your judgment. Then when we compared the formula's predictions to your predictions, we would find that the formula was consistently better than you at predicting loan defaults. Remember, this formula was based only on your subjective judgments, not on an actual history of business loan defaults. If it were based on actual histories, chances are it would perform even better. Still, the observed improvement just by using Brunswik's so-called lens method tells us something about human estimation skills. The key benefit of the formula was consistency. Experts had some good heuristics but apparently could not apply them uniformly.

Brunswik's ideas were controversial for his time. He challenged methods developed by those whose names would eventually become much more well-known and respected than his own (R. A. Fischer, Karl Pearson, and others). This may have been the cause of his long struggle with hypertension and his eventual suicide just two months after publishing his final paper on the topic.

He never saw how influential his work would eventually become. Since the 1990s, researchers have rediscovered Brunswik's works, hundreds of papers have cited him for his innovations, and The Brunswik Society meets annually to foster collaboration among researchers, who are still studying his methods.

In 1996, I started using Brunswik's lens method as a way to evaluate risks for a large number of information technology investments. Software development projects are known for high failure rates for a variety of reasons. Users may reject the new technology, rendering it “shelf-ware.” Projects to develop and implement the technology can be greatly delayed. Some software projects are canceled before any use is ever made of them.

I gave clients lists of hypothetical IT projects for which they would assess the probability of failure to be finished on time and on budget. For each project, I listed the projected cost and duration of the project, the department the project was meant to support, the level of the project sponsor (VP, director, etc.), whether it was a technology and vendor they had used before, and a few other facts the clients believed might tell them something about failure rates. This data was shown to them as a large spreadsheet table where each row was a project and each column was a particular data field (sponsor, projected costs, etc.). The list contained forty hypothetical projects for them to review and for which to assess failure probabilities.

Unknown to the clients, I had duplicated two of the projects in the list so that the two projects each appeared twice in the list (two pairs). It took them forty to sixty minutes to finish evaluating the list and by the time they got down to the thirty-eighth project on the list, they forgot that they had already evaluated an identical project previously in the list. I plotted their first estimate and their second estimate for the same project on the chart similar to what is shown in exhibit 7.5.

What we see is that the second estimate was usually more than 10 percentage points different from the first estimate. Only 22 percent actually gave the same answer each time. In extreme instances, the second and first estimates differed by as much as 35 percent. (Note the point on the right of the chart, below the line, where the first estimate was .85 and the second was .5.)

Since the first edition of this book, I've also had a chance to apply these methods to cybersecurity. My staff and I collected more than thirty thousand individual estimates of likelihoods of cybersecurity events from multiple clients. As with the IT project risks, clients were given multiple pieces of information on which to base their judgments about the probability of whether a given application or network would be breached in the next year. The information they were given included factors such as whether a system had large numbers of users, whether it was hosted by an external vendor, and so on. The data was presented in a large table in which each row was a different system or application and each column was one of the parameters used to inform their judgment. Again, hidden in those lists were duplicate rows—more than two thousand—when all the judgments of all experts across all clients were added up. We were able to show that about 21 percent of the variation in expert judgments was just personal inconsistency.

EXHIBIT 7.5 Agreement between First and Second Estimates of IT Project Failure Probabilities

Fortunately, when we apply Brunswik's method, this inconsistency completely disappears. The formula produces an answer based only on the inputs and when the inputs are identical, the answers are identical. Similar to overconfidence, inconsistency is an error that can be completely removed.

But some inconsistencies may not be entirely random; they may be due to factors that should have no influence on our judgments, and yet they do. Just such an effect appears in what Kahneman and Tversky called framing. The way that people are asked a question affects how they answer it. Similar to most other discoveries in JDM psychology, this should seem like common sense. But if it were common sense, why do none of the risk management methodologies mentioned previously appear to take any steps to account for this?

Here is an example of framing in one of the experiments conducted by Kahneman and Tversky. In 1981, these authors asked survey participants to choose between two treatment programs to try to help six hundred people infected by a new and virulent disease. The survey participants were divided into two groups, and each group was asked essentially the same questions as the other group, but the questions were worded differently.

Group 1 was asked to choose between these two treatment programs:

If program A is adopted, two hundred people will be saved.

If program B is adopted, there is a one-third probability that six hundred people will be saved, and a two-thirds probability that no people will be saved.

Group 2 was asked to choose between these two treatment programs:

If program A is adopted, four hundred people will die.

If program B is adopted, there is a one-third probability that nobody will die, and a two-thirds probability that six hundred people will die.

Note that program A in group 1 is identical to program A in group 2 (of the six hundred, two hundred will be saved and four hundred will die). Program B in each group is also just a different wording of the same option. In group 1, 72 percent of participants preferred program A. In the second group, 78 percent preferred program B.

Professional survey developers, of course, try to take great care to make sure that they don't inadvertently bias their findings by the arbitrary ways they happen to ask a question. Some of the things that seem to affect the responses of survey participants are so subtle that it takes some serious analysis to try to avoid it. When a study produces a response that is more of an effect of the survey method itself than the thing being studied, researchers call that an artifact of the study. For example, if the order of questions in a survey affects responses to the survey (which it apparently can), then survey designers have to build in controls to counter it—such as giving different participants the same questions in a different order.

In any formal risk assessment approach, how much of the outcome is a mere artifact of the method of questioning, and how much is real? How much of the answers of the experts and managers were a function of overconfidence, logical errors, and random inconsistencies? Such questions have never been considered in most of the major best practice risk management methods, but it would seem highly unlikely that something makes these risk assessment tools particularly immune to these effects.

We are not just inconsistent regarding our estimates. We are also very inconsistent in how we apply a key decision criterion: our aversion to risk. Our risk aversion changes daily and we are not consciously aware of the reasons. This is why, as we mentioned in chapter 6, we should take care to state aversion to risk in an unambiguous way. Several studies have shown various random irrelevant factors affect appetite for risk.

An NIH funded study conducted by Brian Knutson of Stanford showed that emotional stimulation caused subjects to take riskier bets in betting games.¹⁸

A small study presented at Cognitive Neuroscience Society meeting in 2009 by a grad student at University of Michigan showed that simply being briefly exposed to smiling faces makes people more risk tolerant in betting games.¹⁹

Risk preferences show a strong correlation to testosterone levels—which change daily.²⁰

Recalling past events that involved fear and anger change the perception of risk.²¹

It is unlikely that these studies have found all of the possible random and irrelevant influences on our risk tolerance. What else could influence decisions we are about to make? Caffeine intake? Fatigue? A particularly frustrating commute that morning? And as much as we would like to believe otherwise, we can't assume that our key decisions in management are somehow immune to these effects. Unless we have quantified and documented risk tolerance as an official policy, as was shown in chapters 4 and 5, our decisions are very likely to vary day-to-day due to arbitrary factors. Perhaps a big decision management just made was because they were more risk averse on a Tuesday morning than they would have been Thursday afternoon.

Our overconfidence, inconsistency, and irrationality—especially with probabilities—would seem to be major obstacles to a more useful risk assessment. Any methodology that doesn't acknowledge these issues is forgoing a significant opportunity for improvement. As we will we see in chapter 8, the most common risk assessment methods make no accounting for these kinds of issues.

ANSWERS TO CALIBRATION TESTS

These are the answers to the calibration questions in this chapter. For additional practice, there are more calibration tests and answers in the appendix.

Answers to Exhibit 7.1

False

True

True

False

True

True

False

True

False

True

Answers to Exhibit 7.3

126 mph

687

3.5 in

1969

1564

2,451 miles

78.5%

8 years

27.32 days

September 26, 1964

NOTES

 1. D. Kahneman and G. Klein “Conditions for Intuitive Expertise: A Failure to Disagree,” American Psychologist 64, no. 6 (2009): 515–26.

 2. A. H. Murphy and R. L. Winker, “Can Weather Forecasters Formulate Reliable Probability Forecasts of Precipitation and Temperature?,” National Weather Digest 2 (1977): 2–9.

 3. D. Kahneman and A. Tversky, “Subjective Probability: A Judgment of Representativeness,” Cognitive Psychology 3 (1972): 430–54.

 4. G. S. Tune, “Response Preferences: A Review of Some Relevant Literature,” Psychological Bulletin 61 (1964): 286–302.

 5. W. Feller, An Introduction to Probability Theory and Its Applications (New York: Wiley, 1968), 160.

 6. E. Johnson, “Framing, Probability Distortions and Insurance Decisions,” Journal of Risk and Uncertainty 7 (1993): 35.

 7. D. Kahneman and A. Tversky, “Subjective Probability: A Judgment of Representativeness,” Cognitive Psychology 4 (1972): 430–54.

 8. D. Kahneman and A. Tversky, “On the Psychology of Prediction,” Psychological Review 80 (1973): 237–51.

 9. A. Tversky and D. Kahneman, “The Belief in the ‘Law of Small Numbers,’” Psychological Bulletin 76 (1971): 105–10.

10. R. Feynman, “Personal Observations on the Reliability of the Shuttle,” Appendix IIF. In William Rogers et al., Space Shuttle Accident Report (Washington, DC: US GPO, 1986).

11. A. Koriat, S. Lichtenstein, and B. Fischhoff, “Reasons for Confidence,” Journal of Experimental Psychology: Human Learning and Memory 6 (1980): 107–18.

12. P. Slovic, B. Fischhoff, S. Lichtenstein, Societal Risk Assessment: How Safe Is Safe Enough? (New York: Plenum Press, 1980).

13. The Columbia Accident Investigation Board Report, Vol. I (Washington, DC: US GPO, 2003), 121.

14. R. Dillon and C. Tinsley, “How Near-Misses Influence Decision Making under Risk: A Missed Opportunity for Learning,” Management Science 54, vol. 8 (January 2008): 1425–40.

15. M. Schrage, “Daniel Kahneman: The Leader Interview,” strategy + business, https://www.strategy-business.com/article/03409?gko=7a903 31.12.2003.

16. M. Simkin and V. Roychowdhury, “Theory of Aces: Fame by Chance or Merit?,” Journal of Mathematical Sociology 30, no. 1 (2006): 33–42.

17. E. Brunswik, “Representative Design and Probabilistic Theory in a Functional Psychology,” Psychological Review 62 (1955): 193–217.

18. C. M. Kuhnen and B. Knutson, “The Neural Basis of Financial Risk Taking,” Neuron, 47 (2005): 763–70.

19. P. Aldhous, “Cheery Traders May Encourage Risk Taking,” New Scientist (April 7, 2009).

20. Paolo Sapienza, Luigi Zingales, and Dario Maestripieri, “Gender Differences in Financial Risk Aversion and Career Choices Are Affected by Testosterone,” Proceedings of the National Academy of Sciences of the United States of America 106, no. 36 (2009).

21. J. S. Lerner and D. Keltner, “Fear, Anger, and Risk,” Journal of Personality & Social Psychology 81, no. 1 (2001): 146–59.

CHAPTER 8
Worse Than Useless: The Most Popular Risk Assessment Method and Why It Doesn't Work

Many are stubborn in pursuit of the path they have chosen, few in pursuit of the goal.

—FREDERICK NIETZSCHE

First, do no harm.

—AUGUSTE FRANÇOIS CHOMEL

Contrary to popular belief, the phrase “First, do no harm” is not actually part of the Hippocratic Oath taken by physicians, but it is attributed to other works of Hippocrates and is considered to be just as fundamental to medicine as the oath itself. The developers of the most popular risk management and decision analysis methods should also make this their most important principle. But because their efforts to develop these methods are often undertaken by practitioners isolated from the decades of research in decision-making and risk, this principle is routinely violated.

If you are one of the first three of the four horsemen of risk management discussed in chapter 5, then you might not be at all familiar with some of the most popular risk management methods promoted by management consultants and international standards organizations. These methods often rely on some sort of qualitative score and they come in a variety of flavors. They are easy to create and to use and, therefore, they have a large and rapidly growing body of users.

As we revealed previously, these simple scoring methods are used to assess risk in terrorism, engineering disasters, and a range of business decisions. They are often in the form of a risk matrix that separately scores likelihood and impact on a chart. As we saw from the surveys in chapter 2, risk matrices and other qualitative methods make up the clear majority of risk assessment methods in enterprise risk management and many specific areas of risk management, such as cybersecurity and project risk management. These qualitative methods are used for almost any problem in which promoters of scoring methods think scientific and quantitative solutions to risk management are impractical or impossible—which, as it turns out, covers many areas.

Unfortunately, any perceived benefit of this approach may be mostly the previously mentioned analysis placebo effect. Even worse, extensive research has shown that these methods often easily violate the “First, do no harm” principle of decision analysis by adding its own sources of error and making the decision worse than it would have been. In this chapter, we will discuss why researchers have declared these popular methods “should not be used for decisions of any consequence” and are “worse than useless.”

A FEW EXAMPLES OF SCORES AND MATRICES

As I've mentioned, qualitative risk scoring methods are easy to make and require no special training or even any prior research. Anyone can develop his or her own scoring method for just about anything. Almost all of them use some sort of the previously described, simple ordinal scale—that is, a scale that indicates a relative order of what is being assessed, not actual units of measure. They may use numeric values or they may simply use labels such as high, medium, or low.

For example, star ratings used by film critics provide an ordinal scale in that they indicate rank order but not actual magnitudes. Two stars are simply better than one star, but not exactly twice as good. Therefore, as a rule, it's generally not a good idea to treat ordinal scales as you would measures of distance or mass. They don't really add or multiply like other measures. Four one-gallon containers of gasoline will pour exactly into one four-gallon gasoline tank. But most movie critics would much rather watch one four-star movie than four one-star movies. Still, almost all scoring systems used in risk assessments add and multiply values on ordinal scales as if they were adding the prices of items in a grocery cart or computing an area by multiplying length and width.

There are a large number of specific scoring methods, but they all can be grouped into two broad categories: the additive weighted scores and the multiplicative risk matrices. Weighted scores may include several ordinal scales for items that are meant to be indicators of risk that are generally added up in some way to produce an aggregate score. Risk matrices, however, generally use just two ordinal scales (e.g., likelihood and impact), or three (e.g., threat, vulnerability, consequence), which are then multiplied together to get an aggregate score. I will refer to both of these qualitative methods as scoring methods.

A simple example of an additive weighted score might be used in evaluating accounts receivable risk of corporate customers for large orders. That is, you might do a lot of billable work and ship a lot of goods, but, after the customer is invoiced, the customer can't or won't pay the bill. If you are evaluating the risks related to doing business with customers in various countries, you could simply list several relevant factors, such as “currency risk,” “political risk,” “credit risk,” and so on. These are usually perfectly reasonable factors to consider but might not be defined in the probabilistic terms described in chapter 6. Instead, they may be reduced to an arbitrary ordinal scale such as a scale of 1 to 5.

Currency risk might be considered to be fairly high, so the managers or their advisors might score it a 4. Perhaps political risk (the possibility of interference by the government, civil conflict, etc.) is thought to be low, so it rates a 1 on this scale. But the order is large, so the order size risk gets a 5. This procedure would be repeated for each additional risk. When finished, simply add the scores. Or, if you want to get a little fancier, choose a weight (e.g., .6, .9, etc.) for each factor, so that you can make some factors more influential than others. When the weighted scores are added up, you might get an answer such as a risk score of 22.5 or 39.1. Then, these values are usually compared to some table that gives general recommendations depending on the score.

For example, the table might say “0–10: Low risk, proceed with the deal” and “40–50: Extreme risk, reconsider the size and conditions of the deal and/or offset risk with insurance.” In this version of a qualitative scoring method, the weighted score uses multiple independent scales. Scales may be weighted very differently, and some scales may be weighted the same.

Another variation I've seen on additive weighted scores is when each factor among several alternatives is ranked from best to worst and the rank orders are used in the weighting. In other words, one alternative is ranked 1 on a factor such as cost, one is ranked 2, and so on, for however many alternatives are considered.

The additive weighted score variety is used in prioritizing major project portfolios, evaluating new business ventures, and even for important public policy issues. Some use this for evaluating IT security or IT portfolios and some government agencies use it to determine funding priorities for toxic waste clean-ups. Another such weighted scoring method was developed by the US Department of Health and Human Services as the basis for vaccine allocation in the case of a pandemic flu outbreak.¹ The US Army developed an additive weighted score called composite risk management for evaluating the risk of military operations. This was also the type of method used by the pharmaceutical company in chapter 3.

The chapter 2 surveys show that the risk matrix approach (the kind that multiplies likelihood and impact) is even more widespread in risk management than the weighted additive score. It certainly seems to get more attention from various international standards organizations. One example of this is the method developed by the National Institute of Standards & Technology (NIST) in a 2002 version of a standard called The Risk Management Guide for Information Technology Systems² (NIST 800–30), as shown in exhibits 8.1 and 8.2. The 2012 version of this standard no longer explicitly mentions risk matrices but our survey in chapter 2 found that people still use this standard for risk matrices (old versions of standards tend to linger). Even though explicit descriptions of risk matrices have been removed, the 2012 version of the NIST 800–30 standard still describes the use of qualitative and semi-quantitative methods—which are still just ordinal scales.

EXHIBIT 8.1 Likelihood Scale Proposed by the National Institute for Standards & Technology for IT Security Threats*

Source: NIST 800–30, Table 3–4, p. 21.

Likelihood | Likelihood Definition
High | The threat-source is highly motivated and sufficiently capable, and controls to prevent the vulnerability from being exercised are ineffective.
Medium | The threat-source is motivated and capable, but controls are in place that may impede successful exercise of the vulnerability.
Low | The threat-source lacks motivation or capability, or controls are in place to prevent, or at least significantly impede, the vulnerability from being exercised.

* This is from the 2002 version of the standard and has since been removed, but our survey shows it is still used.

EXHIBIT 8.2 Impact Scale Proposed by the National Institute for Standards & Technology for IT Security Threats*

Source: NIST 800–30, Table 3–5, p. 25.

Magnitude of Impact | Impact Definition
High | Exercise of the vulnerability (1) may result in the highly costly loss of major tangible assets or resources; (2) may significantly violate, harm, or impede an organization's mission, reputation, or interest; or (3) may result in human death or serious injury.
Medium | Exercise of the vulnerability (1) may result in the costly loss of tangible assets or resources; (2) may violate, harm, or impede an organization's mission, reputation, or interest; or (3) may result in human injury.
Low | Exercise of the vulnerability (1) may result in the loss of some tangible assets or resources or (2) may noticeably affect an organization's mission, reputation, or interest.

* This is from the 2002 version of the standard and has since been removed, but our survey shows it is still used.

According to the still-used 2002 NIST procedure, each of these is converted to points. For likelihood, low, medium, and high are converted to 0.1, .5, and 1.0, respectively. The impact is converted to a scale of 10, 50, 100. The product of these two produces another score, which is itself converted back to another low, medium, high scale. This final result is the risk scale.

This method is not fundamentally different from the methods developed by the standards of COSO, ISO, CobIT, or PMBoK mentioned in chapter 4. Such methods are also promoted by many major consulting firms often used as advisors on the standards development teams. Sometimes these are called 5-by-5s or heat maps (the latter name comes from color-coding methods that make the matrix look like a thermal image, with high risks shown in red and low ones in green). And one might think that risk analysis would be more quantitative in the financial industry, but, actually, banks and bank examiners are required to use a version of risk matrices defined by the Federal Financial Institutions Examinations Council (FFIEC) in areas such as cybersecurity and anti-money laundering (www.ffeic.gov). Thousands of people have even gone through “certification training” in methods such as these.

In multiplicative risk scores different scores are multiplied by each other rather than weighted and added. A common multiplicative score is to multiply scores for likelihood and impact. According the HDR/KPMG survey described in chapter 2, this is the approach used in most basic risk matrices. Note that this is not uncommon, and perfectly valid, for actuaries and other quantitative analysts to multiply a probability and loss to compute an expected loss. But they aren't using a five-point scale. They are using an actual probability and dollar loss. In other words, they may say an expected loss is 0.2 × $10 million = $2 million. The multiplicative score may say the likelihood is a 2 and the impact is a 3 resulting in a risk score of 6, which is then categorized as a medium.

Another variety of the multiplicative risk matrix uses three risk components: threat, vulnerability, and consequence. This is the basis of the model used by the Department of Homeland Security to evaluate terrorism threats. Similar to the other scoring methods, this method requires individuals to choose a score from an ordinal scale. Usually, the scores for threat, vulnerability, and consequence are simply multiplied together to get an overall risk score for each potential risk scenario.

The developers in these areas tend to be experts in some particular domain, such as IT security or public health, but they are virtually never experts in risk analysis and decision analysis methods. They are not developed as a result of rigorous research and there is no empirical evidence that these methods improve decisions at all. In fact, even considering the question of whether decisions are measurably improved seems to be completely absent from every one of the scoring methods I mentioned. The problems boil down to the following three main points.

Problems with the Scoring Methods

Because they are usually developed in isolation from research in this area, not one of these scoring methods considers issues about the perception of risks and uncertainties discussed in chapter 7.

The qualitative descriptions of likelihood are understood and used very differently by different people, even when deliberate steps are taken to standardize the meanings.

Arbitrary features of these scoring schemes add their own sources of error as a result of unintended consequences of their structure.

The first point is a failure to remove or address in any way an existing known source of error in subjective judgment of uncertainty. Not one scoring method even seems to be remotely aware of these observations; phenomena that should have a profound bearing on any method that attempts to use subjective judgments in the analysis of risks. The fact that the people who are required to use these scoring methods are both extremely overconfident and inconsistent in their answers (as explained in the previous chapter) was not considered in the design of these methods.

In addition to failing to remove known expert error, the second and third points just presented are about how scoring methods add more error on their own. The unnecessary introduction of ambiguity and other unintended consequences of ordinal scales detract from the quality of analysis. Now we will discuss how this additional error is often so much that managers are better off relying on their original gut feel.

DOES THAT COME IN “MEDIUM”?: WHY AMBIGUITY DOES NOT OFFSET UNCERTAINTY

I've heard many arguments in favor of popular qualitative methods that are based on an assumption that they somehow alleviate problems with quantitative methods. For example, it is presumed that ordinal scales and verbal labels alleviate a lack of data which quantitative methods required—even simple quantitative methods such as the one shown in chapter 4. It is claimed that managers will not understand quantitative methods or that qualitative methods improve communication. None of this is true.

I will address objections to quantitative methods in more detail in chapter 9, but here we will focus on the problems with popular nonquantitative methods. Behind many of these arguments against quantitative methods is the presumption that the introduction of ambiguity solves the problems. For example, a risk consultant might ask a manager to choose from the following conditions:

An Example Likelihood Scale

Very likely

Likely

Unlikely

Very unlikely

These are actually some of the terms used in the scale developed by the Intergovernmental Panel on Climate Change (IPCC). Similar to most versions of risk matrix standards, the IPCC report assigns specific probabilities to each of the levels of its scale. For example, in the IPCC report, the authors define “very likely” as meaning “greater than 90 percent” and “unlikely” as “less than 33 percent.” Quite a few other verbal likelihood scales, however, do not even specify any probabilities at all. But, either way, the users of these methods will interpret the meanings very differently.

If you still think the use of a verbal scale somehow avoids the issue of a lack of precision, consider that verbal scales themselves actually add imprecision of their own. A JDM researcher, David Budescu of the University of Illinois at Urbana-Champaign, decided to see whether people even understood these statements in a common way. Budescu already knew that the literature on this topic showed that there are large differences in the way people understand such phrases and that their use may lead to confusion and errors in communication.

He conducted an experiment in which subjects read sentences from the IPCC report and assigned numerical values to the probability terms. He showed his subjects a series of statements from the IPCC report where these terms were used. For example, one statement from the IPCC report states, “It is very likely that hot extremes, heat waves, and heavy precipitation events will continue to become more frequent.” Subjects were then asked to assign an equivalent probability to this event. For example, a subject may read the previous statement and estimate that “It is 95 percent probable that hot extremes, heat waves, and heavy precipitation events will continue to become more frequent.”

Budescu found that the respondents' assessments of the meaning of these terms varied widely. More surprisingly, he found they varied widely even when they were given specific guidelines for what these terms meant, as was done in the IPCC report. For example, the word likely was interpreted in different contexts to mean anything from 45 percent to 84 percent. This wide range occurred even though subjects were informed that the guidelines specifically stated that likely should mean “greater than 66 percent” (see exhibit 8.3). The verbal labels a method uses seems to be about as important to how responses are distributed—if not more so—than the defined ranges

Budescu says that this creates an “illusion of communication.” When everyone “agrees” that some event is very unlikely, it turns out they are not agreeing at all. Some would be quite surprised as to how others interpret that term. Apparently, detailed procedures for how those terms should be used is no guarantee that those rules will be followed in practice.

But quite a few methods don't even bother to assign meaningful probabilities to their likelihood scales at all. Words such as probable are meant to stand on their own and, presumably, are expected to be understood in the same way by all users. One example of this from the rules of the Financial Accounting Standards Board (FASB) was pointed out to me by Bob Clemen of Duke University. In the FASB rules regarding “Accounting for Contingent Losses,” loss contingencies are sometimes recognized based on whether they are probable, reasonably probable, or remote. These are each defined as follows:

EXHIBIT 8.3 Variances in Understanding of Common Terms Used in the IPCC Report to Express Uncertainty

Source: David V. Budescu, Stephen Broomell, and Han-Hui Po, University of Illinois at Urbana-Champaign.

Probability Phrase | IPCC Guidelines for Meaning of Phrase | Interpreted Meaning According to Subjects (Distribution of Actual Responses) | Percent of Responses that Violated Guidelines
Minimum of All Reponses | Maximum of All Responses
Very Likely | > 90% | 43% | 99% | 58%
Likely | > 66% | 45% | 84% | 46%
Unlikely | < 33% |  8% | 66% | 43%
Very Unlikely | < 10% |  3% | 76% | 67%

Probable: The future event is likely to occur.

Reasonably probable: The chance of the future event occurring is greater than remote but less than probable.

Remote: The probability the future event will occur is small.

In other words, the FASB has managed to define verbal expressions of likelihood entirely in terms of other verbal expressions of likelihood. The ambiguous nature of this rule means that different accounting firms could come to very different opinions. This encourages its own type of risk by incentivizing less than perfectly unbiased descriptions and actions. The impact of an unfavorable audit in this area can be significant for a corporation, and there is an incentive to shop around for a better opinion. Even years after Enron and Sarbanes-Oxley, acquaintances in the accounting profession confirm for me that this still happens.

Ambiguity about contingent losses in FASB rules encourages optimistic valuations of risks in financial reporting. Corporations will shop around for the most favorably worded opinion.

Budescu was not actually the first to look into the issue of ambiguity in communicating uncertainties. In the 1990s, research on the interpretation of purely verbal expressions of probability was being conducted in the CIA. Veteran CIA analyst Dick Heuer gave twenty-three NATO officers a series of statements about geopolitical and military affairs that each contained words indicating a likelihood.³ For example, “It is likely that country X will have a civil war in the next decade” or “It is unlikely that country Y will be able to develop nuclear weapons in the next twenty years.” The officers were then asked to estimate what probabilities were indicated by the terms highly likely, likely, unlikely, and so on. NATO officers interpreted the word unlikely to mean anything between less than 5 percent likely and 35 percent likely. The variation in responses was roughly consistent with Budescu's findings of the IPCC report, which defined labels with specific ranges of values. Even if you define one category of likelihood to mean 5 percent to 20 percent likely, it matters whether you call that unlikely, somewhat unlikely, or very unlikely.

Furthermore, this ambiguity turns out to have potentially greater implications when scales are applied to the impact of a risk. For most risky events, the reality of impact is that it has a wide range of possible outcomes, probably best represented by something like a 90 percent confidence interval. But the users of most risk matrix methods are forced to provide one particular evaluation of impact. For example, if you are evaluating the risk of a loss of customer data to hackers, the potential losses could include costs of recovering data, compensation to customers, legal costs, and/or the loss of customers. This could be anything from a trivial amount (the hacker was internal and was discovered before releasing the data) to the cost of major litigation while losing a large share of customers. The logical way to capture this uncertainty would be a range like what was introduced in chapter 4.

UNINTENDED EFFECTS OF SCALES: WHAT YOU DON'T KNOW CAN HURT YOU

Tony Cox was among the first PhDs from MIT's risk management program. Because MIT was among the first to have such a program, Tony would be one of the earliest PhDs worldwide in that field. Based on his pedigree, you would not be surprised to learn that he takes a more quantitative view of risk management. In fact, he has spent quite a lot of time publishing rigorous analysis of the problems with qualitative methods such as risk matrices.⁴

He finds that even simple-looking scales have peculiarities with their own unintended mathematical consequences. The errors left in popular scoring methods by being oblivious to biases such as overconfidence, and the errors added by the ambiguity of the labels, should alone be reason enough to doubt the usefulness of most scoring schemes. But that's not the end of it. When we examine them closely, the arbitrary features of the scales themselves appear to add other sources of error. Should your assessments of the most important risks depend on nothing more than the fact that you happened to use one arbitrary scoring method and not another? Unfortunately, it does. I'll break these unintended consequences identified by Cox and others into five general types:

Range compression: Scoring methods inject imprecision by grouping a wide range of values under one category on a scale. This is magnified further by the fact that, even for five- or ten-point scales, only a minority of the scale is used for a majority of the ratings given. If opinion slides a little, it can mean a big change in the standing of alternatives.

Presumption of regular intervals: Scores implicitly assume that the regular intervals of the 1–2–3–4–5 scales approximate the relative magnitudes being assessed.

Presumption of independence: None of the standard or popular scoring methods considers the effects of correlation (tendency to move together) among various factors and risks. This has significant implications for models with subjective scoring methods.

Partition dependence: Seemingly minor differences in how ordinal scales are delimited may have a much bigger impact on scoring behaviors than we think.

Conflation with risk aversion: Estimations of impact and likelihood should be independent of how averse we are to risk, but we may be unable to separate them in practice.

Range Compression

The first item on the list comes from the fact that scoring methods often attempt to turn an otherwise meaningful and unambiguous quantity into a score with only a few possible values (usually three or five). The still-used NIST scale would apparently require both a 1 percent likelihood and an 18 percent likelihood to get rounded off to the same likelihood (low). Likewise, an additive weighted scoring system I've seen applied to IT projects converts the return on investment (ROI) of a project to a five-point scale so it can be added up along with several other factors.⁵ The potential ROI range is so large that the value of 1 alone stands for any ROI between 1 percent and 299 percent. A 2 goes from 300 percent to 499 percent. Yes, a project with an ROI of 299 percent is judged the same as one with an ROI of 1 percent but is only half as good as an ROI of 300 percent.

Tony Cox calls this range compression, and it is magnified when factors are multiplied together, as they typically are in risk matrices. Consider that NIST not only would lump together 1 percent and 18 percent likelihood but also it requires users to lump together very different magnitudes of impacts. If a $100 million impact is considered high, then so must be a $250 million impact (there is no higher category). A risk of a 1 percent chance of losing $100 million would then be given the same ranking as an 18 percent chance of losing $250 million. The latter risk might even be a worse outcome than the ratios of the impacts would indicate. Even a “risk neutral” calculation (probability × loss) would show the second risk is forty-five times greater. But a risk-averse manager would consider the difference to be even greater. Perhaps the $250 million loss would have resulted in bankruptcy, making the risk greater still. Yet, in the 2002 NIST framework still used by many organizations, both of these—with a low likelihood and high impact—would be considered a medium risk. There is not enough resolution in this method to discriminate among some very different risks, which is critical to the intelligent allocation of resources to address the risks. The best description I've heard of this effect is from a sometimes-client and IT security expert Reed Augliere: “Garbage times garbage is garbage squared.”

Range compression may be exacerbated further, depending on whether the users of the method cluster their scores. In a paper I coauthored with Dylan Evans in the IBM Journal of Research & Development, we described some data on how responses on five-point scales were distributed based on over two thousand individual responses on five different methodologies.⁶ We showed that about 80 percent of these responses were a 3 or 4. In one of the five methodologies, a 3 was the most common response, chosen 52 percent of the time. In the other methods 4 was the most common—in one method it was chosen 62 percent of the time. In effect, this clustering of responses magnifies the range compression Cox referred to because most responses are really a choice between just two values. Exhibit 8.4 shows the distribution of scores used by these seven scoring methods.

The chart clearly shows two things. First, the behavior of how the scores are actually used is very similar in each of these methods, developed by different people and used by different people. Second, two of the score choices—3 and 4—make up about 75 percent of all of the answers chosen. The implications of this for the scoring method are important. Because most of the chosen scores ended up being a choice between just two values, changing a 3 to a 4 (or vice versa) arbitrarily has a bigger impact on the priorities of the projects than if the scores were uniformly distributed. In other words, a chart that shows the final results of risk rankings or project priorities tends to have a large number in a small cluster, where small changes can make a big difference between ranks. In experimenting with some of the scoring systems, I found that a change of one value from a 4 to a 3 could change the rank so much that it can make the difference in whether an item is in the critical priority list.

EXHIBIT 8.4 Distribution of Scores from Five Different Five-Point Scales

Because responses tend to be highly clustered, small changes in scores have a large impact on ranks of risks.

I found other very curious scoring behaviors when I looked at all of this data. There seemed to be patterns in responses of which the users of these scoring methods were themselves unaware. Apparently, extreme scores (1 or 5) were much more likely for risks that were evaluated much later in a long list of various risks that had to be evaluated. This effect appeared even though these were different teams answering different questions in different orders. By the time they get to the end of their list, do users start feeling obligated to use part of the scale they haven't used much? The data are not conclusive, but given how sensitive responses are to framing and other effects, it would not surprise me if it were true. And our research shows that the clustering of responses may even exacerbate the rest of the problems I will cover next.

Presumption of Regular Intervals

Range compression is not the only source of error introduced by ordinal scales. When a scale is applied, there is an assumption that the numbers used in the scale at least roughly approximate the relative magnitudes of those items. Exhibit 7.5 shows one case where this simple assumption can be far from the truth. The exhibit shows relative values of “level of project sponsor” in assessing IT project failure risk according to a zero- to three-point scale originally used by one US federal agency. Next to it are the relative magnitudes of the effect of the project sponsor based on actual historical data of project failure rates in that organization (shown so that 3 is maximum for comparison to the original scale).

EXHIBIT 8.5 Comparison of Scales versus Historical Data

In the original weighted score shown on the left of exhibit 8.5, having a senior vice president (SVP) as the champion of the project had literally twice the impact as having a mere VP (the score is a 2 and 1, respectively). A C-level executive such as the CEO, CFO, or CIO would be exactly three times as important for project success as the VP. Yet, when I analyzed the actual completion-rate histories of the portfolio (which we were able to reconstruct for about ten years of data), the differences among VP, SVP, and CEO were not nearly as stark, but they were all much better than a mid-level manager. Instead of being twice as important as a VP, an SVP was barely 10 percent more important. And the C-level executive, instead of being three times as important as a VP, was about 30 percent more important.

This example also illustrates how an arbitrary and seemingly minor change in the scoring system has a larger effect than the developers of the method apparently thought. If the scale were changed to 1 to 4 instead of 0 to 3, then the scale would have made an SVP 50 percent more important than a VP, not twice as important. And the C-level sponsor would have been twice as important instead of three times as important as the VP in ensuring project completion. Depending on how users distribute their scores, minor changes such as these could have led to very different priorities.

We might hope that the psychology of how people might respond to a scale of 0 to 3 versus a scale of 1 to 4 could partly offset this effect but it could also exacerbate it. Human psychology even in mundane issues of using ordinal scales is complex and often surprising.

Presumption of Independence

The issue of correlations among different risks and different factors is significant for all risk analysis but universally ignored in scoring models. In multiplicative risk matrices, the correlation may be among different risks. Two or more medium-impact, medium-likelihood risks plotted on a risk matrix might be a much higher risk if they all happen together. If “loss of warehouse inventory due to natural disaster” and “interruption of manufacturing operations due to workforce unavailability” both occur as a result of a hurricane, then they can't really be modeled as two independent medium-impact events.

Losses can be interdependent in other ways, too. If the warehouse were located in Illinois instead of near the factory in Florida, then the same storm could not cause both events. But if the data center is in Florida, the warehouse in Illinois may have to sit idle just the same until the backup site is functioning. The best risk analysts using Monte Carlo models take care to include correlations and dependencies. They know that if they do not, different risks cannot be evaluated and compared.

The assumption of independence means that how bad risks look may just be an artifact of how the level of granularity of a risk model changes from one area to another. For example, consider how a major supply chain disruption risk could be left as one large event or broken into dozens of specific events for individual vendors. Likewise, you could model a cybersecurity breach as one big risk, large numbers of individual events, or any level of granularity in between. If either of these risks were broken into a large number of independent events, each detailed event would tend to have lower likelihoods on average and some would have lower impact. The risks left grouped together look like a single big risk. In this case, risk prioritization is mostly a function of one risk being modeled with relatively more detail than another risk.

Partition Dependence

The work of Budescu and Cox focused on the consequences of how ordinal scales are defined as ranges of values. How the scales are defined in this manner is called partitioning. In our one-for-one substitution model, you don't need to partition; you can estimate actual quantities for probability and impact. But if you were using an ordinal scale for likelihood or impact, you would have to decide how to divide those amounts into partitions. You could, for example, partition impact in one of the two scales shown in exhibit 8.6

If you gave this impact scale to several different managers working in the same organization and each estimate the impact of dozens of different risk events, we could observe how their choices are distributed. We would expect some differences even assuming the managers were perfectly consistent. For example, a 3 covers a much wider range in the five-point scale than the seven-point scale, so we would expect that this score would be chosen more frequently in the former scale than the latter. But notice that the score of 1 is defined identically between the two scoring methods. We should expect that the percentage of times 1 is chosen in the five-point scale is the same as the seven-point scale.

But that is not what happens. Instead we see that there are fewer responses of 1 in the seven-point scale than the five-point scale. JDM researchers have called this partition dependence.⁷ Experts seem to want to distribute their responses differently independent of how the categories are actually defined. Taken together with what we just discussed about Budescu's and Heuer's research, it appears that users of these scales are not as influenced as we might like by the detailed definitions provided for each partition. Arbitrary features such as the number of points on the scale and what verbal label is used seem to have a significant effect on the actual outcomes of these analysis.

EXHIBIT 8.6 Examples of Impact Scale Partitions

Five-Point Scale |  | Seven-Point Scale
Score | Range ($ Millions) |  | Score | Range ($ Millions)
1 | 1 or less |  | 1 | 1 or less
2 | 1 to 9.99 |  | 2 | 1 to 3.99
3 | 10 to 49.99 |  | 3 | 4 to 14.99
4 | 50 to 99.99 |  | 4 | 15 to 49.99
5 | 100 or more |  | 5 | 50 to 99.99
|  |  | 6 | 100 to 249.99
|  |  | 7 | 250 or more

Conflation with Risk Aversion

Tony Cox points out that in the case of evaluating an uncertain impact, an expert being asked to pick one category for impact may have to combine a subjective judgment of risk aversion along with her estimate of the actual impact. In other words, suppose some event could result in a loss of $1 million to $50 million. If two different assessors were to explicitly discuss this loss, they might agree on this range. But because one assessor is more risk averse, she might think of this event as being high impact whereas another thinks of it as medium.

Here is one example I personally observed in the beginning of my consulting career. I was talking to a client about a scoring method he had applied to risks related to a large project portfolio. To illustrate some of the problems with this approach, I asked one manager, “What does this mean when you say this risk is ‘very likely’?” I pointed to a particular risk plotted on his risk matrix. He responded, “I guess it means there is about a 20 percent chance it will happen.” One of his colleagues was surprised by the response that “very likely” could mean just 20 percent. When he asked for clarification, the first manager responded, “Well, this is a very high impact event and 20 percent is too likely for that kind of impact.” A roomful of people looked at each other as if they were just realizing that, after several tedious workshops of evaluating risks, they had been speaking different languages all along. (Of course, a 20 percent chance per year means almost a 90 percent chance per decade and that could be considered to be “very likely.” But, because time scale was not mentioned in their method, this was also ambiguous.)

Summarizing the Research on Risk Matrices

After his extensive analysis, Cox ultimately draws conclusions that should worry any user of risk matrices. As he states in his most cited paper on the topic:

Risk matrices can mistakenly assign higher qualitative ratings to quantitatively smaller risks. For risks with negatively correlated frequencies and severities, they can be “worse than useless,” leading to worse-than-random decisions.⁸

Still, Cox doesn't necessarily conclude that there is absolutely no way to make use of risk matrices. He merely states that risk matrices “should be used with caution, and only with careful explanations of embedded judgments.” Bear in mind, however, that Cox's standard for “caution” and “careful explanation” is high. He details a set of mathematically rigorous requirements that must be met to make any sense of risk matrices as reasonable representations of risks.

A detailed review of many different methodologies shows that these considerations are simply not present in either the initial design or general use of risk matrices. Three decision analysis researchers—Philip Thomas, Reidar Bratvold, and J. Eric Bickel—reviewed thirty different papers that described various risk matrices. All of these were methods used in the oil and gas (O&G) industry but could easily be mistaken for risk matrices in project management, cybersecurity, military operations, and more.

This analysis of existing risk matrices resulted in what may be the single-most, in-depth review on the topic of risk matrices. The article, titled “The Risk of Using Risk Matrices,”⁹ was printed in the Society of Petroleum Engineers Economics & Management. They combined their findings with a comprehensive literature review of the work up to that point, including the work by Budescu, Cox, me, and many more.

For each of the thirty risk matrices, the authors estimated a “lie factor.” The lie factor, coined by the statistician Edward Tufte, is a measure of how much graphically represented information deviates from actual quantities.¹⁰ Using this metric, the authors showed that most of the methods distorted risks by a factor of at least ten and some by more than one hundred. Combining this with many previous studies on ordinal scales, risk matrices and the psychology of how they are used, the authors concluded the following:

Given these problems, it seems clear to us that RMs should not be used for decisions of any consequence. (p. 63)

Note that, unlike Cox, the authors did not indicate that it may be possible to use risk matrices if only they were designed and used with sufficient caution. They simply saw no value in attempting to salvage risk matrices given that there are already practical and sound alternatives. Instead, they recommend for the O&G industry what this book will also ultimately recommend for risk management in any field:

Instead of [risk matrices], the O&G industry should rely on risk- and decision-analytic procedures that rest on more than 250 years of scientific development and understanding. (p. 64)

DIFFERENT BUT SIMILAR-SOUNDING METHODS AND SIMILAR BUT DIFFERENT-SOUNDING METHODS

Before I proclaim that all simple scoring models are completely useless (or worse), I need to qualify further the types of scores we are talking about and why they are being used. The scoring methods I was just describing use vague ordinal scales to rank components of risk. The actual use and accuracy of each such scale are not based on any kind of underlying probabilistic theory, and no statistics are collected showing that the methods work for truly improving decisions.

Now I'll introduce some methods that might be confused with these scoring methods but that actually add some value. I'll also discuss some more dubious but allegedly mathematically-sound methods that are sometimes used in risk analysis.

They Sound Like Scores, but They Aren't (and They Work)

Some researchers have developed methods that might seem like one of the previous simple scoring methods, yet are not. For example, Egon Brunswik's model (mentioned in chapter 7) ultimately produces a result based on weighted inputs, but remember that the weights were derived through a statistical regression, not subjectively chosen in a workshop. Also, the factors that were used were not reduced to ordinal scales. Real inputs of real measures are used, such as number of system administrators and patch update frequency in cybersecurity risks or loan amount and credit history in loan decisions.

Another JDM researcher I wrote about in How to Measure Anything, was Robyn Dawes at Carnegie Mellon University. In 1979, he wrote a paper titled, “The Robust Beauty of Improper Linear Models.”¹¹ He showed that even very simple models can improve on results from unaided judges. But, similar to Brunswik, Dawes invents no predefined ordinal scales for his models, and his claims of effectiveness are based on real measurements. The methods of both researchers allow several factors to be added up to get a value for something we are trying to evaluate—risks of a construction project, applicants for a job, or diagnoses of cancer patients. And in both methods the factors are items that a judge thinks should be considered in the evaluation.

Dawes performs no optimal fit calculation as Brunswik did. He simply converts each factor into a normalized value so that the average of all the values in a given factor (say, the cost of a construction project in the model evaluating construction project risks) is represented by a zero. Then Dawes computes a standard deviation based on the “normal” probability distribution. If the project cost were just slightly above average, it might be +.5, or if it were far below average it might be −2.3. The sign depends on whether the judge thinks that more of that factor is a good thing. See the example spreadsheet for a Dawes linear model at this book's website, www.howtomeasureanything.com/riskmanagement.

Dawes has published work that shows that this method can marginally outperform unaided decision-makers. (Once again, it is the empirical evidence shown by this research that makes it validated.) According to Dawes, human judges seem to do well at identifying factors whether they are good or bad, but have a hard time considering multiple inputs. This is what his simple approach alleviates.

To summarize, the key differences between Dawes's model or Brunswik's model on the one hand and the naive models promoted by FFEIC, CobIT, PMBoK, and several major consulting firms on the other, are as follows:

Naive scoring methods are developed in complete isolation from modern JDM research. Nothing in the scoring approach is designed to offset the known, measured human tendency toward overconfidence and other biases.

Naive scoring models are not tested against reality. No evidence exists in which outputs of the model are compared to a large sample of actual outcomes (project failures, credit defaults, security breaches, etc.).

Brunswik and Dawes use measurable units such as cost or duration, some of which can be provided by objective measures. The naive scoring methods, however, often attempt to elicit responses to very vaguely defined concepts (e.g., “Rate the alignment with business strategy on a scale of 1 to 5”). Alternatively, naive scoring methods partition otherwise-useful quantities into an arbitrary scale with no consideration as to how the rescaling affects outcomes (“If project ROI is 0 to 50 percent, then score = 1, 51 percent to 100 percent = 2, etc.”). The arbitrariness of the ordinal scale actually adds its own completely unnecessary and rather large rounding error to the decision.

Naive scoring methods do not assess user behavior and how sensitive the model may be to small changes in assumptions.

One scoring method that I do like was developed in 1964 by Fred J. Gruenberger, who was, at the time, with RAND Corporation. He proposed a “measure for crackpots” as a tongue-in-cheek way to evaluate the champions of bogus theories. A more current crackpot index was proposed by John C. Baez, a mathematical physicist (and cousin of folk singer Joan Baez). Gruenberger's original model and Baez's index are both geared toward detecting crackpots with new scientific theories, but the basic concept could be applied to popular risk management methods or, for that matter, popular business methods in general.

Both models give the most points for a lack of empirical verifiability of the claims. That is, if someone can't verify a theory by measurements of real observations, then he scores high as a crackpot. Baez mentions a few items that seem especially relevant for business fads. He gives extra crackpot points for each use of a term such as paradigm shift or invention of a new term without a clear definition. Both models include points for a martyr complex among the proponents of a new theory or method. It goes without saying that these are both for entertainment value only exercises, and neither, of course, is used to support major, risky decisions.

Methods that Aren't Exactly Scoring but Address (Necessarily) Subjective Preferences

There is quite a lot of respected academic work developed regarding the idea that if your preferences are at least coherent or rational, then decisions based on them should be better. That is, we should make preferred outcomes more frequent and undesirable ones less frequent. A decade after John Von Neuman and Oscar Morgenstern developed their expected utility theory (first mentioned in chapter 6), L. J. “Jimmie” Savage both defended and expanded on their theory by further defining what coherent and rational preferences really meant in a rigorous mathematical sense. In his 1954 text, The Foundations of Statistics,¹² Savage proposed a list of axioms for a theory of preference that should describe preferences that are coherent and rational even though they are subjective. Scholarly work on the topic has continued to influence many areas of psychology and decision-making. Eventually, the list of related work would eventually include that of Kahneman and Tversky prospect theory, for which Kahneman won the Nobel Prize in Economics.

Even for choices that could be seen as purely subjective—where to have the company picnic, who was the better singer, and so on—some judgments are just more logical than others. An example of how Jimmie Savage would sometimes explain this idea was relayed to me by his son, Sam Savage. Jimmie asks us to imagine he is in a restaurant and he knows he wants either the duck or the prime rib lunch special. But first, he asks the waiter, “Do you have turkey today?” The waiter says, “Yes.” Jimmie says, “In that case, I'll have the duck.” Jimmie Savage's example is one of how we don't make decisions. The conversation violates one of Savage's proposed axioms of preference. Adding an irrelevant (not preferred) option to (or removing one from) the mix should not have any bearing on which of the remaining options you choose.

Here is a short list of such preference axioms:

No rank reversal (the rule violated in Savage's example): If you prefer option A when given a choice among A, B, and C, then your choice should not change if C is dropped from the list or if another option, D, is added that is already inferior to one of the other options.

Transitivity: If you prefer A to B and B to C, then you should prefer A to C. To say you prefer C to A is logically inconsistent with the first part of the statement.

Indifferent criterion independence: If you are choosing alternatives based on two factors, and you end up preferring A, then adding a third factor for which all the alternatives are equally valued should not change your choice. For example, after ranking three alternatives for the company picnic based on size of the area and price, you choose Lincoln Park. Someone then decides “distance from office” should be added as a factor for consideration. You add it, but find that all three alternatives are exactly the same distance from the office, anyway. Because it is the same value for all three locations, adding this variable should have no bearing on the outcome.

These seem terribly obvious, but it is actually possible for risk managers to create or use scoring systems that violate these rules and not be aware of it. This comes up more often in scoring systems in which all of the factors being considered are expressed as relative ranks. All of the logical consequences of these axioms and more are explored in a method variously referred to as multi-attribute utility theory (MAUT), multi-criteria decision-making (MCDM), multiple objective decision analysis (MODA), and a few more. These methods attempt to account for all sorts of trade-offs between different items and work out the necessary, logical consequences. These methods at least attempt to avoid the problems pointed out by Savage. But models created with these methods are generally not probabilistic and they are often improperly used as substitutes for probabilistic risk analysis.

The use of the term utility may make it sound like all of these are directly derived from the utility theory of Von Neuman and Morgenstern, but, at least in practice if not theory, there are considerable deviations. In decision analysis, and in methods described by Von Neuman's and Morgenstern's method, a utility is about only two competing considerations: risk and reward. The utility is not directly estimated but inferred from choices about bets.

You may recall from chapter 6 how Ron Howard proposed we can estimate risk tolerances by considering how large of a bet we are willing to take on a coin flip where we win x or lose half of x. Knowing how someone answers choices such as these tells us what we need to know about how they would make other choices if they were consistent. We never have to ask them or tell them what the utility of a bet was. We just know that if they accept a particular bet, we can work out other bets they would accept.

Expected utility theory was based on the mathematical fundamentals of risk versus reward and that necessitates the use of probabilities. In applications of MAUT, however, the subject matter expert is often asked to estimate a utility function directly and on several dimensions other than risk and reward.

In decision analysis, uncertainty about forecasts of outcomes is separate from preferences about how much risk one is willing to tolerate. If you are expressing your uncertainty about the duration of a construction project using a subjective range estimate, you are attempting to estimate some real-world measurable quantity. You have not stated anything about what you prefer the project duration to be as opposed to other trade-offs—for example, accelerating a project may increase costs or risks. But if you are considering different alternatives based on the net benefits versus the risks of a project, then you have an issue that fundamentally comes down to a subjective trade-off or preference.

The problem with using preference-modeling methods for risk analysis is that none of these methods is a forecasting method; none predicts what is likely to happen. They are strictly for evaluation of fundamental preferences, not for prediction of the probable consequences of actions—the heart of risk analysis. Putting probabilities on potential outcomes should be fundamental to risk analysis.

Here is a caveat that should apply to whatever application MAUT may have in risk management. I find that a good quantitative model finds very few fundamentally competing objectives. A person may feel the need to trade between objective A and objective B, but in reality these are both just factors in a higher objective, C. For example, a utility curve showing the trade-off between seeking an investment with better tax advantages or one that increases revenues should really be based on a financial calculation, not a subjective preference between tax advantages or revenues (but I have seen preference methods of MCDM and MAUT used this way). For most profit-oriented organizations, the basic trade-off may boil down to simply risk versus return, not trade-offs among a dozen or more objectives. If the real trade-offs are this small of a set, a lot of the more elaborate methods may not apply.

They Don't Seem Like Scores, but They Are

I'll mention one more method that is not exactly in the scope of this book but, because it is very popular and some users have applied it to risk analysis, I feel it is necessary to address briefly. The analytic hierarchy process (AHP) is another method that attempts to help decision-makers make rational trade-offs between alternatives based only on stated preferences. AHP was developed by Thomas Saaty in the 1970s, and it employs a mathematical method to attempt to minimize the number of transitivity errors decision-makers might make when considering problems with large numbers of competing objectives and trade-offs among them. AHP is certainly successful if we ignore the possibility of an analysis placebo (mentioned in chapter 3) and measure success by the number of passionate advocates.

AHP resorts to a type of arbitrary score in the sense that users are asked to evaluate the relative importance of criteria, so that “slightly more important” means a 3, “absolutely more important” means a 9, and so on. Some users are apparently unaware of this arbitrary conversion because analysts can hide the actual scale from users who simply give verbal responses—and we know the problems that introduces.

AHP runs into other problems by violating Savage's axioms. It used to violate rank reversal, but proponents (who originally argued rank reversal is rational) have now fixed the problem (which they first argued was not a problem). But other logical problems with AHP have been discovered. It now appears to violate the indifferent criterion axiom.¹³ Other problems are found with the mathematical methods themselves.¹⁴

Enthusiastic supporters of AHP claim that AHP is “mathematically proven” and enjoys a “broad consensus” among decision analysts. As I speak to decision analysis experts from around the country, I find this to be far from the truth. In fact, everyone I talk to seems to at least acknowledge the existence of serious controversy about the method. Robin Dillon-Merrill (from chapter 7) is a long-standing member of the Decision Analysis Society and she observes, “Most decision analysis experts don't consider AHP a legitimate part of decision analysis.” In an email exchange I had with Tony Cox in 2008, he went even further, and was willing to go on the record with the following:

AHP bears the same relation to decision analysis as alternative medicine bears to mainstream modern medicine: Its advocates passionately defend it, but mainstream practitioners note that there is no evidence that it works better than (or as well as) other methods, except in pleasing those who use it. Advocates point to the large numbers of satisfied users, and to publications extolling the supposed virtues of the methods, as evidence of respectability and efficacy; while critics object that the alternative methods lack a sound logical or scientific foundation and generate results that typically have not been demonstrated to compare favorably with those from mainstream methods.

I've reviewed a large number of the publications Cox refers to as extolling AHP. Every article I found was, in fact, merely a case study about the application of AHP to some problem—the question of whether the decision was any better than it would have been if other methods had been used is usually not even raised. I have more decision analysis experts willing to go on record denouncing AHP than I care to list, but you get the point.

I'm told some AHP proponents feel vindicated by Saaty's being recognized with the Impact Prize from Institute for Operations Research and the Management Sciences (INFORMS) in 2008. But the carefully worded award states, “This is not a research award. The awards committee is not judging the quality of a body of work. Instead, emphasis will be placed on evaluating the breadth of the impact of an idea or body of research.” By that measure alone, I'm sure Saaty deserved the award. But that is not the same as evidence of the effectiveness of AHP, especially for risk management.

AHP proponents say it is evolving and some problems have been addressed. But Karen Jenni, a PhD decision analyst whose advisor was Baruch Fischhoff, sees little use in this. She asks, “Why keep fixing AHP when other methods already work that don't violate the axioms?” I agree. We are only being fair. All risk analysis methods (or misapplied preference analysis methods) must still be evaluated by the ultimate crackpot test: does it actually improve forecasts of risk events and are decisions actually improved? More important, whatever the benefits of AHP and some of the other methods we discussed are, they can't be the only tools used in risk management unless they can be validated as forecasting tools—which isn't their basic purpose.

Ron Howard, the thought leader in decision science who actually coined the term “decision analysis,” had the same criticisms of AHP. His comment on AHP could easily be applied to any of the dubious decision making methods reviewed here: “Why, then, do inferior processes find favor with decision makers? The answer  is that they do not force you to think very hard or to think in new ways. …In decision making, as in many other pursuits, you have a choice of doing something the easy way or the right way, and you will reap the consequences.”¹⁵

NOTES

 1. US Dept. of Health and Human Services, Draft Guidance on Allocating and Targeting Pandemic Influenza Vaccine (October 17, 2007).

 2. National Institute of Standards & Technology, Risk Management Guide for Information Technology Systems, NIST 800–30 (2002).

 3. Richards J. Heuer Jr., Psychology of Intelligence Analysis (Langley, VA: Center for the Study of Intelligence, Central Intelligence Agency, 1999).

 4. L. A. Cox, “What's Wrong with Risk Matrices?” Risk Analysis 28, vol. 2 (2008): 497–512.

 5. M. Parker, R. Benson, and H. E. Trainor, Information Economics: Linking Business Performance to Information Technology (Englewood Cliffs, NJ: Prentice-Hall, 1988).

 6. D. Hubbard and D. Evans, “Problems with Scoring Methods and Ordinal Scales in Risk Assessment,” IBM Journal of Research and Development 54, no. 3 (April 2010).

 7. K. E. See, C. R. Fox, and Y. Rottenstreich, “Between Ignorance and Truth: Partition Dependence and Learning in Judgment under Uncertainty,” Journal of Experimental Psychology: Learning, Memory and Cognition 32 (2006): 1385–402.

 8. L. A. Cox, Jr., “What's Wrong with Risk Matrices?,” Risk Analysis 28, no. 2 (2008).

 9. P. Thomas, R. Bratvold, and J. E. Bickel, “The Risk of Using Risk Matrices,” Society of Petroleum Engineers Economics & Management 6, no. 2 (April 2014): 56–66.

10. E. Tufte, The Visual Display of Quantitative Information, 2nd ed. (Cheshire, CT: Graphics Press, 2001).

11. R. M. Dawes, “The Robust Beauty of Improper Linear Models in Decision Making,” American Psychologist 34 (1979): 571–82.

12. L. J. Savage, The Foundations of Statistics (New York: Dover Publications, 1954).

13. J. Perez, J. L. Jimeno, and E. Mokotoff, “Another Potential Shortcoming of AHP,” TOP 14, vol. 1 (June 2006).

14. C. A. Bana e Costa and J. C. Vansnick, “A Critical Analysis of the Eigenvalue Method Used to Derive Priorities in AHP,” European Journal of Operational Research 187, no. 3 (June 16, 2008): 1422–28.

15. Ron Howard, “The Foundations of Decision Analysis Revisited,” Advances in Decision Analysis, (Cambridge University Press, 2007).

CHAPTER 9
Bears, Swans and Other Obstacles to Improved Risk Management

The perfect is the enemy of the good.

—VOLTAIRE

The truth is much too complicated to allow anything but approximations.

—JON VON NEUMANN

Even if every argument I made up to this point were accepted by all managers, there would still be some serious conceptual obstacles to overcome from some corners. Risk is often perceived as beyond measurable, and any attempt to manage risk may not be considered feasible. Even the simple quantitative model I proposed in chapter 4 to replace the risk matrix will be seen as overly complex or (ironically, compared to the alternative) too simple to capture risks. Most of these objections to risk management boil down to some fundamentally different ideas about basic concepts such as the nature of models, how to assess the relative performance of models, and basic concepts of measurement and probability. We need to address these obstacles to make progress.

I argue that the probabilities and consequences of events can be measured in a meaningful way. In one of my previous books, How to Measure Anything, I argue that measurement is simply a quantitatively-expressed reduction in uncertainty based on observation. The objective of measurement is to improve (even just slightly) our current knowledge about an unknown quantity that is relevant to some decision. By this standard, the objective of quantitative assessments of risk is to improve on the unaided intuition of managers, not to attain perfect clairvoyance. We quantify the probabilities and losses from various events and use these values in calculations (quantitative models) that will reduce the error of managers and allow them to make better bets.

The obstacles to this position are often strongly held opinions about quantitative modeling of risks, even by some who have risk management in their job titles. Some object to the very idea that quantitative risk management is ever possible in any situation. Others accept that quantitative methods are possible in some fields, but not in their specific industry or organization. Some base these objections on the fact that some unusual events could never have been predicted or that their problems are too complex or immeasurable. Each of these ideas may result in a potential source of resistance to improved risk management.

In my interviews and research, I was sometimes surprised to find out how passionate some people were about their positions on the topics of probability and risk. You might even think that we were talking about one of the more controversial issues in religion or politics and not the nature of risk. But even though, for whatever reason, this seems to be a touchy subject with some people, we need to be aware of these opposing views and learn to address them directly.

ALGORITHM AVERSION AND A KEY FALLACY

In another book, How to Measure Anything in Cybersecurity Risk, my coauthor and I used an old joke to explain a common kind of objection we were both hearing in regard to the use of quantitative methods in risk assessment. You've probably heard it before, but in case you haven't here it is:

Two hikers are heading out for a day on some new hiking trails. One hiker is wearing his running shoes instead of his regular hiking boots. The other asks, “Why are you wearing running shoes instead of hiking boots?” to which the first hiker responds, “I just heard there were bears in the woods today. I wore these shoes so I could run faster.” His friend, confused, reminds him, “But you know you can't outrun a bear.” The hiker with the running shoes replies, “I don't have to outrun a bear. I just have to outrun you.”

This describes a recurring type of fallacy when evaluating models of anything. One hiker was assuming that the objective was to beat the bear and the other realized that the real objective was to beat the alternative meal for the bear. I call this the exsupero ursus fallacy. This is what Google produced when I used it to translate “beat the bear” into Latin (of course, all recognized fallacies should have proper-sounding Latin names).

To illustrate this fallacy, let's apply it to a topic outside of risk management. Suppose a car buyer had a choice between buying two nearly identical automobiles, Car A and Car B. The only difference is that Car B is $1,000 more expensive, has fifty thousand more miles, and was once driven into a lake. But buyer chooses Car B because Car A doesn't fly. Neither does Car B, of course, but for some reason the buyer believes that Car A should fly and therefore chooses Car B. The buyer is committing the exsupero ursus fallacy.

Such reasoning sounds absurd in the car-buying analogy but this is routinely what happens when managers choose among alternative models for decision-making. There is empirical evidence that people will be less forgiving of errors by algorithms even though those are less than the errors of humans. Berkeley Dietvorst at the University of Chicago and two other JDM researchers from Wharton, Joseph P. Simmons, and Cade Massey, conducted experiments to investigate what appears to be a common, but unproductive, “algorithm aversion.”¹

In the various experiments, subjects were rewarded for making accurate estimates about two different topics—the performance of graduate students based on undergraduate performance data and the ranking of airport traffic by state based on various other demographic and economic data. The subjects could choose in advance whether they were going to use an algorithm to generate their estimates or their own judgment and, in one of the experiments, the judgments of past participants. In some cases, subjects were given no data about past performance of estimates from either the humans or the algorithms. In other cases, they were shown performance data for the humans, the algorithms, or both before they had to choose which to rely on for their own estimates.

Dietvorst and his colleagues found that there was a slight preference for the algorithms over the humans when subjects were given no data on past estimations or only the data on the humans estimates. But when subjects were shown estimation performance data for algorithms and, in some cases, both algorithms and humans, they became much less likely to choose the algorithms. Averaged across multiple experiments, 62 percent chose the algorithms when shown no data on past performance or only the data on humans. The share who chose the algorithms dropped by almost half (down to 32 percent) when shown data on past algorithm estimates, even though the human estimates had more error.

The human error was 15 percent to 29 percent higher than the algorithms in estimating graduate student performance, and humans had almost twice the error of the algorithms when estimating air traffic. In all the experiments, the subjects who stuck with the algorithms made more money than those who didn't. The researchers concluded that many subjects were just more intolerant of algorithm error than their own error or the error of other humans. The subjects in the study seemed to be holding algorithms to a reference point that didn't apply to humans. In other words, they committed the exsupero ursus fallacy.

Dietvorst points out an anecdote regarding the forecasts of the statistical models developed by Nate Silver's New York Times blog, “FiveThirtyEight” in the 2012 elections. Silver predicted not only the overall outcome of the election but also the outcome in all fifty states exactly. And he had a good track record in 2008 when he correctly called forty-nine of fifty states. Still, prior to the 2012 election, pundits criticized Silver's methods as “exaggerated, attention-grabbing exactitude.”² The results in 2012 silenced the critics—but not for long after Dietvorst's research was published.

In 2016 Silver calculated that it would be more likely that Hillary Clinton would win. He was pilloried for it when Trump won. Silver himself seemed to lament his assessment and wrote in his blog how he “screwed up” on Trump.³ Actually, he only missed just five states and gave Trump a higher chance of victory than did other odds-making sites. The night before the election Silver estimated Trump's chances of a win at 29 percent whereas several pundits were giving him odds of just 15 percent and even lower than 1 percent. In fact, if we look at Silver's track record instead of one forecast, we see that he was well calibrated (recall that being calibrated in probabilities means that when he said something was, for example, 80 percent likely the opposite happened just 20 percent of the time, etc.).

According to the critics, Silver's “error” is that he isn't right 100 percent of the time regardless of his overall success rate, how well calibrated he is, or how well he did compared to pundits who couldn't tell a standard deviation from a significance level. Silver's estimate wasn't even an error if you look at all of his estimates together. Did pundits believe that if something is 29 percent likely then it cannot possibly happen? Do they equate anything less than 50 percent to mean the same as 0 percent? Events that are 29 percent likely have to happen 29 percent of the time and Silver's probabilities match the observed frequencies very well when we look at his entire body of work instead of individual forecasts.

Regardless, Silver's Trump prediction was enough to send pundits and the public on a tear about the failure of polls and statistical models. And remember, there were plenty of people who weren't using algorithms who guessed wrong, but pundits haven't spent nearly as much time lambasting subjective judgment of experts. The fact that Silver again did well on the 2018 midterms hardly seems to have dampened this reaction.

We also see algorithm aversion at work in Michael Lewis's book Moneyball on how, in 2002 and 2003, the Oakland A's baseball team used statistical models to put together a team on a shoestring budget.⁴ Oakland had more wins than any other team in their division, even though they had the lowest payroll in the division, resulting in a cost per win less than half as much as the rest of the division. But, as with Silver's work, the critics seized on anything that was short of perfect performance by the team as “proof” of the shortcomings of statistical methods. And what was the proof the critics pointed to? It was the fact that the underdog Oakland A's remarkable twenty-game winning streak wasn't longer. Clearly, the critics were holding algorithms to a very different standard than the alternative. In his book's afterward section, Lewis summarized his own journey in his research:

By the end of the 2003 baseball season I had learned something from publishing Moneyball. I learned that if you look long enough for an argument against reason you will find it. (p. 298)

ALGORITHMS VERSUS EXPERTS: GENERALIZING THE FINDINGS

In Dietvorst's research, the algorithms beat the humans in estimates of a couple of arbitrary topics. Now, how often do algorithms beat humans in other, more practical domains? Large numbers of studies and thousands of data points have been gathered to answer this question. Depending on the study, you can conclude that algorithms beat humans somewhere between most of the time and nearly always.

For more than half a century, researchers have been comparing forecasts from human experts to statistical models. One researcher, Paul Meehl, starting comparing various areas of human judgment to statistical models in the 1950s continuing nearly up until he died in 2003. Initially, he was investigating expert judgment within his own field of clinical psychology,⁵ but soon branched out into areas as diverse as business failures and the outcomes of sporting events. No matter where he looked, he found that the statistical model was almost always outperforming the human expert. In 1986, he summarized his findings to date like this:

There is no controversy in social science which shows such a large body of qualitatively diverse studies coming out so uniformly in the same direction as this one. When you're pushing 90 investigations [now many more], predicting everything from the outcome of football games to the diagnosis of liver disease and when you can hardly come up with a half dozen studies showing even a weak tendency in favor of the [human expert], it is time to draw a practical conclusion.⁶

Since then, Meehl continued to gather corroborative results and other researchers did the same. Another 136 individual studies were assessed by other researchers including Meehl. Using even more demanding and cautious statistical standards, they ventured to make a conclusion on only about half of them. Still, of those where they felt they could make a clear conclusion, algorithms beat humans 4 to 1. That is, of those where conclusive results were found, 80 percent were found in favor of the algorithm.⁷

Perhaps one very large, long-term study with thousands of data points would address lingering questions about the conclusiveness of these findings. Fortunately, just such a study was conducted. Philip Tetlock tracked the forecasts of 284 experts in many topics over a twenty-year period, ultimately gathering eighty-two thousand individual forecasts in a variety of domains including covering elections, wars, economics, and more. Tetlock summarized these findings in his book Expert Political Judgment: How Good Is It? How Can We Know?⁸ His conclusion is more strongly worded than the previously mentioned studies:

It is impossible to find any domain in which humans clearly outperformed crude extrapolation algorithms, less still sophisticated statistical ones. (p. 53)

So, yes, in many cases we are better off betting on the algorithm over the human. Even if we don't go so far as to assert that an algorithm will always beat a human, we have good reason to at least doubt any presumption that the human must be the better performer. We should track performance and compare the models.

To those employing the exsupero ursus fallacy, however, the relative performance of the methods are not relevant. The measure they would use is to simply try to identify a time the algorithm ever erred and use that as the basis for assuming the human expert is preferred. A single event, no matter how rare, is enough to reject the algorithm regardless of whether any other model (including human intuition) has ever met the same standard of prediction accuracy.

Some individuals will point out several historical disasters as evidence of the impossibility of risk analysis. I have seen, for example, many skeptics of algorithms “prove” the ineffectiveness of algorithms by pointing out how they failed to exactly predict the events of September 11, 2001, the rise of Google or Facebook, major stock market crashes, and various engineering disasters. (Some of these skeptics are even billed as experts in risk management.) So, do these examples of various disasters really tell us anything about the effectiveness of quantitative risk analysis? Actually, they all boil down to some variation of exsupero ursus.

The most basic form of the fallacy is that the algorithm must be perfect in order to be preferred to experts regardless of how imperfect the experts might be. In fact, as this form of the fallacy goes, even extremely unusual events must be exactly predicted for a model to be of any use, regardless of the track records of expert intuition alone. This is like saying that, in order for my insurance company to compute the premium for my life insurance, it cannot just compute the odds of my death in a given period of time. Instead, it must predict the exact circumstances of my death, which, for all I know, may be an extremely unlikely event. For example, there is a tiny chance my cause of death will be due to being hit by a falling airplane while lying in bed. If I were killed in this way, should anyone challenge the actuaries and say, “Aha—you could never have predicted that, so actuarial science is a fraud”? No, actuarial science is in no danger of being debunked because, similar to the casino, the objective is to make good bets over time, not predict individual causes of death.

The need for perfection is implied when we assume that a single error is sufficient to prove the case. Yes, a single error does show a model isn't perfect, but it isn't sufficient to show one model is more or less imperfect than another model. A casino, for example, correctly computes that a bet on a single number in the game of roulette has only a 1 in 37 chance of winning for the player (a loss for the casino). If a player bets a large amount on a single number and wins, was the casino wrong about the 37-to-1 odds against it? No. Even if we allow for the possibility that the wheel is biased, that single spin doesn't prove the odds were wrong. Only a large number of spins could conclusively show that the wheel might be biased and the assumed odds were wrong.

Just as one spin in roulette is not conclusive proof that odds were computed incorrectly, neither is one disaster or, in the case of Silver's forecasts or the Oakland A's, one election or one baseball game. Of course, the critic of algorithms ignores all the cases in which experts not using algorithms were wrong. Relative performance is not the issue for them. Again, to them the algorithm must be nearly perfect regardless of the frequency and size of the experts' errors.

Another type of fallacy sometimes made in conjunction with exsupero ursus is to even assume that a quantitative method was used at all. I've seen algorithms take the blame even in situations where algorithms were not used for risk analysis. Were the problems related to Chernobyl, Fukushima, Hurricane Katrina, major cybersecurity breaches, or the Great Recession really because of a quantitative risk analysis method or the lack of it?

For example, one individual (who called himself a risk expert) pointed out to me that the 1940 Tacoma Narrows Bridge collapse in Tacoma, Washington, is an example of the failure of quantitative risk analysis. The first Tacoma Narrows Bridge has become a famous case study of engineering disasters. The culprit in question was a failure to account for aeroelastic flutter. The winds in the Tacoma Narrows valley caused the bridge to swing, the swings amplified the aerodynamic effects, and the aerodynamic effects amplified the swings. For the few months that the bridge was in use, it got the nickname Galloping Gertie for this easily noticeable swinging. But on November 7, 1940, the swings became so severe they tore the bridge apart. It was used right up to the point of its destruction, where one man barely escaped with his life.

Again, single anecdotes like this say nothing about the relative performance of one model over another. But, aside from that, it is by no means clear what “quantitative risk analysis” methods would have been used. The event certainly predates some of the more powerful methods we refer to, including Monte Carlo simulations and calibration training of experts. So how did this individual know what quantitative risk management methods were used in order to be able to claim quantitative methods failed? Of course, he had no idea. On further discussion we established that he simply assumed that quantitative methods were used because, well, they were engineers and engineers quantify everything. After conducting risk assessments in a few areas involving engineering problems (mining, construction, aerospace, etc.), I can tell you that most of the methods we introduced were often unfamiliar to the engineers.

There are many other arguments that the reader may hear that are ultimately just variations on this basic fallacy. Here is a quick review of a few.

Other Common Forms of Exsupero Ursus

“Quantitative models depend on their assumptions” or “Garbage in, garbage out.”

“Each situation is unique, therefore we can't extrapolate from historical data.”

“We lack the data for a quantitative model.”

“This is too complex to model.”

“How do we know you've modeled all the variables?”

In each of these cases, the follow-up question should be “Compared to what?” or “How does intuition alleviate this problem?” Expert intuition does not somehow avoid the problem of garbage in, garbage out. If experts are working on bad information, they will also make bad judgments. Nor do experts even remotely model all the variables or make up for any lack of data. And if a problem is so unique that extrapolation from past experience is impossible, how exactly is the expert's experience avoiding that problem?

Regarding whether a problem is too complex to model, they are modeling the problem whether or not they think they are. They may be modeling the problem in their heads even though complex problems are exactly the type I don't want to just do in my head with hidden assumptions. Ironically, it is also argued that a quantitative model is not complex enough. Introducing the simple one-for-one substitution model described in chapter 4 will generate many questions similar to the previously mentioned “How can we include all the correlations?” and “How do we know we have all the factors included?” and more. Of course, these are all legitimate questions and later chapters will begin to discuss how the simple model in chapter 4 can be further improved by considering these issues. But I rarely see questions such as these asked of a previously used qualitative risk matrix. This is just algorithm aversion again. The quantitative method is apparently required to handle levels of complexity that were never asked of a method that merely labels a risk as medium.

Sometimes, an objection related to complexity is not just about the problem being complex but more about the method itself being too complex. The implication is that the quantitative model is impractical for real-world problems. I've heard some version of this many times. The most obvious response to this is to simply point out how many real-world problems I've applied this to. I've been doing some form of quantitative management consulting for thirty years and nobody has ever hired me to solve a purely theoretical problem with no practical implications. My team and many others like us routinely apply these methods to help organizations with real decisions.

Remember, the only question is, given all these challenges, how do the errors of experts compare to the errors of algorithms?—and that is the question Meehl and other researchers already answered.

A NOTE ABOUT BLACK SWANS

The exsupero ursus fallacy is reinforced by authors of very popular books who seem to depend heavily on some version of the fallacy. One such author is former Wall Street trader and mathematician Nassim Taleb. He wrote The Black Swan and other books critical of common practice in risk management, especially in (but not limited to) the financial world, as well as the nonquantitative hubris of Wall Street.

A heretic of financial convention, he argues that Nobel Prize–winning modern portfolio theory and options theory (briefly mentioned in chapter 5) are fundamentally flawed and are in fact no better than astrology. In fact, Taleb considers this prize is itself an intellectual fraud. After all, as he rightly points out, it was not established in the will of Alfred Nobel, but by the Royal Bank of Sweden seventy-five years after Nobel's death. He even claims that once, in a public forum, he riled up one such prizewinner to the point of red-faced, fist-pounding anger.

Taleb bases a lot of his thesis on the fact that the impact of chance is unappreciated by mostly everyone. He sees the most significant events in history as being completely unforeseeable. He calls these events black swans in reference to an old European expression that went something like “That's about as likely as finding a black swan.” The expression was based on the fact that no European had ever seen a swan that was black—until Europeans traveled to Australia. Until the first black swans were sighted, black swans were a metaphor for impossibility. Taleb puts September 11, 2001, stock market crashes, major scientific discoveries, and the rise of Google in his set of black swans. Each event, he argues, was not only unforeseen but utterly unforeseeable based on our previous experience. People will routinely confuse luck with competence and they will presume that the lack of seeing an unusual event to date is somehow proof that the event cannot occur.

Managers, traders, and the media seem to be especially susceptible to these errors. Out of a large number of managers, some managers will have made several good choices in a row by chance alone. This is what I called the Red Baron effect in a previous chapter. Such managers will see their past success as indicators of competence and, unfortunately, will act with high confidence on equally erroneous thinking in the future. Taleb recognizes the problems of overconfidence researched by Kahneman and others. Indeed, Taleb says Kahneman is the only Economics Nobel Prize winner he respects.

I think part of Taleb's skepticism is refreshing and on point. I agree with many of Taleb's observations on the misplaced faith in some models and will discuss this further in the next chapter. I might even include Taleb as one source of inspiration for identifying new categories of fallacies (and giving it a Latin name in order to sound official). Taleb coined a fallacy he refers to as the ludic fallacy, derived from the Latin word for “games of chance.” Taleb defines the ludic fallacy as the assumption that the real world necessarily follows the same rules as well-defined games of chance.

Now, here is where Taleb errs. He doesn't just argue that risk management is flawed. He argues that risk management itself is impossible and that all we can do is make ourselves antifragile.⁹ I think he is just using a very different definition of risk management—which even he uses inconsistently. No matter what he calls it, he is promoting a particular set of (vaguely defined) methods that have the objective of reducing risk. This reduction in risk will require resources. Using the definition I propose in chapter 6, determining how to use resources to reduce risk is part of risk management. He actually contradicts himself on this point when he promotes redundancy as a method of becoming antifragile and refers to it as the “central risk management property of natural systems.” So, yes, we are both talking about risk management. He focuses on particular approaches to it, but it is risk management just the same.

Confusion and inconsistency about whether managing fragility is, in practice, part of managing risks is not the only problem in his thesis. Taleb commits every form of the exsupero ursus fallacy throughout most of what he writes. Specifically, (1) he presumes the lack of perfection of one model automatically necessitates use of the other regardless of relative performance, (2) he commits the anecdotal fallacy when looking for evidence of relative performance, and (3) he presumes that a given model was even being used when he identifies them as the culprit in major risk events.

In an interview for Fortune Taleb claimed, “No model is better than a faulty model.”¹⁰ Again, having no model is never an option. One way or another, a model is being used. Taleb's model is simply his common sense, which is, as Albert Einstein defines it, “merely the deposit of prejudice laid down in the human mind before the age of eighteen.” As with every other model, common sense has its own special errors.

We've seen the research that shows overwhelming evidence of the flaws of unaided intuition compared to even simple statistical models, and Taleb offers no empirical data to the contrary. Taleb does briefly mention the work of Meehl but dismisses it. Without making any mention of the huge numbers of conclusive results by Meehl and his colleagues, Taleb claims the entire body of research is invalid by claiming “that these researchers did not have a clear idea of where the burden of empirical evidence lies” and goes on to suggest that they lacked “rigorous empiricism.” He offers no details about how more than one hundred peer-reviewed, published studies by several researchers veers from the required rigorous empiricism.

Kahneman, who actually is a psychologist like Meehl, would apparently disagree with Taleb on Meehl's methods. Taleb considers Kahneman a significant influence on his work, but who does Kahneman consider to be a significant influence on his work? Meehl.¹¹ I wouldn't presume to speak for Kahneman but I wonder if he might point out to Taleb how the burden of proof was accepted and met overwhelmingly by Meehl, whereas Taleb's evidence merely amounts to, at best, selected anecdotes of shortcomings or entirely imagined straw man arguments. Taleb even sometimes cites the work of Phil Tetlock to support some other point he makes but never references Tetlock's enormous twenty-year study where he concluded that it was “impossible” to find a domain where humans clearly outperformed algorithms.

Instead of relying on large controlled studies, Taleb commits the error of arguing that single events effectively disprove a probabilistic model. He uses the apparent unforeseeability of specific events as evidence of a flaw in risk analysis. The implication is that if quantitative analysis worked, then we could make exact predictions of specific and extraordinary events such as 9/11 or the rise of Google. When arguing against the use of various statistical models in economics he states that “the simple argument that Black Swans and tail events run the socioeconomic world—and these events cannot be predicted—is sufficient to invalidate their statistics.”¹² Yes, the rare events—black swans—are individually impossible to predict precisely. But unless he can show that his alternative model (apparently his intuition) would also have predicted such events exactly, then he commits exsupero ursus when he says imperfection alone is sufficient to prefer intuition over statistics.

In addition to Kahneman, it is worth pointing out others whose work Taleb cites to make a point but who, if you actually looked at what they are doing, would contradict Taleb. For example, Taleb says he admires the mathematician Edward Thorp, who developed a mathematically sound basis for card counting in blackjack in the 1960s. Now, if the objective of card counting was to predict every hand, even the most extraordinarily rare combinations as Taleb would seem to require, then Ed Thorp's method certainly fails. But Ed Thorp's method works—that's why the casinos quit letting him play—because his system resulted in better bets on average after a large number of hands. Taleb is also a fan of the mathematician Benoit Mandelbrot, who used the mathematics of fractals to model financial markets. Similar to Thorp and Taleb, Mandelbrot was equally unable to predict specific extraordinary events exactly, but his models are preferred by some because they seem to generate more realistic patterns that look like they could be from real data.

If anecdotal evidence were sufficient to compare model performance, one could simply point out that Taleb's investment firm, Empirica Capital LLC, closed in 2004 after several years of mediocre returns.¹³ He had one very good year in 2000 (a 60 percent return) because while everyone else was betting on dot-com, he bet on dot-bomb. But the returns the following years were far enough below the market average that the good times couldn't outweigh the bad for his fund.

Similar to the news pundits rejecting Nate Silver's findings or the sportscasters rejecting the methods used by the Oakland A's, Taleb merely shows that it is possible to find an error in a model if one looks hard enough. Again, the question is not whether to model (intuition is a model, too) or whether one model is imperfect (both models are imperfect) but which measurably outperforms the other and does so in many trials not just single anecdotes.

Finally, Taleb makes the error of presuming what methods were actually being used when he blames them for an event. He argues, for example, that the downfall of long-term capital management (LTCM) disproves options theory. Recall that options theory won the Nobel Prize for Robert Merton and Myron Scholes, both of whom were on the board of directors for LTCM. The theory was presumably the basis of the trading strategy of the firm. But an analysis of the failure of LTCM shows that a big reason for its downfall was the excessive use of leverage in trades—an issue that isn't even part of options theory. That appeared to be based on intuition.

Taleb also states that the crash of 1987 disproved modern portfolio theory (MPT), which would seem to presume that at least some significant proportion of fund managers used the method. I find fund managers to be tight-lipped about their specific methods, but one fund manager did tell me how “learning the theory is important as a foundation but ‘real-world’ decisions have to be based on practical experience, too.” In fact, I found no fund managers who didn't rely partly, if not mostly, on intuition. Finally, if we are looking for explanations of the mortgage crisis, neither MPT nor options theory had anything to do with the practice of giving out mortgages to large numbers of people lacking the ability to pay them. That was more of a function of a system that incentivized banks to give risky loans without actually accepting the risk.

Finally, Taleb seems to make a variety of other points that, similar to the previous points, seem so inconsistent he ends up undermining the point he makes. For example, explaining the outcomes in terms of the narrative fallacy committed by others is sometimes itself a narrative fallacy. Arguing that “experts” don't know so much is not supported by quoting other experts. He argues that rare events defy quantitative models, but then gives specific examples of computing rare events with quantitative models (he shows the odds of getting the same result in a coin flip many times in a row and argues the benefits of Mandelbrot's mathematical models in the analysis of market fluctuations).

Taleb criticizes the use of historical data in forecasts but apparently sees no irony in his argument. He looks at several examples in which history was a poor predictor. In other words, he is assessing the validity of using historical examples by using historical examples. What Taleb and others prove with such examples is merely that what I will call a naive historical analysis can be very misleading. Taleb demonstrates his point by using the example of a turkey. The turkey had a great life right up until Thanksgiving. So, for that turkey, history was a poor indicator. So how is Taleb able to see this problem? He simply looks at the larger history of turkeys.

All he is doing is using what we may call a history of histories, or meta-historical analysis, to show how wrong naive historical analysis can be. The error in historical analysis in a stock price, for example, is to look only at the history of that stock and only for recent history. If we look at all historical analysis for a very long period of time, we find how often naive historical analysis can be wrong.

Taleb's own “experience,” as extensive as it might be (at least in finance), is also just a historical analysis—just a very informal type with lots of errors in both recall and analysis, as shown in chapter 7. No thinking person can ever honestly claim to have formed any idea totally independent of previous observations. It just doesn't happen.

Even Taleb's ludic fallacy seems to be a fallacy itself. Sam Savage calls it the “ludic fallacy-fallacy.” As Savage describes it, we cannot rationally address real-world problems of uncertainty “without first understanding the simple arithmetic of dice, cards, and spinners.” Of course, Taleb is right when he says we shouldn't assume that we have defined any problem perfectly. That certainly would be an error, and if that were Taleb's point, that would be valid. But, again, whether a particular model is perfect is not the right question. The most relevant question is whether a probabilistic model—even a simple one—outperforms the alternative model, such as intuition.

MAJOR MATHEMATICAL MISCONCEPTIONS

It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so.

—MARK TWAIN

One of the surveys I mentioned in chapter 2 was conducted for research related to my fourth book, How to Measure Anything in Cybersecurity Risk. Among other topics in that survey, I asked questions to assess attitudes and preferences about the use of quantitative methods in assessing cybersecurity risks. I also asked questions meant to assess basic literacy about quantitative methods in risk management. The multiple-choice questions on quantitative methods included questions related to common misconceptions about statistics, probability, sample size, and so on. Each of the questions' four or five possible responses included an “I don't know” response.

The median score in the stats literacy portion of the survey was barely above what someone would get if they were guessing. But the actual data don't match what we would see from that number of people randomly guessing. First, the number of both very good scores and very bad scores was more than we would expect if it were just a bunch of people guessing. Also, the stats literacy score was correlated to the responses about attitudes toward quantitative methods (we should see no correlation, of course, if one of these were answered randomly). If someone scored below the median on the statistics literacy portion, they were more than twice as likely to be above the median on resistance to quantitative methods.

Curiously, the most resistant to quantitative methods were not those who scored low because they chose “I don't know” a lot. Those who chose “I don't know” frequently were not more resistant than those who scored well. The most resistant were those who thought they did know but were wrong. In other words, the resistance comes from people who thought they understood basic concepts of statistics and probability but, in fact, were simply in possession of one or more misconceptions.

The Dunning-Kruger effect I mentioned in chapter 3 seems to be at work. Of those who scored below the median on the statistics literacy questions, 63 percent rated themselves as being at or above the median. They thought they knew at least as much about statistics and probability as their average peer, but did not. So, what are the misconceptions about risks that cause the trouble Mark Twain's quote is warning us about? Some of the most influential misconceptions are related to statistical tests, simulations, and even the basic concept of probabilities.

Fundamental Misconceptions about Probability

If you implement a quantitative risk model, even one as simple as what is described in chapter 4, you may eventually hear someone say, “There is no way I can know the exact probability.” You will recall from the previous chapter that some form of this objection may be used to justify qualitative scales. Actually, it is another type of exsupero ursus fallacy. We cannot presume the alternative method—the qualitative scale—somehow makes up for a lack of knowledge of any kind. But this response is so common it is worth repeating myself a bit in order to dive into it further.

As pointed out in the previous chapter, we use probabilities because we are uncertain, not in spite of being uncertain. Chapter 6 explained how we use the perfectly mathematically valid Bayesian subjectivist approach to statistics. Whether this interpretation or the alternative frequentist interpretation is more valid is a very technical academic debate that has lasted nearly a century. But it is certainly an error to assume that only the frequentist interpretation is applicable. The only practical position for real decision-makers is that both are equally valid in some way. But, as first pointed out in chapter 6, it is a fair criticism of the frequentist interpretation that it makes most uses of probabilities impossible in practical decision-making.

Remember, you always know your pragmatic operational probability, as defined by Bruno di Finetti in that same chapter. You act every day as if some events are more likely than others. Now, if you had to bet on whether a company you own stock in will announce it had a major product recall this year or whether a coin flip will land on heads, your choice will indicate whether you believe the chance of a product recall is greater than, less than, or about the same as a coin flip (if you are indifferent). In di Finetti's use of probability, saying that you don't know the real uncertainty is an oxymoron. You are the one with the uncertainty and you are the world's leading expert at estimating your own uncertainty. In the sense that di Finetti used the term, a probability is a statement about the lack of information an observer has, not about the thing being observed. His use of the term is consistent with the subjectivist, Bayesian use of the term.

As far as we know, all probability may ultimately just be a lack of knowledge. Perhaps, in principle, if we could describe every detail of a physical system, such as rolling dice, then we could predict outcomes exactly. If we measure with perfect precision parameters, such as the dimensions mass of the dice, their friction and elasticity against surface of the craps table, the rotation of the dice the instant they were thrown, the initial height above the table, air density, and many other factors in a detailed physical simulation, then we should be able to predict the roll with as much confidence as we could predict the movement of gears in a clock. So, is the roll of dice a “true” random event or just another example of our limited knowledge of a very complex system? Either way, the uncertainty of the observer is the relevant meaning of the term probability.

Famous statisticians in the mid-twentieth century, such as Ronald A. Fisher and Harold Jefferies, even made a road show out of this ongoing debate. A lot of the arguments they would have made may sound academic and pedantic in a book about pragmatic risk management but it really is at the basis of a lot of perceived obstacles to using probabilities. I suspect most frequentists don't really know they are frequentists and aren't aware of any alternative meaning of probability. A few are aware of the debate and consciously take the position of frequentist. But, after several decades, the debate is not over. So instead of going into the details of the pros and cons of each side, I will only say this. Everyone, including frequentists, are Bayesian subjectivists when it comes to betting their own money.

Fortunately, I have noticed that this type of objection almost disappears after someone goes through the “calibrated probability assessment” training I first described in chapter 6. (I will describe it further in chapter 11.) Recall that in calibration training someone learns how to assign probabilities so that they are right just as often as they expect. That is, over a large number of estimates, of all they times they said they were 90 percent confidence, 90 percent of those outcomes happened. Of all they times they said something was 70 percent likely, 70 percent happened, and so on. Once someone sees that they can actually learn how to subjectively assess calibrated probabilities, they begin to see that it is not just a way of describing a thing, it is a way of describing their own uncertainty about a thing.

Misconceptions about Statistical Tests

In 2017, I was on an organizing committee for the American Statistical Association (ASA) Symposium on Statistical Inference. A key objective of the event was to emphasize the need to clarify what “statistical significance” is and discuss the problems with its use. Even within the scientific community, the meaning of statistical significance is routinely misunderstood and misrepresented in published literature. The speakers at the event presented many examples of the abuse of statistical significance in peer-reviewed scientific journals.

So, we shouldn't be surprised that most casual uses of the term by nonscientists are on shaky ground. For example, you might even have heard someone point out, “This measurement is not valid because it was not a statistically significant sample size.” Let's be clear about this first: there is no such thing as a statistically significant sample size. There is statistical significance and there is sample size, but there is no universal number of samples that if we were one short of that threshold, no inference can be made and if we have just barely enough, all of a sudden we can make an inference.

Suppose, for example, we are testing a new pain-killing drug in a clinical trial. We give the drug to a group of people we call the test group and a placebo to people we call a control group. People are randomly assigned to the groups and they don't know whether they are taking the placebo or the real drug. There will be some variation by chance. Some individuals in the placebo group may start feeling better, and the drug may not work for everyone in the test group. Even if the drug was no better than a placebo, we might by chance observe a difference in results that favors the drug. So how do we test the effectiveness of the drug when random variation is at work?

I'm simplifying a bit, but in statistical significance calculations we are basically asking, “If this observation were just a random fluke, how likely would it be?” (More specifically, we ask for the probability of that result and all of the even more extreme results.) We compare that probability, known as the p-value, to a fixed threshold known as the significance level. Significance levels are mostly just conventions that vary depending on the field of research. In fields such as social sciences, significance levels are set to 0.05, but in other fields they may be 0.01 or 0.001. The most popular test seems to be p < .05. That is, if the p-value is less than the stated significance level of 5 percent, then we declare the result to be statistically significant.

To compute statistical significance, we need a specific hypothesis and all the data (not just the number of samples but the entire set of values of the individual samples) as well as the stated significance level. There is simply no way to compute statistical significance based on only knowing the number of samples was, say, twelve or twelve thousand. We can have a statistically significant result with a very small sample (we can use something called the student-t distribution for samples as small as two), and we could have a result based on thousands of samples that was not statically significant. It depends on the individual sample values as well as the specifics of the hypothesis.

More important, notice that we aren't computing the probability that the drug works or even how well it works. We are just computing how likely the result would be if it were a fluke. This critical distinction has been the source of another confusion about how to use scientific research to inform real decisions. Statistical significance says nothing about whether we learned something or whether that reduction in uncertainty, no matter how small, had value.

These problems and many others have fed a growing movement within statistics to rethink statistical inference in science. In fact, the tag line for that 2017 ASA event I was involved in was “Scientific Method for the 21st Century: A World beyond p < .05.” After the event, the journal The American Statistician published an entire issue on this specific topic. I was an associate editor on that issue and I coauthored one of the articles about proposed solutions for producing useful probabilities from scientific research.¹⁴

So, if you hear someone casually throwing around statistical significance as an objection to a use of probabilities in decision-making, they are probably making two errors. First, they are just assuming that a sample size is too small to be useful without doing the necessary math. Second, they are assuming that statistical significance alone, which does not establish the probability that a hypothesis is actually true, is ever relevant to practical decision-making.

Misunderstandings about statistical significance, as pervasive as it is, is just part of a larger set of misconceptions that lead to skepticism about quantitative methods. I spend some time in my webinars and seminars correcting misconceptions about statistical significance and its relevance to decisions.

In the previously mentioned survey cybersecurity professionals, it is interesting that the most popular incorrect response to all the questions was “There is insufficient information to answer the question.” The stats literacy questions were multiple choice and this response was one of the choices in every one of them—but it was never the correct choice. Every question provided all the information necessary to answer it. I conducted follow-up interviews with some survey respondents and some of them used the “insufficient information” response frequently. In every case when I asked them what information would be sufficient to answer the question and exactly how they would use it in a calculation, not one of them could answer completely. In other words, even though they said the information was insufficient, they had no idea what would be sufficient and what they would do with the information if they had it.

Here is one of those questions. Assume the probability of an event, x, occurring in your firm sometime next year is 20 percent. The probability of this event goes to 70 percent if threat t exists. There is a 10 percent probability that threat t exists. Which of the following statements is true?

If the threat t does not exist, the probability of the event x must be less than 20 percent.

If the event x does not occur, then t does not exist.

Given that the event x occurs, the probability that threat t exists must be greater than 50 percent.

There is insufficient information to answer the question.

I don't know.

Answer A is correct. The weighted average of two conditional probabilities—threat t existing or not—must add up to 20 percent.¹⁵ For the same reason, answers B and C must be false. The only other potentially correct answer would be “I don't know” if, in fact, the person didn't know.

The incorrect “insufficient information” answer (D) was chosen by 26 percent of the respondents. Two of the respondents who chose D were part of a follow-up interview. One mentioned that he had no idea what other information would be required or how it would be used but was confident that the information provided was insufficient. The other person said that threat t could be much worse than indicated, which is just changing the question. He also mentioned that he doesn't know how t and x are correlated. (Correlation is a another routinely misapplied concept.) I pointed out that the statement about conditional probability is a type of correlation and it has an exact answer. He provided a series of additional arguments that revealed several fundamental misconceptions that he confidently held as fact. He used the “insufficient information” response on almost every question and was one of the most resistant to the use of quantitative methods in risk assessment.

Miscellaneous Myths about Simulations

Other objections are just plain weird. Among the strangest of these criticisms is that Monte Carlo simulations assume normal distributions. The first time I heard this I thought it was just a one-off misconception held by someone who just misunderstood the concepts. But then I heard it a couple more times during the Q&A in conferences, and I've heard it from participants in the webinars I give online. I confirmed with other simulation experts that they also hear this peculiar objection.

I'm not sure how this idea got started, but it's wrong. Perhaps people are confusing something with other methods in statistics in which a normal distribution has to be assumed (for example, there is a simplified method for estimating a population proportion in which a normal distribution is a good fit if the sample size is large enough). Maybe they have seen a simulation at some point in which someone used a normal distribution that would be unrealistic—such as changes in stock prices. To set the record straight, every Monte Carlo simulation tool on the market—including Excel (yes, it is entirely practical to run simulations in Excel)—has many different shapes of distributions.

My staff and I routinely use no less than four or five distributions and sometimes more. If you go to www.howtomeasureanything.com/riskmanagement you will find a downloadable spreadsheet of several distinct distributions. In practice, I find that normal is not even the most common by far when we build Monte Carlo simulations. In fact, the downloadable one-for-one substitution spreadsheet described in chapter 4 doesn't have a single normal distribution in it.

I've also heard, “Aren't the outputs of Monte Carlo simulations just random?” The implication is that because Monte Carlo simulations rely on random sampling, the output is just random. Individual scenarios are random, but a simulation typically uses thousands of scenarios—or hundreds of thousands. The scenarios create an overall pattern that is repeatable. For example, an individual roll of two dice at the craps table is random. But if you roll the dice, say, ten thousand times you will find that the frequency of results follows a triangular pattern, where a 7 is the most common result, occurring about six times as often as a 2 and about six times as often as a 12. You can run this simulation again with a different set of ten thousand rolls and you will find almost exactly the same result again. If you run one hundred thousand scenarios in each simulation, you will find the output of the simulations match even more closely. If you ran ten more simulations of a million scenarios each, they will all match almost exactly.

The Stanford mathematician Keith Devlin has said the same about gambling in casinos. Individual bets are uncertain but the casino profits from the overall pattern: “The customers are gambling. The casinos are absolutely not gambling.” The pattern of the entire simulation, not the individual scenarios, is what we are interested in when we want to know whether we should invest in specific risk mitigations.

There is another set of myths about Monte Carlo simulations that are particularly odd because of their source: analysts who would otherwise be considered quants, at least in some types of quantitative methods. Because of the source of the misunderstandings, I will deal with them in the next chapter “Where Even the Quants Go Wrong.”

WE'RE SPECIAL: THE BELIEF THAT RISK ANALYSIS MIGHT WORK, BUT NOT HERE

For a risk manager or chief risk officer, there is usually not a wholesale rejection of the notion that risk can be assessed and managed (the claim some make, but which none actually live by). But it is common to argue that any methods that might have more quantitative validity, for some reason, just don't apply to their environment.

Many managers see their own environments as somehow uniquely complex. I've applied quantitative methods in nuclear power, insurance, mass media, military logistics, software projects, large construction projects, security, and issues of public health and safety. Yet, I still periodically hear, “Yes, but none of those are exactly like our business.” True, but none of any of the previously mentioned applications are exactly like the others, and we still used quantitative models effectively.

If I point out the usefulness of conducting some aspects of risk management more like an actuary might conduct them, I may hear the objection, “But the insurance industry has a lot of data—we have none.” Here, I'll reiterate a few more points from my first book, How to Measure Anything:

Whatever your measurement problem is, it's been done before.

You have more data than you think.

You need less data than you think.

Getting more data (by direct observation) is more economical than you think.

(An addition to the original list): You probably need completely different data than you think.

Each of these assumptions is much more productive than the typical set of assumptions that people start with (that is, the very opposite set of the previous assumptions). If we simply assumed, as most people usually do, that we don't have enough data or that this has never been measured before, then the inquiry will stop at that point. But resourceful managers will not stop at that imagined barrier.

When people say they don't have enough data, have they actually determined how much they need and what can be inferred from the data they have (no matter how little it is)? Did they actually determine—or even consider—the cost of getting new data based on new observations? Did they determine that the data they think they need even applies to the problem, or that some other more obvious measurement would be more relevant? The answers to these questions should be the results of specific calculations (which I will discuss in more detail later). When people make these claims, it is virtually guaranteed that they have done none of this math.

One 2001 book on environmental risk analysis characterized actuarial risk as being limited to “provid[ing] only aggregate data over large segments of the population and for long time duration.”¹⁶ There are at least two errors in this claim. The first actuary I asked about this disagreed—apparently the authors of the book didn't collaborate with any actuaries about this definition. Christopher (Kip) Bohn, the actuary I quoted previously, said, “I wouldn't agree with that at all. Ideally, actuaries would like to have lots of data but sometimes that's just not the case. Even when there is historical data, there are things that have changed and the data that you have is no longer applicable.”

Yes, it is true that insurance companies have quite a lot of data on certain types of insurance claims, and this information is critical to computing risks. When most people think of insurance, they think of retail consumer insurance that most people would be familiar with—that is, life, auto, health, and so on. But insurance companies also have to deal with situations in which they have very little data, and that is often in the areas where they have the greatest exposure. For example, the mortality tables in insurance are based on a great deal of data about the deaths of men and women at various ages, degrees of healthiness, and so on. But how much data do they have about a pandemic virus or a major change in health trends that may affect their risks of offering life insurance?

Bohn says, “For a while, we were seeing people getting older, but now we see people getting more obese and the lifespan trend begins to turn.” If an insurance company offers a life insurance product that has a fixed premium as long as the policy is active, then future changes in mortality trends may mean that they pay life insurance claims far too frequently and too soon. Unfortunately, this risk can't be diversified by selling more life insurance to more people.

And, unknown to some people, insurance companies insure fairly rare events for which they have little if any historical data:

Major event insurance: The International Olympic Committee and cities where the Olympics were held have taken out insurance to protect against cancellations due to terrorism or other disasters. Since the modern revival in 1896, the games have been canceled only three times—once due to World War I and twice during World War II.

Rocket launch insurance: The $10 million X-Prize for the first privately funded manned flight of a reusable vehicle to an altitude of 100 km was insured in case someone won it (which someone did). The premium cost $5 million—which the insurer would have kept if no one had claimed the prize. Now, the payloads on relatively new rockets by companies like SpaceX are also insured. Aon International Space Brokers (yes, that is a real business name) insures just such events.

Coupon insurance: For risk of over-redemption of coupons, retailers buy this insurance just in case far too many people decide to redeem a coupon. Retailers know that only a small percentage of coupons will be used but that a large number have to be distributed just to reach those who would use it. But there is a risk that a promotion might be unexpectedly successful (or that hard economic times force more coupon clipping) and that the retailer might lose money on it.

Credit risk insurance in developing or high-risk nations: Some insurers underwrite credit risks (the risk of receivables not getting paid) in developing economies or high-risk regions, including war zones, where there is risk of government default or intervention. Such insurance is called confiscation, expropriation, nationalization, and deprivation (CEND) insurance.

How much data do these insurers have for such policies? How many data points are there for civil wars in any country? There may be many data points for product promotions, but isn't every product promotion different? We will see later that quantitative methods are useful in many areas even where there is much complexity, a lot of unknown unknowns, and an apparent lack of data.

We have only scratched the surface of a comprehensive list of the main fallacies, misconceptions, and cognitive obstacles to understanding risks and risk management methods. I was recently talking to a government agency manager about quantitative methods for risks of certain kinds of terrorist attacks. The manager said, “We can't compute the odds of an event that never happened.” That was from an authoritative source, he said—a “respected PhD.” Yet, other respected PhDs go right on doing exactly that—they compute the odds of events that have never occurred. The nuclear power industry, for example, uses quantitative models to assess the odds of 1-in-100-year or even 1-in-500-year events—which is, of course, much longer than the nuclear power industry has been in existence. The methods for doing this simply involve knowing the probabilities of failures of each component in a system (for which the industry has extensive historical failure data) and building quantitative models.

This is just one more example of what I'm sure is a very long list of illusionary obstacles to quantitative risk management. By the end of this book, I hope to overturn a few more of these misconceptions.

NOTES

 1. B. Dietvorst, J. Simmons, C. Massey, “Algorithm Aversion: People Erroneously Avoid Algorithms after Seeing Them Err,” Journal of Experimental Psychology: General 144, no. 1 (2015): 114–26.

 2. M. Gerson, “Michael Gerson: The Trouble with Obama's Silver Lining,” Washington Post (November 5, 2012).

 3. N. Silver, “How I Acted Like a Pundit and Screwed Up on Donald Trump,” www.FiveThirtyEight.com (May 18, 2016).

 4. M. Lewis, Moneyball (New York: W. W. Norton & Company, 2003).

 5. Paul E. Meehl, Clinical versus Statistical Prediction: A Theoretical Analysis and a Review of the Evidence (Minneapolis: University of Minnesota Press, 1954).

 6. Paul Meehl, “Causes and Effects of My Disturbing Little Book,” Journal of Personality Assessment 50 (1986): 370–75.

 7. R. M. Dawes, D. Faust, and P. E. Meehl, “Clinical versus Actuarial Judgment,” Science (1989), doi: 10.1126/ science. 2648573; William M. Grove and Paul E. Meehl, “Comparative Efficiency of Informal (Subjective, Impressionistic) and Formal (Mechanical, Algorithmic) Prediction Procedures: The Clinical-Statistical Controversy,” Psychology, Public Policy, and Law 2 (1996): 293–323; William M. Grove et al., “Clinical versus Mechanical Prediction: A Meta-Analysis,” Psychological Assessment 12, no. 1 (2000): 19–30.

 8. Philip E. Tetlock, Expert Political Judgment: How Good Is It? How Can We Know? (Princeton, NJ: Princeton University Press, 2006).

 9. N. Taleb, Antifragile: Things That Gain from Disorder (New York: Random House, 2012).

10. E. Gelman, “Fear of a Black Swan: Risk Guru Nassim Taleb Talks about Why Wall Street Fails to Anticipate Disaster,” Fortune (April 3, 2008).

11. E. Goode, “Paul Meehl, 83, an Example for Leaders of Psychotherapy,” New York Times (February 19, 2003).

12. N. Taleb, Antifragile: Things that Gain from Disorder (Incerto) (New York: Random House, 2014).

13. S. Paterson, “Mr. Volatility and the Swan,” Wall Street Journal Online (July 13, 2007).

14. D. Hubbard and Alicia L. Carriquiry, “Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance,” The American Statistician (March 2019).

15. The law of total probability requires that the probability weighted conditional probabilities of x must add up to the probability of x. We can write this as Pr(X)= Pr(X|T) Pr(T)+Pr(X|Not T) Pr(Not T)=(.1)(.7)+(.9)(A)=.2. Solving for A, we get 0.144, which is less than 0.2. In any simple case with just two conditions (in this case, having threat T and not having threat T), if one condition increases a probability, then the other must decrease it in order for the total probability equation to balance. For further reading, see www.howtomeasureanything.com/riskmanagement for a spreadsheet explanation of this problem.

16. C. C. Jaeger, O. Renn, and E. A. Rosa, Risk, Uncertainty, and Rational Action (London: Earthscan, 2001).

CHAPTER 10
Where Even the Quants Go Wrong: Common and Fundamental Errors in Quantitative Models

There is perhaps no beguilement more insidious and dangerous than an elaborate and elegant mathematical process built upon unfortified premises.

—THOMAS C. CHAMBERLAIN, GEOLOGIST (1899)

In theory there is no difference between theory and practice. In practice, there is.

—YOGI BERRA

When it comes to improving risk management, I admit to being a bit biased in favor of quantitative methods in the assessment, mitigation, or deliberate selection of risks for the right opportunities. I think the solution to fixing many of the problems we've identified in risk management will be found in the use of more quantitative methods—but with one important caveat. In everything I've written so far, I've promoted the idea that risk management methods should be subjected to scientifically sound testing methods. Of course, we should hold even the most quantitative models to that same rigor. They get no special treatment because they simply seem more mathematical or were once developed and used by highly regarded scientists. Even though in the previous chapter I criticize a lot of what Nassim Taleb says, this is where we are in total agreement.

The idea that the mere use of very sophisticated-looking mathematical models must automatically be better has been called crackpot rigor (recall the discussion of this term in chapter 8) and a risk manager should always be on guard against that. Unfortunately, the rapid growth in the use of sophisticated tools has, in many cases, outpaced the growth in the skills to use these tools and the use of questionable quantitative methods seems to be growing out of hand.

Science has evolved to its current advanced state because some scientists have always questioned other scientists, and even widely accepted scientific ideas could never, in the long run, withstand contradictory findings in repeated, independent tests. This chapter is an attempt to apply the same skepticism we've applied to the risk matrix to more quantitative methods in risk assessment and risk management.

A SURVEY OF ANALYSTS USING MONTE CARLOS

Remember, the one-for-one substitution model mentioned in chapter 4 is an example of a Monte Carlo simulation. It is just a very limited form of a Monte Carlo simulation focusing on risks. But Monte Carlos can address questions beyond disastrous losses and consider uncertainties about the opportunities in decisions such as whether to pursue a new product or increase the capacity of a factory. We can apply them to entire portfolios of software projects, R&D, and other investments so that we can prioritize them on the basis of risk and return. To see an example of how a Monte Carlo can be applied to another category of decisions, go to www.howtomeasureanything.com/riskmanagement to download an Excel-based simulation applied to a capital investment decision.

PC-based Monte Carlo simulation tools have been widely used for decades. The Monte Carlo tools @Risk and Crystal Ball, were released in the late 1980s, while I was still writing bespoke Monte Carlo simulations using Fortran, BASIC, and even the Lotus 123 spreadsheet. By the 1990s Excel-based versions of these tools were introduced and the user base was growing quickly.

As the sales of these tools were increasing, so was the possibility of misuse. In 2008, I conducted a survey to see if this was the case. Using a list of simulation conference attendees, I recruited thirty-five users of @Risk and Crystal Ball for a survey of their work. Each of these users was asked for details about the last one to three Monte Carlo models they constructed. Data for a total of seventy-two individual Monte Carlo models was gathered (an average of just over two models per user).

The modelers in the survey claimed to be fairly experienced on average. The average years of experience were 6.2 and the median was just 4 years (this skewed distribution is due to the fact that a few people had over 15 years of experience but there were many at the bottom end of the scale). Most of the models were not terribly complicated—73 percent had fewer than fifty variables. Those surveyed worked on a variety of Monte Carlo applications including the following:

Business plans

Financial portfolio risks

Sales forecasts

Information technology projects

Mining and oil exploration

Pharmaceutical product development

Project schedule and budget forecasts

Engineering and scientific models such as radar simulations and materials strength

Competitive bidding

Capital investments in the steel industry

Alternatives analysis on supply chains and inventory levels

Building construction risks

Product variations in manufacturing

I asked them questions about where they got their data from and about quality control on their models. Here is what I found:

There were a lot of subjective estimates but no calibration of probabilities. An overwhelming majority of those surveyed—89 percent—used some subjective estimates in models. On average, the percentage of variables in all models that were subjective estimates was 44 percent. However, not one of the modelers ever used—or had even heard of—calibration training. As discussed in chapter 7, this would mean that almost all estimates were overconfident and all of the models understated risks. In fact, the most uncertain variables that had bigger impacts on the output were the most likely to rely on expert estimates.

When I asked about validating forecasts against reality, only one respondent had ever attempted to check actual outcomes against original forecasts. This question produced a lot of hand-waving and carefully qualified statements from the other respondents. The one person who claimed he did do some validation of original forecasts could not produce the data for it. Instead, he offered only anecdotal evidence.

Although 75 percent of models used some existing historical data, only 35 percent of the models reviewed used any original empirical measurements gathered specifically for the model. Furthermore, only 4 percent ever conducted an additional empirical measurement to reduce uncertainty where the model is the most sensitive. In contrast, I find that, based on sensitivity analysis and computing the value of further measurements, all but three of the over 150 models I've personally developed in the last twenty years required further measurement. It appears that most modelers assume that they can model only on subjective estimates and the existing data they are given. The idea of conducting original empirical research is almost completely absent from Monte Carlo modeling.

I could have made the sample in this survey a much larger sample if I had included the clients I had trained myself, but I didn't want to bias the sample by including them. However, when I asked those I trained about models they built before I met them, the results were the same. Of those who did build quantitative models based even partly on subjective estimates, none had used calibration training in their organizations prior to the training they did with us. This includes large groups of economists and statisticians who routinely performed Monte Carlo simulations on a variety of critical government policy decisions and major technology and product development projects.

Since this first survey in 2008, I've conducted other surveys regarding project management, cybersecurity, and enterprise risk management (ERM). I introduced some of the findings of these surveys in chapter 2. In each of these cases I asked whether they were using Monte Carlo simulations or other quantitative methods, such as Bayesian networks, statistical regression, and so on. Of the minority of those in project management who use Monte Carlos, I still find that subject matter experts are the main source of input but that calibration training still does not occur most of the time (only one in six Monte Carlo users in project management said they used calibrated estimators).

Again, the subsequent research showed that the adoption of quantitative tools may be outpacing the knowledge of how to use them correctly. Recall that in the 2015 cybersecurity survey we asked respondents a set of questions regarding basic literacy in probabilistic methods. Those who said they used Monte Carlo tools, Bayesian networks, or historical regression did not, on average, perform better than other respondents on statistical literacy questions.

We also see some indications that the concept of statistical significance, as explained in the previous chapter, may be misapplied in quantitative decision models. Although we didn't ask this question directly in any of the surveys, some of those who said they used sampling methods and controlled experiments to inform their models indicated in free-form responses how they sought measures of statistical significance. This is worth further investigation, but it agrees with some anecdotal observations I've made in consulting as well as the observations of many statisticians I met at the American Statistical Association (ASA). Statistical significance alone cannot tell us, for example, the probability that a new drug works or that a new training program improves customer satisfaction. As explained in the last chapter, a result at the .05 significance level is not the same as a 95 percent chance that the hypothesis is true, but at least some quantitative models appear to be using the results of significance tests this way.

Of course, we shouldn't necessarily extrapolate findings in a cybersecurity survey to other fields, and we certainly shouldn't conclude too much from anecdotes and a few free-form responses in surveys. But we should at least consider the possibility that the lack of a conceptual foundation to use popular quantitative tools properly is a problem in project management, finance, supply chain, and other areas of risk assessment. Just because someone is using a tool doesn't mean what they build with it makes sense.

THE RISK PARADOX

Jim DeLoach at the risk management consulting firm Protiviti observed, “Risk management is hopelessly buried at the lowest levels in organizations. I see risk analysis focus on the chance that someone will cut off a thumb on the shop floor.” The paradox in risk management that I've observed anecdotally over the years, and that seems to be observed by many risk experts I talk to, is that there is a significant misalignment between the importance of a risk and the amount of detailed, quantitative analysis it receives.

THE RISK PARADOX

The most sophisticated risk analysis methods used in an organization are often applied to low-level operational risks, whereas the biggest risks use softer methods or none at all.

My standard anecdote for this risk paradox comes from the 1990s when I was teaching a seminar on my applied information economics (AIE) method to what I thought was an audience of chief information officers (CIOs) and IT managers. I asked if anyone had applied Monte Carlo simulations and other quantitative risk analysis methods. This was almost entirely a rhetorical question because I had never seen anyone raise a hand in any other seminar when I asked that question. But this time, one manager—from the paper products company Boise Cascade—raised his hand.

Impressed, I said, “You are the first CIO I've ever met who said he used Monte Carlo simulations to evaluate risks in IT projects.” He said, “But I'm not a CIO. I'm not in the IT department, either. I analyze risks in paper production operations.” I asked, “In that case, do you know whether they are used in your firm on IT projects?” He responded, “No, they are not used there. I'm the only person doing this in the firm.” I then asked, “Which do you think is riskier, the problems you work on, or new IT projects?” He affirmed that IT projects were much riskier, but they received none of his more sophisticated risk analysis techniques. Here are just a few more examples of the risk paradox:

As mentioned in chapter 3, Baxter, similar to many other pharmaceutical companies, uses quantitative risk models on stop-gate analysis—the assessment of the decision to move ahead to the next big phase in the development of a new product. The reason sophisticated methods are justified for that problem is the same reason they are justified in oil exploration—it is a large capital outlay with a lot of uncertainty about the return. But legal liabilities, like the heparin case described in chapter 3, may turn out to be much larger than the capital investments in the next phase of a new drug.

During and before the 2008 financial crisis, banks that routinely did some quantitative risk analysis on individual loans rarely did any quantitative risk analysis on how economic downturns or system-wide policies would affect their entire portfolio.

Long-term capital management (LTCM) used the Nobel Prize–winning options theory to evaluate the price of individual options, but the big risk was the extent of the leverage they used on trades and, again, how their entire portfolio could be affected by broader economic trends.

Insurance companies use advanced methods to assess the risks accepted by insurance products and the contingent losses on their reserves, but major business risks that are outside of what is strictly insurance get little or none of this analysis—as with AIG and their credit default swaps.

There are some risk analysis methods that have been applied to the risks of cost and schedule overruns for IT projects, but the risks of interference with business operations due to IT disasters are rarely quantified. A case in point is the enterprise resource planning (ERP) system installed at Hershey Foods Corp. in 1999. Meant to integrate business operations into a seamless system, the ERP project was months behind and the cost ran up to $115 million. They attempted to go live in September of that year but, over their all-important Halloween season, they were still fixing problems with order processing and shipping functions of the system. Business was being lost to competitors and they posted a 12.4 percent drop in revenue. This risk was much greater than the risk of the ERP cost overrun itself.

This sequestration of some of the best risk analysis methods causes problems with the further evolution of risk management. The relative isolation of risk analysis in some organizations means that different analysts in the same organization may work in isolation from each other and build completely inconsistent models. And the lack of collaboration within firms makes another important step of risk management almost impossible—a cooperative initiative to build models of industrial economics and global risks across organizational boundaries (more on that in the last chapter of the book).

Too Uncertain to Model Quantitatively?

Perhaps the risk paradox is partly a function of some persistent confusion I mentioned in previous chapters. There is a culture among some otherwise-quantitative modelers of excluding things from risk analysis because they are uncertain.

I once spoke with the head of a university interdisciplinary group, which she called a collaborative for modeling risks. She mentioned that this particular issue caused strain among the team. The director of this interdisciplinary effort described some of her frustration in dealing with what she called the modelers. She explained that “modelers are saying that because we can't estimate the actions of people, we have to leave those variables out.” I thought this was odd because as a modeler I routinely include so-called “people variables.” When I model the risk and return of implementing some new information technology in a firm, I often have to include uncertainties such as how quickly users will begin to effectively use the new technology. I've even made models that include uncertainties about whether particular bills would pass in Congress or the action of Saddam Hussein's forces in Iraq.

I came to find that when she said modeler she was talking about a group of bridge construction engineers who, for some reason, put themselves in charge of building the Monte Carlo simulations for the risks the group assessed. To the engineers, only variables about the physical parameters of the bridge seemed real enough to include. Those whom the director referred to as the modelers and non-modelers didn't talk to each other, and there were people on her staff who had what she called a professional divorce over this. In her world, modelers are typically coming from engineering and hard sciences, and non-modelers are coming from political science, sociology, and so on. Non-modelers are arguing that you have to put in the people variables. Modelers are saying that because (they believe) they can't measure the people variables, they have to leave them out of the model. The modelers are saying the important things are the tensile strength of materials and so on.

This presents two important issues. First, why would one group of subject matter experts (SMEs) presume to be in charge of building the Monte Carlo model as opposed to some other group of SMEs? I would generally see engineers as just one other type of SME involved in a modeling issue that requires multiple types of SMEs. But more to the point, why leave something out because it is uncertain? The whole point of building a Monte Carlo model is to deal with uncertainties in a system. Leaving out a variable because it is too uncertain makes about as much sense as not drinking water because you are too thirsty.

A similar exclusion of variables that are considered “too uncertain” sometimes happens in models made for oil exploration. When analysts estimate the volume of a new oil field, they build Monte Carlo simulations with ranges for the area of the field, the depth, the porosity of the rock, the water content, and so on. When they run this simulation, they get a range of possible values for how much oil is in the field. But when it comes to modeling one of the most uncertain variables—the price of oil—they sometimes don't use ranges. For the price of oil, they may use an exact point.

The reason, I've been told, is that the geologists and scientists who run the Monte Carlos are either too uncertain about the price or that management simply gives them an exact price to use. But this means that when management is looking at the analysis of an oil exploration project, they really aren't looking at the actual risks. They are looking at a hybrid of a proper risk analysis based on ranges and an arbitrary point estimate. They undermine the entire purpose of the Monte Carlo.

They further violate the output of a Monte Carlo in other ways. Sometimes, analysts producing Monte Carlos are told to collapse their perfectly good distributions to a single point for “accounting purposes.” You can't give them the range that represents your uncertainty—so you're told—so you have to pick one number. If you have an oil field that has somewhere between two and six billion barrels, should you tell the investors it has exactly four billion?

The executives know that the cost of overestimating the amount of oil in their reserves can be much higher than the cost of underestimating reserves. So, because they would rather underestimate than overestimate, they tend to pick a number that's in the lower end of the range. Steve Hoye, prior to starting his job at Crystal Ball, was in the oil business for twenty years starting in 1980. As a young geophysicist, he saw this firsthand. In an email communication with me, he pointed out other incentives that affect how distributions are converted to points:

There are benefits to underestimating and sometimes serious consequences for overestimating. Shell had a 20 percent write down in 2004 on their reserves. They had to go back to investors and tell them they didn't have as much reserves as they thought. It's a great study in the cost of being wrong. In Texaco, where I worked, they had a big write down in the 1970s and senior management was reshuffled as a result.

The tendency to conservatively underestimate is, therefore, understandable. But now imagine every manager is doing this for every oil field. One study found that, because of the practice of systematically converting distributions to conservative points and then adding the points together, oil reserves are systematically underestimated.¹

One study found that, because of the practice of systematically converting distributions to conservative points and then adding the points together, oil reserves are systematically underestimated.

Usually, big oil does a good job of quantifying risks. As Hoye puts it, “There are enormous risks in oil, huge capital outlays, and multiple years before a payoff. The success rates are one-in-eight in exploratory projects. And that's the good rate.” But the strong incentive to model risks well may be undercut when the results are communicated. “Oil companies are dealing with an asset they cannot touch, but they have to make public pronouncements of the value of these assets,” says Hoye. Perhaps the best way to deal with it is to share the actual uncertainty of the distribution with investors. A range has a chance of being right whereas a point estimate will almost always be wrong.

John Schuyler with Decision Precision is another longtime expert at Monte Carlo simulations for oil exploration who sometimes sees odd hybrids between deterministic and stochastic models. He observes, “Many people might run a Monte Carlo, take the mean and put it in a deterministic model or reduce [the ranges] to ‘conservative’ or ‘optimistic’ points … All of this is coming up with a horribly contrived result.” Schuyler adds, “All that good Monte Carlo simulation upstream is kind of going to waste.”

This attitude of excluding uncertainties because they are too uncertain is pervasive in many industries. In mid-2008, I had a lengthy discussion with an economist who made a living doing business case analyses for luxury home developments. He indicated that his business was not going to be affected much by strains on the mortgage system because, he claimed, the high-end houses and second home market were less affected.

Although he was familiar with Monte Carlo simulations, I was very surprised to learn that, even with the risks and uncertainties in real estate, he conducted a deterministic, fixed-point analysis of the developments. I said risk has to be a major component of any real estate development investment and he would have to include it somehow. His position was that it would be too difficult to determine ranges for all the variables in his models because he just didn't have enough data. He saw no fundamental irony in his position: because he believed he didn't have enough data to estimate a range, he had to estimate a point.

This is based on the same misconception about precision and probabilities I discussed regarding scoring models. If modelers exclude something because it is more uncertain than the other variables, they will invariably exclude some of the most important sources of risks in a model. Taken to the extreme, some analysts exclude probabilistic models altogether and choose models based on point estimates. Until we can begin to see that probabilistic models are needed exactly because we lack perfect information, we will never be able to conduct a meaningful risk analysis.

“Too Unique” to Model Quantitatively?

Obviously, “too unique” or “very unique” are oxymorons, because something is either unique or not and there cannot be levels of uniqueness. But such terms are invoked to make a case for another imagined obstacle to the use of more empirical methods. It is the belief that separate events are so unusual that literally nothing can be learned about one by looking at another. It is said that each IT project, each construction project, each merger is so special that no previous event tells us anything about the risks of the next event. This would be like an insurance company telling me that they cannot even compute a premium for my life insurance because I'm a completely unique individual.

Although we know insurance companies don't let that stand in the way of good risk analysis, many other fields are not immune to this misconception. Even some scientists, such as geologists who study volcanoes (volcanologists), seem to have woven this into their culture. This is the very reason why the risk of a catastrophic eruption of Mount St. Helens in 1980 was ignored by volcano experts. (See The Mount St. Helens Fallacy box.)

THE MOUNT ST. HELENS FALLACY

Fallacy: If two systems are dissimilar in some way, they cannot be compared. In effect, this fallacy states that if there are any differences at all, there can be no useful similarities.

On May 18, 1980, Mount St. Helens in the Cascade Range of Washington State exploded, in the most destructive volcanic event in US history. More than fifty people were killed, 250 homes were destroyed, and more than two hundred square miles of forest was leveled.

Prior to the eruption, rising magma had formed a bulge on the north side that protruded so far it became unstable. At 8:32 a.m. the huge bulge slid off and uncorked the magma column resulting in a lateral eruption (meaning it erupted out of one side).

Scientists who previously studied the volcano found no geological evidence that a large lateral explosion had ever occurred on Mount St. Helens before … and therefore ignored the possibility. As US Geological Survey geologist Richard Hoblitt stated, “Before 1980, the volcanic-hazards assessments for a given volcano in the Cascade Range were based on events that had previously occurred at that volcano. The 1980 directed blast showed that unprecedented events are possible and that they need to be considered.”²

Scientists had to ignore even the basic physics of the system to conclude that, because it had not happened before, it could not happen now. There is no way the bulge could have been stable and so a landslide had to release pressure. Hopefully, unprecedented events are now considered systematically, but that message has not sunk in for everyone. In a Discovery Channel special on volcanoes, one volcanologist said, “No two volcanoes are exactly alike. So in order to study a volcano you really have to study the history of that volcano.” Put another way, this is Taleb's turkey—by looking at that turkey it would never be apparent that it's about to be killed. We only know this from looking at the history of other turkeys.

But, actually, looking at other volcanoes does tell us something about a particular volcano. If not, then what exactly is the expertise of a volcano expert? I might also call this the fallacy of close analogy. That is, the belief that unless two things are identical in every way, nothing learned from one can be applied to the other. Think about it: our experience is almost always based on learning fundamental principles learned from situations that were not exactly identical to situations we apply them to. If we cannot infer fundamental principles that apply to many things by observing a few less-than-perfectly-identical things, then none of our experience matters.

Indeed, from a risk analysis point of view, volcanoes not only have something in common with other volcanoes but also they have a lot in common with completely different categories of events. As we will see next, there is something in common even among diverse events such as forest fires, power outages, wars, and stock markets.

FINANCIAL MODELS AND THE SHAPE OF DISASTER: WHY NORMAL ISN'T SO NORMAL

I spent part of the last chapter describing what I believe to be errors in the argument of Nassim Taleb, but I also pointed out that he is absolutely correct on other key points. He points out (as have quite a few economists) that many of the most lauded tools in finance, especially some of those that won the Nobel, are based on some assumptions that we know to be false by simple observation. Nobel Prize–winning theories such as options theory and modern portfolio theory assumed (at least initially) a particular distribution of potential returns and prices that make extreme outcomes appear much less likely than we know them to be. These theories use an otherwise-powerful tool in statistics and science known as a Gaussian or normal probability distribution, such as the one shown in exhibit 10.1.

The normal distribution is a bell-shaped symmetrical probability distribution that describes the output of some random or uncertain processes. The bell shape means that outcomes are more likely to be near the middle and very unlikely at the tails. The shape can be fully described by just two dimensions—its mean and standard deviation. Because this is a symmetrical and not a skewed (i.e., lopsided) distribution, the mean is dead center. The standard deviation represents a kind of unit of uncertainty around the mean.

EXHIBIT 10.1 The Normal Distribution

SIMPLE RANDOM SURVEY EXAMPLE USING A NORMAL DISTRIBUTION

If you haven't thought about normal distributions lately, here is a very simple example. The math for this and a more detailed explanation can be found at http://www.howtomeasureanything.com/riskmanagement.

Normal distributions are useful for showing the error in a random sample. If a random survey of commuters says drivers on average spend twenty-five minutes each way in a commute to work, then that means the average of all the responses in the survey is twenty-five minutes. But to determine how far from reality this survey result could be, the standard deviation of the error of the estimate is computed, which can then be used to determine a range with a given confidence. To communicate how far off the mean of the survey might be from reality (which he could only know if one surveyed all commuters), the statistician often computes a confidence interval (CI)—a range that probably contains the real average of the entire population of commuters.

The width of this range is directly related to the standard deviation. Let's say the statistician determines the standard deviation of the error of the estimate is two minutes and that he decides to show this range as a 90 percent confidence interval (meaning he is 90 percent confident that the range contains the true answer). By referencing a table (or an Excel function), he knows the upper bound of a 90 percent CI is 1.645 standard deviations above the mean and that the lower bound is 1.645 standard deviations below the mean. So he computes a lower bound of 25 − 1.645 × 2 = 21.71 and an upper bound of 25 + 1.645 × 2 = 28.29. Voilà, the survey shows with 90 percent confidence that the average commute is between 21.7 minutes and 28.3 minutes.

The normal distribution is not just any bell shape, but a very particular bell shape. If you are saying that the distribution of hits around a bulls-eye of a target on a firing range is normal, then you are saying that—after a sufficiently large number of shots—68.2 percent of the shots land within one standard deviation of the center, 95.3 percent are within two standard deviations, 99.7 percent are within three, and so on. But not all distributions exactly fit this shape. To determine whether a normal distribution is a good fit, statisticians might use one of the mathematical goodness-of-fit tests, such as the Chi-square test or the Kolmogorov-Smirnov test (K-S test). This test may be a popular, but probably irrelevant, for distributions used in risk analysis.

The main concerns for risk analysts are at the tails of the distributions, and some goodness-of-fit tests, such as the K-S test, are insensitive to how “fat” the tails are. I mentioned in chapter 9 how this might not work well. If we apply the normal distribution to Dow Jones daily price changes from 1928 to 2008, we would find a standard deviation of about 1.157 percent for a daily price change (as a percentage relative to the previous day). Because the bounds of a 90 percent CI are 1.645 standard deviations away from the mean, that means that about 90 percent of daily price changes would be within 1.9 percent of the previous day. In reality, about 93 percent fell within this range, but it's close. But when we get further out from the average trading day, the normal distribution drastically understates the likelihood of big drops. As first mentioned in chapter 9, a normal distribution says that a 5 percent price drop from the previous day should have had a less than 15 percent chance of occurring even once during that eighty-year period whereas in reality, it happened seventy times.

But, because the K-S test focuses on the main body of the distribution and is insensitive to the tails, an analyst using it would have determined that normal is a pretty good assumption on which to base a financial model. And for a risk analyst who worries more about the tails, it is wrong by not just a little, but a lot. With the Dow Jones data, the likelihood of even more extreme events—such as a 7 percent single-day price drop—will be underestimated by a factor of a billion or more. Note that this distribution is the basic assumption, however, for the Nobel Prize–winning theories of modern portfolio theory and options theory—two very widely used models. (Note: A technical person will point out that absolute price changes are actually the lognormal cousin of a normal distribution, but because I expressed the data in terms of price changes as a ratio relative to the previous day, I can apply the normal distribution.)

What shape do financial crashes really take? It turns out that financial disasters take on a distribution more similar to the distribution of volcanic eruptions, forest fires, earthquakes, power outages, asteroid impacts, and pandemic viruses. These phenomena take on a power-law distribution instead of a normal distribution. An event that follows a power law can be described as following a rule like this: “A once-in-a-decade event is x times as big as a once-in-a-year event,” where x is some ratio of relative severity. If we plot events such as these on a log/log scale (where each increment on the scale is ten times greater than the previous increment), they tend to look like straight lines. In exhibit 10.2 you can see the power-law distribution of fatalities due to hurricanes and earthquakes. In the case of earthquakes, I also show the magnitude measurement (which is already a log-scale—each increment indicates an earthquake ten times more powerful than the previous increment).

From the chart, you can see that power-law distributions are closely represented by a straight line on a log-log chart of frequency versus magnitude. A once-in-a-decade worst-case earthquake would kill about one hundred people. That's about ten times the damage of an earthquake that happens about every year. This means that x in the rule would be ten in this case. The same ratio applies as we move further down the line. An earthquake that would kill a thousand people (in the United States only) is a once-in-a-century event.

EXHIBIT 10.2 Power-Law Distributions of Hurricane and Earthquake Frequency and Severity

Many of the systems that seem to follow power-law distributions for failures are the kinds of stressed systems that allow for both common mode failures and cascade failures. Forest fires and power outages, for example, are systems of components in which a single event can affect many components and in which the failures of some components cause the failures of other components. Hot, dry days make everything more likely to burn and one tree being on fire makes its neighbors more likely to catch fire. Peak energy use periods strain an entire power grid and power overloads in one electrical subsystem cause strain on other subsystems.

Unfortunately, many of the systems that matter to business have a lot more in common with power grids and forest fires than with systems best modeled by normal distributions. Normal distributions apply best to problems in which, for example, we want to estimate a mean in a system with a large number of individual and independent components. If you want to estimate the proportion of heads you will get in a thousand flips of a coin, the normal distribution is your best bet for modeling your uncertainty about the outcome. But financial markets, supply chains, and major IT projects are complex systems of components in which each of the following occurs.

Characteristics of Systems with Power-Law Distributed Failures

The entire system can be stressed in a way that increases the chance of failure of all components, or the failure of one component causes the failure of several other components, possibly in parallel (i.e., a common mode failure).

The failure of those components in a system start a chain reaction of failures in series (cascade failure).

The failure of some components creates a feedback loop that exacerbates the failures of those components or other components (positive feedback).

Taleb points out that applying the normal distribution to markets seems to be a bad idea. Using this distribution, a one-day drop of 5 percent or greater in the stock market should have been unlikely to have occurred even once since 1928. I looked at the history of the Dow Jones index from 1928 to the end of 2008 and found that, instead, such a drop occurred seventy times—nine times just in 2008. We will also be discussing this more, later in the book. Models have to be tested empirically, regardless of how advanced they appear to be. Just because a quantitative model allegedly brings “rigor” to a particular problem (as the Nobel Prize committee stated about one award), that is no reason to believe that it actually works better than an alternative model.

Various fund managers have said that fluctuations in 1987 and 2008 were an extreme case of bad luck—so extreme that they were effectively far more unlikely than one chance in a trillion-trillion-trillion.³ If there is even a 1 percent chance they computed the odds incorrectly, bad math on their part is far more likely. In this case, the fact the event occurred even once is sufficient to cause serious doubt about the calculated probabilities.

Let's look at how close the history of the financial market is to the power laws. Exhibit 10.3 shows how the frequency and magnitude of daily price drops on the S&P 500 and Dow Jones Industrial Average (DJIA) appear on a log-log chart. The solid lines show actual price history for the two indices and the dashed lines show the Gaussian approximation of them. In the range of a drop of a few percentage points, the Gaussian and historical distributions are a moderately good match. For both indices, price drops of 1 percent are slightly overstated by the Gaussian distribution and between 2 percent and 3 percent price drops, the historical data matches Gaussian. The K-S test would look at this and determine that the normal distribution is close enough. But once the price drops get bigger than about 3 percent from the previous day's closing price, the two distributions diverge sharply.

EXHIBIT 10.3 Frequency and Magnitude of Daily Price Drops in the S&P 500 and DJIA (Log-Log Chart)

Clearly, the real data from either index looks a lot more like the downward-sloping straight lines we see on the log-log frequency and magnitude charts for hurricanes and earthquakes. The more strongly curving normal distribution applied to the same data indicates here that the normal distribution of these price drops would put a 6 percent or greater drop in a single day at something less frequent than a one-in-ten-thousand-year event.

In the actual data a price drop that large has already occurred many times and probably would occur at something closer to once every few years. After the 1987 crash, when both indices lost more than 20 percent in a single day, some analysts claimed the crash was something on the order of a once-in-a-million-year event. The power law distribution puts it closer to once in a century or so. Or, to put it another way, it has a reasonably good chance of occurring in a lifetime.

Although I'm a booster for the firms that developed powerful tools for Monte Carlo, some of the most popular products seem to have one major omission. Of all the wide assortment of distribution types they include in their models, most still do not include a power-law distribution. But they aren't hard to make. I included a simple random power-law generator in a spreadsheet on www.howtomeasureanything.com/riskmanagement.

Another interesting aspect of stressed-system, common-mode, cascade failures in positive feedback cycles is that if you model them as such, you may not even have to tell the model to produce a power-law distribution of failures. It could display this behavior simply by virtue of modeling those components of the system in detail. Computer models of forest fires, flu epidemics, and crowd behavior show this behavior naturally. The use of the explicit power law should still be required for any model that is a simple statistical description of outputs and not a model of underlying mechanisms. Therefore, financial models either will have to replace the normal distribution with power-law distributions or they will have to start making more detailed models of financial systems and the interactions about their components.

FOLLOWING YOUR INNER COW: THE PROBLEM WITH CORRELATIONS

Many systems we want to model are like herds of cattle—they tend to move together but in irregular ways. Cattle do not move together in any kind of formation like marching soldiers nor do they move entirely independently of each other like cats. Trying to describe the way in which one cow follows another with one or two numbers—such as “ten feet behind”—is sure to leave out a lot of complexity. Yet, this is exactly what is done in many quantitative risk models.

When two variables move up and down together in some way we say they are correlated. Correlation between two sets of data is generally expressed as a number between +1 and −1. A correlation of 1 means the two variables move in perfect harmony—as one increases so does the other. A correlation of −1 also indicates two perfectly related variables, but as one increases, the other decreases in lockstep. A correlation of 0 means they have nothing to do with each other.

The four examples of data in exhibit 10.4 show different degrees of correlation. The horizontal axis could be the Dow Jones and the vertical axis could be your revenues. Or the horizontal axis could be a number of mortgage defaults and the vertical axis could be unemployment. They could be anything we expect to be related in some way. But it is clear that the data in the two axes in some of the charts is more closely related than the data in other charts. The chart in the upper-left-hand corner is just two independent random variables. The variables have nothing to do with each other and there is no correlation. In the lower-right-hand corner, you can see two data points that are very closely related.

EXHIBIT 10.4 Examples of Correlated Data

Correlated random numbers are not difficult to generate given a coefficient of correlation. We can also use a simple formula in Excel (= correl()) to compute the correlation between two data sets. See the spreadsheet at www.howtomeasureanything.com/riskmanagement for simple examples that both generate correlated numbers and compute correlations among given data. Tools such as Crystal Ball and @Risk enable the modeler to specify correlations among any combination of variables.

Remember, correlations are just another level of detail to add to a quantitative model, and excluding them doesn't mean you are better off with a qualitative risk matrix model. Whether you can ever capture all the correlations is not a reason to stick with a risk matrix over even a simple quantitative model. After all, risk matrices have no way to explicitly include correlations even if you wanted to include them—with quantitative models you at least have that choice.

Having said that, modelers should be aware that excluding important correlations will almost always lead to a systematic underestimation of risks. If you are considering the risks of a construction project and you build a Monte Carlo with ranges for detailed costs for each part of a major facility, you might find that these costs may be correlated. If the costs of one part of the building rise, it is probably for reasons that would affect the costs of all parts of the multibuilding facility. The price of steel, concrete, and labor affects all of the buildings in a facility. Work stoppages due to strikes or weather tend to delay all of the construction, not just one part.

If the costs of different buildings in a facility were being modeled as independent variables, extremes tend to average out - like rolling a dozen dice. It would be unlikely for a dozen independent variables to all move up and down together by chance alone. But if they are correlated at all, then they do tend to move up and down together, and the risks of being over budget on one building are not necessarily offset by another building being under budget. They tend to all be over budget together.

Correlation significantly increases the risks, but even the savviest managers will ignore this. In a January 15, 2008, press release from Citigroup, CEO Vikrim Pandit explained the reported $9.83 billion loss for the fourth quarter of 2007: “Our financial results this quarter are clearly unacceptable. Our poor performance was driven primarily by two factors [emphasis added]—significant write-downs and losses on our sub-prime direct exposures in fixed income markets, and a large increase in credit costs in our U.S. consumer loan portfolio.”⁴

But these are not two independent factors. They are more like one factor. The housing market affects both of these. They would tend to move up and down together more often than not, and any risk model that treated them as independent significantly understated the risk. Another respected financial expert, Robert Rubin, Secretary of the Treasury under Bill Clinton, described the 2008 financial crisis as “a perfect storm” and said, “This is an extremely unlikely event with huge consequences.”⁵ Perfect storm seems to imply the random convergence of several independent factors—which probably was not the case.

The other big error in correlations is not the exclusion of relationships among variables but modeling them with a single correlation coefficient. Consider the two data sets shown in exhibit 10.5. Although the movement of the vertical axis data with the horizontal axis data is obviously different in the two charts, the typical calculation of a correlation would give the same coefficient for both. The one on the right could be approximated by a single “best-fit” correlation and the error around it, but the one on the left is both more complex and more precise. If we tried to model correlations that are historically related in the way the left-hand chart shows by using a single correlation coefficient, the Monte Carlo would generate something that looks like the chart on the right.

EXHIBIT 10.5 Same Correlation Coefficient, Very Different Patterns

A correlation is a gross approximation of the relationship between two variables. Often, the relationship between two variables is best described by a more complex system than a single number. It's like the difference between knowing someone's IQ and knowing how the brain actually works.

Furthermore, simple correlations are not even close to being constant and, because the reasons for their correlations are not known, the correlations change without warning. John Joseph, a commodity trading advisor and principal with Sema4 Group in Dallas, Pennsylvania, has found that currency correlations change suddenly even after years of what seems like a consistent correlation. He points out that the correlation between the British pound and the Japanese yen relative to the dollar was positive from 1982 until 2007.

Then it swung in one year from a +0.65 correlation to −0.1. Most analysts modeling currency risk based on a year's worth of data would state with high confidence the correlation between the yen and the pound and that it would probably continue. But in reality, they have no basis for this confidence because this level of analysis explains nothing about the underlying system.

There is an alternative to using that single coefficient as a basis for correlation. When we model our uncertainties about the construction costs of a facility, we know that the price of steel, other materials, and labor affects all of the costs of all of the buildings. This can be modeled explicitly without resorting to correlation coefficients, and it will be a much more realistic model. It is like basing risk analysis of Mount St. Helens on the physics of systems of rock structures, pressure, and gravity instead of basing it on just the history of that volcano. The types of models that would also show power-law distributed failure modes by explicitly modeling things such as common mode failures do not need to resort to the very rough approximation of a coefficient of correlation.

THE MEASUREMENT INVERSION

Consider a decision analysis model for a new product. You have uncertainties about the cost and duration of development, materials costs once production starts, demand in different markets, and so on. This would be just like a typical cost-benefit analysis with a cash flow but instead of exact numbers, we use probability distributions to represent our uncertainty. We can even include the probability of a development project failure (no viable product was developed and the project was cancelled) or even more disastrous scenarios such as a major product recall. Any of these variables could be measured further with some cost and effort. So, which one would you measure first and how much would you be willing to spend? For years, I've been computing the value of additional information on every uncertain variable in a model.

Suppose we ran ten thousand scenarios in a simulation and determined that 1,500 of these scenarios resulted in a net loss. If we decide to go ahead with this product development, and we get one of these undesirable scenarios, the amount of money we would lose is the opportunity loss (OL)—the cost of making the wrong choice. If we didn't lose money, then the OL was zero. We can also have an OL if we decide not to approve the product but then find out we could have made money. In the case of rejecting the product, the OL is the difference between the lease and the money we made on the widgets if we would have made money—zero if the equipment did not make money (in which case we were right to reject the idea).

The expected opportunity loss (EOL) is each possible opportunity loss times the chance of that loss—in other words, the chance of being wrong times the cost of being wrong. In our Monte Carlo simulation, we simply average the OL for all of the scenarios. For now, let's say that given the current level of uncertainty about this product, you still think the lease is a good idea. So we average all 1500 scenarios the OL was positive (we lost money) and 8500 scenarios where OL was zero (me made the right choice). Suppose we find that the EOL is about $600,000.

The EOL is equivalent to another term called the expected value of perfect information (EVPI). The EVPI is the most you would reasonably be willing to pay if you could eliminate all uncertainty about this decision. Although it is almost impossible to ever get perfect information and eliminate all uncertainty, this value is useful as an absolute upper bound. If we can reduce the $600,000 EOL by half with a market survey that would cost $18,000, then the survey is probably a good deal. If you want to see a spreadsheet calculation of this type of problem, go to this book's website at www.howtomeasureanything.com/riskmanagement.

This becomes more enlightening when we compute the value of information for each variable in a model, especially when the models get very large. This way we not only get an idea for how much to spend on measurement but also which specific variables we need to measure and how much we might be willing to spend on them. I have done this calculation for more than 150 quantitative decision models in which most had about fifty to one hundred variables (for a total of about 10,000 variables, conservatively). From this, I've seen patterns that still persist every time I add more analysis to my library. The two main findings are:

Relatively few variables require further measurement—but there are almost always some.

The uncertain variables with the highest EVPI (highest value for further measurement) tend to be those that the organization almost never measures, and the variables they have been measuring have, on average, the lowest EVPI.

I call this second finding the measurement inversion, and I've seen it in IT portfolios, military logistics, environmental policy, venture capital, market forecasts, and every other place I've looked.

THE MEASUREMENT INVERSION

The persistent tendency to focus on the least valuable measurements at the expense of those more likely to improve decisions.

It seems that almost everybody, everywhere, is systematically measuring all the wrong things. It is so pervasive and impactful that I have to wonder how much this affects the gross domestic product. Organizations appear to measure what they know how to measure without wondering whether they should learn new measurement methods for very-high-value uncertainties.

How does tendency toward a measurement inversion affect risk assessment and, in turn, risk management? Highly uncertain and impactful risks may tend to get much less analysis than the easier-to-list, mundane events. The possibility of existential risks due to a major product recall, corporate scandal, major project failure, or factory disaster get less attention than the listing of much more routine and less impactful events. Conventional risk matrices are often populated with risks that are estimated to be so likely that they should happen several times a year. I've even seen risks estimated to be 80 percent, 90 percent, or even 100 percent probable in the next twelve months. At that level, that is more of a reliable cost of doing business. Of course, cost control is also important but it's not the same as risk management. If it is something you routinely budget for, it might not be the kind of risk upper management needs to see in a risk assessment.

Also, as an analyst myself as well as a manager of many analysts, I can tell you that analysts are not immune to wanting to use a modeling method because it uses the latest buzzwords. Perhaps an analyst just recently learned about random forests, Bayesian networks, or deep learning. If she finds it interesting and wants to use it, she can find a way to make it part of the solution. The measurement inversion shows that our intuition fails us regarding where we need to spend more time reducing uncertainty in probabilistic models. Unless we estimate the value of information, we may go down the deep rabbit hole of adding more and more detail to a model and trying to gather data on less relevant issues. Periodically, we just need to back up and ask if we are really capturing the main risks and if we are adding detail where it informs decisions most.

IS MONTE CARLO TOO COMPLICATED?

One issue with the adoption of Monte Carlo–based methods for addressing risks is the concern that Monte Carlos are too complex. Even some of those who use fairly quantitative methods in other ways apparently see the Monte Carlo as abstruse.

A book published in 1997, Value at Risk, expressed one reservation about this “weakness” of the Monte Carlo method.⁶ After acknowledging that “Monte Carlo is by far the most powerful method to compute value at risk,” it goes on to say:

The biggest drawback of this method is its computational cost. If one thousand sample paths are generated with a portfolio of one thousand assets, the total number of valuation calculations amounts to 1 million. When full valuation of assets is complex this method quickly becomes too onerous to implement on a frequent basis.

I've been running Monte Carlo simulations on a variety of risk analyses since the 1980s and even more regularly since the mid-1990s. Most of my models had fifty or more variables, and I routinely ran fifty thousand scenarios or more. That's a total of 2.5 million individual values generated, conservatively, each time I ran a Monte Carlo. But I don't recall, even on the computers of the mid-1990s, a simulation taking much more than sixty minutes. And I was running on uncompiled Excel macros—hardly the best available technology. My laptop now has a processor that is hundreds of times faster than my 1994 PC and has thousands of times as much RAM. Sam Savage further improves these calculations speeds by using a fast distribution calculation that would run calculations such as that in seconds.

Think of how much additional computing power would really cost if you wanted faster simulations. If Monte Carlos are “by far the most powerful method” (with which I agree), how much better off would you be if you were managing a large portfolio slightly better? Would it justify spending a little more on a high-end PC? Spending money on computing power for just one machine used by your risk analyst is trivial for virtually any risk analysis problem that would justify hiring a full-time person.

Still, my team and my clients get by just fine with good computers running Excel. The idea that Monte Carlo simulations today are onerous at all is some kind of retro-vacuum-tube thinking. Steve Hoye agrees: “In the old days, Monte Carlo was a big mainframe, but now with Excel-based tools, those assumptions are no longer applicable.”

Aside from the computing power issue, the idea that it is just too complex is also unfounded. Hoye goes on to point out, “Some people will argue that Monte Carlos are justified only for special cases. I think a lot of people have a misperception that it is difficult to understand and academic, therefore it's in their best interest not to have to deal with it.” Every time I've seen analysts object to the use of Monte Carlo simulations, they were never talking from experience. In each case, they knew very little about the method and had no basis for judging whether it was too complex.

Complexity, after all, is relative. I've always stated that my most complex Monte Carlo models were always far simpler than the systems I was modeling. I would model the risks of a software development project with more than a million lines of code. My model was one big spreadsheet with fewer than a hundred variables. And it would take less time and money than even the most trivial parts of the project I was analyzing.

My most complex Monte Carlo models were always far simpler than the systems I was modeling.

For our purposes, the one-for-one substitution model in chapter 4 itself should be enough to address concerns about complexity. Even though it is applied to an extremely simple framework for risk assessment, it is a legitimate example of a Monte Carlo simulation. The math is all done for you. The only real challenge at this point is the nonquantitative issue of how you want to define your risks. In the last section of this book, we will provide some pointers on that, too.

NOTES

 1. “Have We Underestimated Total Oil Reserves?” New Scientist 198, no. 2660 (June 11, 2008).

 2. R. Carson, Mount St. Helens: The Eruption and Recovery of a Volcano (Seattle: Sasquatch Books, 2002), 69.

 3. Some analysts indicated that the crash of 1987 was 13 standard deviations from the norm. In a normal distribution, such an event is about one chance in about 10³⁹. Others indicated it was a 16 or 20 standard deviation event—one chance in 10⁵⁸ and 10⁸⁹, respectively.

 4. Vikram Pandit, Citigroup press release (January 15, 2008).

 5. Interview with Fareed Zakaria, CNN (October 26, 2008).

 6. P. Jorion, Value at Risk (Burr Ridge, IL: Irwin Professional Publications, 1997).

PART THREE
How to Fix It

CHAPTER 11
Starting with What Works

The most important questions of life are, for the most part, really only problems of probability.

—PIERRE SIMON DE LAPLACE (1812)

In part 2 of this book, we discuss the “why it's broken” part of the failure of risk management. So far, we have focused mostly on the problems with risk analysis, but, as stated previously, this is not simply conflating risk analysis with risk management. It should be clear that risk management must be informed by some type of assessment of risk. This is true regardless of whether some managers (and well-known authors) believe they are analyzing risks or managing risks at all.

We can't fix risk management if we don't fix risk analysis. We've discussed several problems with risk analysis and a little historical context for how the problems evolved. This included the following observations:

Different areas of risk management evolved very different solutions and most were narrowly focused (but some were much further from the mark than others).

Differences in the definition of risk and related concepts lead to confusion in the industry.

There are systematic problems with how experts assess uncertainties and risks.

Many popular solutions to risk analysis and risk management are actually worse than useless.

There are common conceptual obstacles to adopting better methods.

Even quantitative analysts are not immune to avoidable errors and, similar to the qualitative methods, do not usually measure their own performance.

What we need to change should be clear by now. Softer scoring methods and half-baked, hybrid deterministic methods are of no value—stop using them. Do not continue to use your previous methods while you make a gradual transition to better methods. Go cold turkey. Don't continue to use the previous methods in parallel with better methods simply because “that's what management understands.” Abandon them altogether. Do not hang onto an ineffectual method simply because it took time and money to develop and everyone is vested in it. Write it off as a complete loss. Any feeling that it was working was a placebo effect … a mirage. Adopt better methods now, or your risk management efforts will continue to be a failure. If you quit wasting effort in the methods I've spent much of this book debunking, you will more quickly be able to develop the replacement method.

Fortunately, explaining how to start fixing the problems will be simpler than explaining what is wrong with existing methods. For the parts of risk management that lie beyond risk analysis, I'll also offer suggestions that will help support the organization, implementation, and desired scope of risk analysis. Think of risk management as initially simple but evolving over time.

The Three Parts to Improving Risk Management (The Final Three Chapters of This Book)

Start simple but better: In this chapter, we will show why just doing the math like we do in the one-for-one substitution is an improvement over intuition or the popular soft methods such as risk matrices. We will show how even subjective estimates of probabilities can be improved and we will explain some very simple empirical methods for estimating risks. We will wrap up this chapter with just a few considerations for using the one-for-one substitution properly.

Continuously improve: In chapter 12 we will give a high-level review of ways to move beyond the one-for-one substitution. This will consist of measuring the performance of the model itself and a cursory review of several more advanced modeling methods to aspire to.

Expand and connect the institution: In the last chapter, we will discuss some broader issues for changing the culture of risk management within the organization and society as a whole.

Now, we will discuss methods shown to be a measurable improvement on existing popular methods and get started using them.

SPEAK THE LANGUAGE

To improve risk management, we need to avoid the problems introduced by some common methods and focus on methods that are shown to measurably improve estimates and decisions. To be clear, the proposed improvements are still not perfect by a long shot. Remember, insisting on perfection for these methods while settling for even greater errors with existing methods is the exsupero ursus fallacy. Instead we will focus on some immediate improvements with a simple approach and describe how we can continue to improve on it.

In short, we need to speak the language of probabilities. This is what Sam Savage calls the arithmetic of uncertainty. That means that we need to use actual probabilities to represent our uncertainty and do the proper calculations with them to avoid common errors of intuition. We will get started with by building on the one-for-one substation model as discussed in chapter 4 (downloadable at www.howtomeasureanything.com/riskmanagement).

Quantifying the Appetite for Risk

Speaking the right language must involve quantifying how much risk we are willing to take. This is fundamental to risk management and provides a natural mechanism for involving the highest levels of management in the organization.

Recall from the research described in chapter 7 that the tolerance for risk changes subconsciously and frequently due to irrelevant external factors. A verbal paragraph explaining how a moderate risk is meaningless and saying that there is no tolerance for risk in other areas is unrealistic. The solution is to agree on risk tolerance in quantitatively unambiguous terms and to document it. Follow the procedure outlined in chapter 4 to elicit a quantitatively expressed risk tolerance from management. This also fits directly into the one-for-one substitution model you can download.

Break It Down, Then Do the Math

When estimates are extremely uncertain, such as the revenue losses due to a major product recall, it makes sense to decompose the problem into a few quantities that might be easier to estimate: how big is one batch of the recalled product? Historically, what has been the effect of a product recall on sales of other products in our firm or similar firms? What is the cost of the recall campaign? How would these change if it were a simple quality defect or a child-safety defect? Often, we can improve estimates of things we feel we don't know at all by doing simple calculations.

In previous chapters we discussed how Paul Meehl and other researchers showed how using statistical models—even sometimes very simple ones—measurably outperformed subject matter experts in a variety of fields. Other research we reviewed shows our intuition fails us in many ways with even some of the simplest problems involving probabilities—so let's not just do the math in our heads. In fact, even without doing a detailed analysis of historical data, just doing the math with subjective estimates of quantities provides an improvement. Meehl makes an obvious but useful observation when thinking about any estimation problem:

When you check out at the supermarket, you don't eyeball the heap of purchases and say to the clerk, “Well it looks to me as if it's about $17 worth. What do you think?” The clerk adds it up.¹

Meehl is simply proposing that we improve estimates by decomposition. This was certainly not a new idea when Meehl wrote those words in the 1980s but Meehl found it necessary to restate the point. For centuries, accountants, engineers, tailors, butchers, carpenters, and others have computed estimates of things by breaking them into parts even if some of the initial quantities were expert estimates.

A Nobel Prize–winning physicist who worked on the Manhattan Project, Enrico Fermi, was known for teaching his students at the University of Chicago to apply commonsense decomposition to estimation problems that sounded particularly difficult to his students. One famous example of this is when he asked his students to estimate the number of piano turners in the city of Chicago. At first stumped, the students were shown that they could roughly estimate the answer by first estimating a few things they might have less uncertainty about—like the number of households in the city, the share of households with pianos, how often they required tuning, and so on. Once they've done that, the rest is a matter of simple arithmetic.

Applying this method to the most fanciful-sounding problems that, at first, were apparently intractable, also became known as Fermi problems and Fermi decompositions. Fermi's intuition on the value of decomposition had since been confirmed with empirical studies by Meehl and others. In the 1970s to the 1990s, decision science researchers Donald G. MacGregor and J. Scott Armstrong, both separately and together, conducted experiments about how much estimates can be improved by decomposition.²

For their various experiments, MacGregor and Armstrong recruited hundreds of subjects to evaluate the difficulty of estimates such as the circumference of a given coin or the number of pairs of men's pants made in the United States per year. Some of the subjects were asked to directly estimate these quantities, and a second group was instead asked to estimate decomposed variables, which were then used to estimate the original quantity. For example, for the question about pants, the second group would estimate the US population of men, the number of pairs of pants men buy per year, the percentage of pants made overseas, and so on. Then the first group's estimate (made without the benefit of decomposition) was compared to that of the second group. Armstrong and MacGregor found that decomposition didn't help much if the estimates of the first group already had relatively little error—such as estimating the circumference of a US 50-cent coin in inches. But when the error of the first group was high—as they were with estimates for men's pants manufactured in the United States or the total number of auto accidents per year—then decomposition was a huge benefit.

One of their studies found that for the most uncertain variables, a simple decomposition of no more than five variables could reduce error by 96.3 percent. Note that this result is just the average—so although some had less error reduction some had much more. In all, they could see error reductions on the order of about one tenth or one-hundredth of the error without the decomposition. Again, just doing the math explicitly, even if the inputs themselves were subjective estimates, removes a source of error. Clearly, decomposition helps estimates.

The Arithmetic of Uncertainty and Monte Carlo

When you decompose highly uncertain problems, such as the risk of a major factor accident or critical information systems being hacked, even the estimates of the decomposed values will be highly uncertain. Even if the inputs in this calculation are uncertain, we use the things we know more about to compute things we know less about.

For very simple probabilities, we can just use basic arithmetic in our decompositions. For these, there are “closed-form” solutions in which a calculation can produce an exact answer in finite steps. These are also called analytic solutions. For example, suppose there are two events, A and B, that could happen next year. Their probabilities are 10 percent and 20 percent, and consequences if they occurred are exactly $2 million and $1 million, respectively. We can easily work out the probability of losing nothing (neither happened, 90 percent × 80 percent = 72 percent), $1 million (only A happened, 10 percent × 80 percent = 8 percent), $2 million (only B happened, 90 percent × 20 percent = 18 percent), or $3 million (both happened, 10 percent × 20 percent = 2 percent).

However, even common situations involve problems for which there is no simple analytic solution. For example, there is no simple solution to adding up the risks in the one-for-one substitution model. Unlike the previous example, each of the risks is a continuous range of impacts, and they follow a particular distribution—in this case the lognormal distribution. We use this distribution for losses because it can't produce a zero or negative value (after all, what would a negative loss from a safety accident or data breach even mean?) while allowing for very large possible losses.

Consider assessing the simple case of just six risks listed in the one-for-one substitution model. Suppose three had a 5 percent chance of occurrence per year with an impact range of $5 million to $20 million. Then suppose the rest had a 15 percent chance of occurrence per year with an impact of $100,000 to $10 million loss. The impact range represents a 90 percent confidence interval on a log-normal distribution (the same distribution used in the one-for-one substitution model). Now, what is the chance per year of losing more than $30 million due to these risks, $100 million, and so on? There is no closed form solution for this even without considering more complex and more realistic problems. Even a brilliant physicist such as Fermi would not attempt to do that math in his head. This is the type of problem the Monte Carlo simulation was specifically designed for. In fact, Fermi was also one of the original contributors to the development of Monte Carlo simulations along with Nicholas Metropolis and Stanislaw Ulam.

In the Manhattan Project, they used the Monte Carlo for estimating solutions related to neutron interactions. But it applies to many otherwise unsolvable problems, including computing a loss exceedance curve from several risks of various types. As discussed in chapter 4, the Monte Carlo converges on a solution by sampling many possibilities. For each sampled scenario, the math is done as if we were computing everything deterministically. Then we just keep repeating this sampling and doing the calculation again. After, say, one thousand trials are sampled, we may find that in ninety trials the losses were greater than $10 million and our loss exceedance curve will show that there is a 9 percent chance of losing more than $10 million next year to these events.

In a Monte Carlo simulation there will be some random sampling error but if we want to reduce that error, we simply sample more trials. Using the what-if data table method found in Excel for this simulation, we can make a much larger simulation if we wanted because a single worksheet in Excel handles a million rows and more than sixteen thousand columns. Recall from chapter 4 that the formula our one-for-one substitution model uses for a pseudo random number generator (PRNG) can generate one hundred million trials in a way that performs well in statistical tests of true randomness. In other words, the practical limit for your simulations is how much memory and processor you want to buy and how long you want to wait for the answer.

Why NASA Assesses Uncertainty with Monte Carlos

In addition to this basic research on the benefits of decomposition in controlled environments, there is evidence of the benefits of decomposition, statistics, and simulations in real-world environments. An aerospace engineer who specializes in cost estimation, Ray Covert, observed these benefits directly while working as a contractor for NASA. From 2005 to 2012, he spent most of his time building cost and mission analysis models for space missions. He used the Monte Carlo method along with historical data.

Covert routinely tracked his results against reality. He found that whereas his Monte Carlo–based method for cost analysis still slightly underestimated mission costs on average, he did better than the deterministic methods based on point estimates of costs. A slight majority of his estimates were within 10 percent of (and some are slightly over) the actual, whereas all estimates from the standard accounting methods underestimated by 25 percent to 55 percent.

NASA offered another interesting opportunity for tracking the effectiveness of different methods. For more than one hundred interplanetary space probe missions, NASA has evaluated risks with both the five-by-five risk matrices (yes, the type debunked in chapter 7) as well as probabilistic methods. Covert finds that the five-by-five risk matrices do not match well with observed reality when results are compared with facts. He says, “I'm not a fan of the five-by-five methods. Both Shuttle disasters and other satellite failures never show up on those charts.”

Instead of five-by-fives, Covert uses a mission failure model developed by David Bearden of Aerospace Corporation.³ This is a historical model that produces a very good fit with actual mission failures of planetary space missions. Bearden developed a type of complexity index using thirty-seven factors, such as how tightly the trajectory has to be managed, whether a foreign partnership was used, and the number of unique instruments. He finds, when he looks at actual, historical data of mission failures, that all failures are for missions where the schedule and budget were very tight for a given level of complexity.

Complexity alone is not a good predictor of a mission failure, but if a complex mission had tight budget and time constraints, mission failure is not only much more likely but can be overwhelmingly likely. When Bearden looked at the distribution of mission schedules for a given level of complexity, he found that almost all of the partial or complete failures occur in the bottom third of durations. Missions that are in the top half for length of schedule and amount of budget for a given complexity never had any failures whether partial or complete. Bearden calls the area where there is not enough time or money to develop a system with a given complexity the no-fly zone. By looking at historical data, most modelers could probably find similar no-fly zones for projects or investments of any kind.

There is an interesting moral of the story here for modelers in general. When NASA missions are under tight time and budget constraints, they tend to cut component tests more than anything else. And less testing means more failures. The same is true with the models of your organization's risks—the less testing, the more failures. The problem is that because testing almost never occurs in risk models, failures of risk models are much more likely than any space mission failure.

Although we need to take care to avoid the problems I explained in chapter 10 regarding Monte Carlo models, it is critical for mastering the analysis of risk in your organization. There is a good reason why Monte Carlo simulations are routinely adopted for the analysis of the biggest risks not just at NASA but also nuclear power safety, oil exploration, and environmental policy. The fact is that when it comes to risks that big, the best risk analysts trust nothing else.

GETTING YOUR PROBABILITIES CALIBRATED

A Monte Carlo simulation requires probabilistic inputs and, as we saw in the previous chapter, many of these will need to rely on estimates from subject matter experts. Remember, even if quantitative estimates are initially subjective, they still avoid the errors introduced with qualitative scoring methods. We will also discuss some simple empirical methods for validating and improving initial estimates but we are already on a better path if our experts provide their judgments in quantitative terms. This way, we can also track quantitatively expressed opinions and improve them with training.

The methods used in improving the subjective probabilities estimates of experts are called debiasing or calibration. Calibration training not only measurably improves the expert's ability to assess odds but also it forms the basis of an intuition for understanding probabilistic models in general. In my experience, the sorts of objections found in chapter 9 have effectively evaporated by the time subjects go through calibration training. Just as defining a quantitative risk tolerance with management builds their acceptance of quantitative methods, so does calibration training build acceptance among the subject matter experts (SMEs).

The most important part of calibration is repetition and feedback. In an intense, half-day workshop, I give a series of tests to SMEs on whom we will rely for estimates. You saw examples of such tests in chapter 7, but that was just a toe in the water. In the appendix, you will find additional, longer tests. As with the sample tests in chapter 7, these include both true/false questions as well as 90 percent confidence interval questions.

Let's review again your performance on the small tests in chapter 7. Remember, we need to compare your expected results to your actual results. Since the range questions asked for a 90 percent confidence interval (CI), you should expect 90 percent of the actual answers to be within your ranges. However, if you are like most people, you got less than that within your stated bounds at first. Granted, these are very small samples so the test can't be used to measure your calibration precisely, but it's a good approximate measure. Even with this small sample, if you are getting less than 70 percent of the answers within bounds, then you are probably overconfident. If you got less than half within your bounds (as most people do), then you are very overconfident.

Also, recall that for the true/false questions, you said you were 50, 60, 70, 80, 90, or 100 percent confident. Convert each of the percentages you circled to a decimal (i.e., 0.5, 0.6, … 1.0) and add them up. Let's say your confidence in your answers was 1, .5, .9, .6, .7, .8, .8, 1, .9, .7 making your total 7.9. So your expected number correct was 7.9. Again, 10 is a small sample, but if your expected number correct is, say, 8.7 and your actual correct was 6, you may be overconfident.

If you are like most people, you did not do well even for these small tests in exhibits 7.1 and 7.3. But before we start to practice with more calibration tests (provided in the appendix), we can learn a few simple methods for improving your calibration.

The Equivalent Bet

One powerful method for improving calibration exploits the fact that most people are better at assessing odds when they pretend to bet money. Here is an example: without looking up the answer, provide your 90 percent CI estimate for the average weight of a six-foot-tall, American male. Now, suppose I offered you a chance to win $1,000 in one of the two following ways:

Option A: You will win $1,000 if the true answer turns out to be between the numbers you gave for the upper and lower bounds. If not, you win nothing.

Option B: You draw a marble at random from a bag of nine green marbles and one red marble. If the marble is green, you win $1,000. If it is red, you win nothing (i.e., there is a 90 percent chance you win $1,000).

Which do you prefer? Drawing the marble has a stated chance of 90 percent that you win $1,000, and 10 percent chance you win nothing. If you are similar to most people (about 80 percent), you prefer to draw from the bag instead of betting on your answer. But why would that be? The only explanation is that you think you have a higher chance of a payoff if you draw from the bag. The conclusion we have to draw is that the 90 percent CI you first estimated is really not your 90 percent CI. It might be your 50, 65, or 80 percent CI, but it can't be your 90 percent CI. You have overstated your confidence in your estimate. You express your uncertainty in a way that indicates you have less uncertainty than you really have.

An equally undesirable outcome is to prefer option A; you win $1,000 if the correct answer is within your range. This means that you think there is more than a 90 percent chance your range contains the answer, even though you are representing yourself as being merely 90 percent confident in the range.

The only desirable answer you can give is if you set your range just right so that you would be indifferent between options A and B. This means that you believe you have a 90 percent chance—not more and not less—that the answer is within your range. For an overconfident person (i.e., most of us), this means increasing the width of the range until options A and B are considered equivalent.

You can apply the same test, of course, to binary questions such as those shown in exhibit 7.1. Let's say you said you were 80 percent confident in your answer to the question about Napoleon's birthplace. Again, you give yourself a choice between betting on your answer being correct or drawing a marble at random. In this case, however, there are eight green marbles and two red marbles in the bag for a payoff 80 percent of the time. If you prefer to draw, that means you are probably less than 80 percent confident in your answer. Now let's suppose we change the marbles in the bag to seven green and three red. If you then consider drawing a marble to be just as good a bet (no better or worse) as betting on your answer, then you should say that you are really about 70 percent confident that your answer to the question is correct.

In my calibration training classes, I've been calling this the equivalent bet test. As the name implies, it tests to see whether you are really 90 percent confident in a range by comparing it to a bet that you should consider equivalent. There is research that indicates that betting money significantly improves a person's ability to assess odds,⁴ but even pretending to bet money improves calibration significantly.⁵ Because most JDM researchers use an urn in this example, they call it the equivalent urn (EQU). But this has also been done with examples of cards, dice, and dials as the analyst sees fit.

More Calibration Strategies

We build on the equivalent bet and provide additional calibration strategies with each test. Several researchers suggest that one reason for lack of calibration (which is usually overconfidence) is failing to think about the ways in which one can be wrong—in other words, questioning basic assumptions and presumptions. Sarah Lichtenstein suggested correcting for this by spending some time thinking of why your range should contain the answer and why it might not. Think of two pros and two cons for each estimate. This causes us to think very differently about our estimates. Experts are used to immediately taking the stance of defending an estimate instead of questioning it. Flipping that habit gives us a chance to evaluate our own estimates more dispassionately. Gary Klein, first mentioned in chapter 3, goes further by suggesting that you skip the pros and cons approach and instead simply assume you are wrong and explain why. This technique has been called Klein's premortem.

Another corrective method involves a way to avoid anchoring. Kahneman and Tversky first discovered anchoring among subjects in estimating experiments. They described it as a tendency to adjust from some previously acquired point value—even when the previous number was randomly chosen or unrelated. In one experiment, Kahneman and Tversky discovered that subjects' estimates of the number of physicians on the island of Manhattan were influenced by the previous number elicited on the test—the last four digits of the subject's social security number.

Kahneman and Tversky found that it is natural, but misleading, for many estimators to think of a single “best estimate” first, then to attempt to determine some kind of error around it. For example, if an SME is asked to estimate a range for next quarter's sales, it may be natural for her to think of one best number ($20 million) and then to imagine how far off she can be ($5 million, resulting in a range of $15 to $25 million). But this tends to cause SMEs to provide narrower ranges than they need to realistically represent uncertainty. Kahneman and Tversky found that the best way to elicit this estimate is to ask for the probability that sales will be over a particular amount. Then ask for the chance that it will be over some higher amount. By iteration, you can find two sales values that the expert believes there is a 95 percent of exceeding and a 5 percent chance of exceeding. Those two values are equivalent to the 90 percent CI.⁶

Take the tests in the appendix and try applying each of the methods listed in this chapter in each test. It will take practice, but if you apply these methods by habit your calibration will improve. The tests in the appendix are longer than the examples in chapter 7 (twenty questions), but the same process of evaluation we used on the small example tests applies. You become calibrated when your expected number correct comes very close to your actual number correct. That is, you are calibrated when you get about 90 percent of the answers within your 90 percent CI for the range questions. For the binary questions, you are calibrated when the sum of the assessed probabilities of being correct is about the same as the actual number correct.

The Results of Calibration Training

This will go a long way to developing the basic skills of thinking about risk probabilistically, even for management with no statistical training. In my own calibration workshops, where I have trained people with a variety of technical and nontechnical backgrounds, I find that about 85 percent of all participants actually reach calibration within a statistically allowable error. Another 10 percent improve significantly but don't quite reach calibration, whereas just 5 percent seem to resist any calibration at all.

SUMMARY OF METHODS TO CALIBRATE PROBABILITY ESTIMATES

Repetition and feedback: Take several tests in succession, assessing how well you did after each one and attempting to improve your performance in the next one. Continue to track performance after training is complete.

Equivalent bets: For each estimate set up the equivalent bet to test whether that range or probability really reflects your uncertainty.

Consider how you might be wrong: Assume for a moment that you are wrong and think of a reason why. The reason you think of might cause you to rethink the confidence in your original estimate.

Avoid anchoring: Think of range questions as two separate binary questions of the form “Are you 95 percent certain that the true value is over/under [pick one] the lower/upper [pick one] bound?”

The good news is that the people we were going to rely on most for estimates were almost always within the group that achieved calibration. Those who resisted calibration were generally not the SMEs we were going to count on for estimates. The individuals who were not successfully calibrated were often lower-level support staff rarely involved in making or supporting managerial decisions. The explanation may be a lack of motivation to do well because they knew they would not be called on for input for the real decision being analyzed. Or, perhaps, those who routinely made risky decisions for the firm were already going to be more receptive to the idea of calibration.

One more item will go a long way to producing an organization that can think about risk probabilistically. A formal system that documents forecasts made by SMEs, tracks the results, reports them, and provides incentives to continue improving will fundamentally change the way an organization thinks about decisions under uncertainty. I will explain more about creating this calibrated culture in the last chapter.

USING DATA FOR INITIAL BENCHMARKS

Even after training in calibrated probability assessment, it is useful to have some benchmarks as the basis for estimates. It sometimes seems that you may have no idea about the likelihood or impact of a risk. (Note that these are issues that almost never come up during using purely nonquantitative methods.) This partly stems for the persistent belief that the SME is trying to estimate some kind of true uncertainty. Again, we treat uncertainty as a property of the individual expert, not the thing the expert is uncertain about. Different experts may have different knowledge of a situation and would therefore have different levels of uncertainty.

To help kick-start you in a few estimates, here are a few strategies to keep in mind. In my first book, How to Measure Anything: Finding the Value of Intangibles in Business, I propose three simple working assumptions to get someone started on what seems to be a difficult measurement problem. I call them working assumptions because, although they may turn out to be false, you should assume they're not and only reluctantly conclude they are false after at least a little effort.

It's been measured before

You have more data than you think

You need less data than you think

It's Been Measured Before

For the first working assumption, at least try a few searches on the internet before you give up on it. If this seems like an extremely important risk, you might try even harder and look for academic research. Is there research on the failure rates of large IT projects? The rates and costs of major data breaches? The frequency of natural disasters that could shut down operations? The scale and frequency of major industrial accidents? Yes, there is. And even if the research doesn't exactly apply to your situation, it can be informative for your calibrated estimate.

Personally, I like the idea of citing research sources for estimates of risks. It gives the estimates extra credibility and you will look like you did your homework. Start with a search on Google or Bing or both. It's a good idea to use more than one search engine. Include additional search terms such as survey, standard deviation, respondents, or university. These may be more likely to produce studies with real data instead of just articles from random bloggers. And don't forget to consider data on government sites. Ask yourself what government agencies would track the item in question. Finally, don't forget to ask the original search engine: a librarian.

One objection might be the black swan event. The biggest risks are those that we couldn't even conceive of. The reaction seems to be that if we can't perfectly predict or even imagine the biggest risks, any risk analysis is therefore useless. This should be obviously nonsensical. The fact that periodically someone dies in a car accident because of something that is thrown off of a bridge, doesn't mean we should disregard the much more common events where the risks are mitigated by seat belts, air bags, antilock braking, and collision avoidance. And it is certainly not irrational for airplane inspectors to pay more attention to more common causes of maintenance failures. Regardless of whether you can even identify all possible events, it would be negligent to ignore the data about events so common that large studies would have been published about them.

You Have More Data Than You Think

Now let's suppose that you either don't find such research or it is too far removed from your specific situation that it can't even be the basis of improving a calibrated estimate. In that case (which is hard to believe in many situations), let's consider the next working assumption—you have more data than you think. You may have a lot of data if you think of the thing you are considering as being only one example of a class of similar things. Sure, each person, project, product, and company is unique but that doesn't mean that there are no ways in which they are comparable. If you are considering your chance of a death, a major project failure, a recall of defective product, or the chance of a major data breach, it is helpful to think of a list of such things and count how often the event occurred in that list.

This category of similar things is called a reference class. Daniel Kahneman recommended thinking about reference classes to estimate a baseline case for uncertain quantities. He defines the baseline case as “the prediction you make about a case if you know nothing except the category to which it belongs.”⁷

If you are a major retailer trying to estimate a baseline for a major data breach, you could follow this procedure.

Make a list of major retailers: Do this with no consideration for the event you are trying to estimate. In other words, don't choose them based on whether or not they had a breach. In fact, ask someone to make the list without telling them what it is for. Just ask them to make a list of similar companies. If you are, for example, a major hotel chain, you may want to tell the person compiling the list to stick to major hotel chains or businesses with online sales exceeding some amount.

Find a source of major data breaches: There are multiple sources. For starters, the Wikipedia page “Major Data Breaches” is usually fairly up-to-date, but you will want to use other industry reports as well. A few Google or Bing searches will round out the sources. Perhaps not all events will be reported to the public, but the biggest events are the ones you should be more interested in, and they are more likely to be publicly available. Furthermore, if you are estimating something like damage to reputation, such events are publicly available by definition. There is no such thing as a secret damage to reputation.

Decide on the period of time you want to consider for the breaches: Perhaps you believe the past four years are the most relevant because breach rates may be higher or lower in the previous years due to increased threats or increased controls in the industry.

Count all of the companies in the company list that also appear on the list of companies breached in the stated period of time: To limit selection bias, only count the overlap of the two lists that were previously prepared and resist the urge to modify them as you count. For this reason, it may be helpful to ask the same research assistant to compare the lists without knowing what the data will be used for.

Suppose you make a list of twenty-five comparable companies and you cross-referenced that list with a list of breaches from the past four years. Do you have twenty-five samples in your data? Actually, you have one hundred company-years of data. If you observed six breaches out of twenty-five companies in four years, you could say your baseline chance of a company in that list having a breach next year is 6 percent. Again, this is just a baseline to start with. If you have reason to believe this chance may be higher or lower than the rest of your reference class, use your calibrated estimate.

A mistake often made in an exercise such as this is that someone feels their situation is so unusual that it defies any such classification. Each manufacturer is unique, so nothing can be learned by asking how often industrial accidents occur in similar manufacturers. This is the Mount St. Helens fallacy discussed in chapter 10. If it were not possible to draw inferences from situations that are similar but not quite identical, then the entire insurance industry would be impossible. Not only that, but there could not even be any claim of experience of almost any kind.

That doesn't mean that there are not situations that could drastically change an estimate within a reference class. In our example, we only looked at twenty-five companies that met some criteria—perhaps they were major hotel chains. If you don't think those are all relevant comparisons, you may limit the list further. If you are trying to estimate the chance of a product recall, it is fair to say that the recall rate of new drugs is different than the recall rate of smartphones or baby strollers. But then you simply define a smaller reference class—for example, the class of new drugs instead of the class of all products. Or, if more resolution in the reference class is needed, use the class of new pain drugs instead of all new drugs.

Of course, the tighter you make your reference class, the smaller your sample size is to make an inference from. Even if you believed you are so unusual in the world that you are beyond compare, you might still consider your own history. If a client of mine is struggling to estimate a probability of an event, I often ask, “Has it happened before?” More specifically, “How long have you worked here and, in your time here, have you seen this event occur?” In this case the reference class is a number of years in that organization. If they observed that it happened once in ten years, that might be the baseline for the chance of it happening next year.

You Need Less Data Than You Think

Now, if you have a large reference class like, say, one thousand and you had two hundred hits (e.g., red marbles in an urn, data breaches among companies, etc.), the simplest baseline assumption is to use 20 percent as a probability. But if we had a reference class of ten and there was only one hit? What if there were no hits out of ten observations? Surely, we can't assume that means the event has no chance of occurring in the next observation (e.g., one draw of a marble, one company for one year, etc.). This may seem counterintuitive, but you have some support for a baseline even in these cases.

One potentially useful way to think about this problem is to consider the urn we used in the equivalent bet problem. Only this time, we will say we have no idea what the proportion of the marbles in the urn are red (the rest are green). In other words, as far as we know, the proportion of red marbles could be any possible value (no red, all red, and anything in between) and all possibilities are equally likely. Quantitatively, we would call this a uniform distribution between 0 percent and 100 percent.

Now suppose we drew at random five marbles and all five were green. The sample proved conclusively that the marbles in the urn aren't all red. At the same time, we certainly haven't proven that there are no red marbles. Suppose we keep drawing marbles and after ten draws we still found no red marbles. Can we make an inference about the chance that the next marble drawn will be red even though we haven't drawn one yet?

As weird as this sounds, yes, we can, and it applies to real-world situations. We can use an approach from Bayesian statistics, briefly mentioned previously in the book. In Bayesian methods, we have a prior state of uncertainty and we update our state of uncertainty with additional data. In this case, the uniform distribution of 0 percent to 100 percent for the proportion of red marbles is our prior. This particular probability distribution is a type of uninformative prior. An uninformative prior (also called a robust prior) is an extremely conservative assumption in which we start with the state of knowing virtually nothing about this proportion other than its mathematical limits—that is, it can't be more than 100 percent or less than 0 percent. Lacking any information to the contrary, we assume that all proportions are equally likely.

Using Bayesian methods, we can update our prior probability to get a new, or posterior, probability. Each marble we draw changes the shape of our working probability distribution. Even if we only draw marbles of one color after several draws, there is still a chance that the next draw can be the other color. The shape of this distribution is called a beta distribution. A spreadsheet you can download from the book website will show how this distribution of an estimate of a proportion from a reference class changes. We will discuss a bit more about this in chapter 12, but, for now, we can focus on a simple version of this problem. You don't have to exactly estimate the proportion of red marbles (or the proportion of companies hit by a data breach). When we are estimating a probability of an event in our risk register, it's sort of like assessing the chance that the next marble drawn will be red.

If we knew the proportion of red marbles exactly, we would know exactly the probability the next marble drawn is red. That is, if we know the proportion of 10 percent, then the probability the next randomly drawn marble is red is 10 percent. But our uncertainty only allows us to put probabilities on each of the proportions. That's what the beta distribution tells us—the probability of various proportions of red marbles, frequency of data breaches, factory fires, and so on. It might sound complicated but if all we want to know is the chance the next marble drawn is red, all we need is the probability weighted average of all the possible proportions given our observations so far. The formula for this is simply:

If we treat a draw of a marble as a year of observation in your firm, then computing the probability you will experience a given event in the next year is just like computing the probability that the next marble is a hit. Even if you haven't observed the event once in four years (i.e., drew four green marbles and no reds) then your baseline of the chance the event occurs the next year (i.e., the chance that the next marble drawn is red) is equal to (0 + 1)/(0 + 4 + 2) = 0.1667.

Remember, you could also define a larger reference class. In the previous example of data breaches, your reference class was not four years or even twenty-five companies, but one hundred company years. If it has not yet happened in that industry, then you might start with a probability that the event will happen in a particular firm in the next twelve months is (0 + 1)/(0 + 100 + 2), or 0.0098.

Notice that this will give us a higher probability of a hit than simply dividing the number of hits by the number of samples, as Kahneman would suggest, especially when the number of hits and samples is small. But this baseline calculation uses the very conservative starting point of maximum uncertainty. That is, you knew virtually nothing about this event until you considered the observations from your reference class.

This may seem like an absurdly simple method for estimating such uncertain events, but it is a special case of Bayesian statistics and the beta distribution. This solution has been known since the eighteenth century, when the mathematician Pierre-Simon Laplace (quoted at the start of this chapter) worked out a simple solution to this problem. He called it the rule of succession.

There may be cases for which this method produces what seems to be unreasonable results but it's not because Laplace's math is wrong. If this baseline seems unreasonable, it can only be because you actually know more than nothing before looking at the reference class. Perhaps you have a reason to believe the event may be becoming more or less likely than the historical observations in your reference class. In that case, you could look at more companies but over a shorter period of time (because this threat is new). Perhaps you believe your firm is sufficiently different from the other firms in your reference class. Again, it's only a baseline—adjust accordingly.

A Reference Class Error: Revisiting the Turkey

Making obviously irrational conclusions from historical observations involves what we could call a reference class error. This is the type of error one would make when rejecting the use of reference classes while actually using a reference class to make the point, albeit a different one. In our urn example, suppose you have sampled many large urns and you usually found at least some red marbles after many draws. If you started drawing from another urn and had not found a red marble after twenty random draws, you know that it would be irrational to conclude the urn has no red marbles because of your experience with other urns. Note that using our formula for computing the probability of drawing a red marble never equals zero even if you drew only green marbles after one thousand draws. It just becomes very unlikely. Similarly, if you have not observed a ransomware attack at your firm or a fire bringing down data center operations, you don't conclude that it will never happen because you have heard of it happening elsewhere. Your reference class is larger than your own firm's experience. Although you may not be carefully counting hits and misses, you are drawing from a reference class of many firms over many years.

Now let's look at Nassim Taleb's turkey example, described in chapter 9, through this lens. We know it is irrational to conclude the turkey will live forever because the experience of that particular turkey is not the only reference class. That is, you are aware that other turkeys eventually get killed after an easy, well-fed life. Likewise, you know the fact that you haven't died yet does not mean that you are immortal because you have the reference class of human mortality in general, even if you are not an actuary with detailed actuarial tables. I would argue that by using the turkey example as part of a case against the utility of historical observations, Taleb was simply making a reference class error.

Taleb derived his example from the philosopher and mathematician, Bertrand Russell. Russell's example was based on a chicken instead of a turkey but, similar to Taleb, Russell was using it as an example of the limitations to inductive reasoning. Inductive reasoning does not provide the proof in the sense that deductive reasoning would. It can only use observations to assess the probability of something. Of course, inductive reasoning is central to probabilistic modeling and, I would argue, life in general. I'm not alone on this point. Among others, I think Laplace would agree with me. But Russell argued against all inductive reasoning when he wrote the following:

The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.⁸

Ironically, Russell and Taleb only know that bird immortality is irrational precisely because they are using inductive reasoning from historical observations. That is, they are using their knowledge of a larger reference class. Now, I realize I'm in way over my head challenging thinkers like Russell and Taleb but I agree with Russell on part of his statement: “more refined views as to the uniformity of nature” are useful.

CHECKING THE SUBSTITUTION

Of course, it's not all about the math. I've been making the case for using quantitative methods and using them properly, but there are some important nonquantitative considerations when using even the simple one-for-one model. There are some improvements we will review in chapter 12 and some organizational issues we will cover in the last chapter.

For now, we will take the one-for-one substitution model fairly literally. That is, however you filled out the original risk matrix is how you fill out the one-for-one substitution. Whatever group of individuals you assembled to provide initial input and to approve the output is the same. The risks will also be the same with possibly a few caveats we will discuss in the following.

We can start with simply listing a set of risks. This is often referred to as a risk register even if an organization is using nonquantitative methods. As we pointed out in chapter 4, the simplest way to get started translating a risk matrix to this list is to create one line in the one-for-one substitution spreadsheet for each dot on a risk matrix as shown in exhibit 11.1.

EXHIBIT 11.1 Mapping the Nonquantitative Matrix to a Simple Quantitative Representation.

Now, regardless of whether you had a risk matrix or some other list to start with, you might consider a few modifications. There are a couple of simple rules. First, try to include as many potential risks as you can think. Second, filter out nonrisks and redundant risks.

Be as Complete as Practical

Listing every possible risk may be unachievable. But most firms could probably improve on the list of risks they generated. Here are a few ideas that may help make it less likely that you will leave out a potentially important risk:

Include the entire enterprise: All parts of the organization should be included in the identification of risks and even persons from various levels within each part of the organization. And don't let one arbitrary subset of the organization run the risk assessment, or the risks will be slanted in that direction to the exclusion of other risks. Industrial engineers may focus on risks related to industrial accidents, legal counsel may focus on litigation risks, IT may focus on IT risks, and so on.

Look outside: Vendors and customers have a special place in risk analysis as do utilities, municipal, state, and federal agencies. Each thinks of different events when they think of disasters, and your organization depends on them in different ways. Even competitors can be a source of ideas. Any publicly traded firm must disclose what it believes are risks in its Form 10-K in their SEC filings (just search for the EDGAR database online). Looking at past events in organizations that have little to do with you can be enlightening. If you do an internet search on news articles related to the term disaster, for example, you will find that many events that occurred in other organizations are the types that could have occurred in your firm. In a similar fashion, although I've never had cancer, my insurance company looks at a larger group of individuals to determine that it is still possible for me.

Think big: The worst-case scenario you thought of might not be even close. What sorts of events have completely or nearly destroyed even remotely similar organizations? What sorts of events have caused such great harm to the public that it involves extraordinary acts of governments to intervene? A rogue trader brought down the 233 year-old Barings Bank. The engineering disasters at the Union Carbide pesticide plant in Bhopal, India, killed thousands and permanently disabled thousands more. Events of that scale may not seem possible in some industries but you should at least try to think about the possibilities before you give up on identifying these risks. At a minimum, what could cause a complete change of executive management? What would cause you to lose most of your market share? Events that have not happened in the past decade or two are seen as effectively impossible by many managers. Think about major catastrophes in the last century and whether anyone would have thought them to be possible just a few years before. There is no reason to believe they can't happen again and some may have actually gotten more likely.

Brainstorm the combinations: A risk manager should consider combinations of events from the previously listed sources. Considering all combinations would usually be infeasible, but even combinations of the more likely events could lead to other risks. Ask how the occurrence of one event increases the probability or impact of another event. The common mode failures of the sort that happened on Flight 232 or the cascade failures (a domino effect) of major banks in 2008 could be revealed only by this kind of analysis. Pretend you are in the future looking back at a failure. One interesting method that changes the pace in brainstorming is the previously mentioned “premortem” from the psychologist Gary Klein. He describes his approach as “the hypothetical opposite of a post-mortem”: unlike a typical critiquing session, in which project team members are asked what might go wrong, the premortem operates on the assumption that the patient has died, and so asks what did go wrong. The team members' task is to generate plausible reasons for the project's failure.⁹

Now, Apply a Filter

Determine what constitutes a risk. As pointed out earlier in this book, Walmart probably doesn't think of shoplifting as a risk. Shoplifting is a cost of doing business. Costs need to be managed, too, of course, but we don't need to lump them in with risks. The practical consideration is what you want to show up on your LEC.

I noted earlier that I've seen organizations list events as risks that are so frequent they happen several times a year on average. Projects being delayed, minor fines or lawsuits, rejecting a batch of raw materials, and short interruptions of some business process may be so common that allowances for them are even considered in the budget. There is nothing mathematically wrong with including such events but that is probably not what decision-makers expect to see on an LEC. Some good rules of thumb about what to call a risk would be as follows:

It doesn't happen every year. A risk is unexpected. It would not have been included in a budget or other plans. A risk is usually something that is less likely than 50 percent per year.

The impact is potentially large enough that it actually has to be reported to top management when it occurs.

Is failing to reach an aggressive sales goal a risk? If that counts, does not winning the lottery count as a risk? I think this is a legitimate issue and different organizations may have reasons to approach this differently. Perhaps there are situations in which not getting a major award counts as a risk. It is possible that not winning a major contract could be seen as a risk if the business was counting on it to avoid bankruptcy. Again, there is nothing mathematically incorrect about including such things in an LEC. But it should be clearly communicated and agreed on.

It's not uncommon to see a risk that is actually a corporate decision, such as “insufficient budget to finish project x” or “lack of executive support for x.” I would recommend that the decisions of the people your risk analysis is trying to inform are not themselves risks.

Be careful about listing overlapping risks. Suppose you list “regulatory fines” and “major data breach” among your risks. Does the impact in major data breach include regulatory fines?

Just starting with the one-for-one substitution model described in chapter 4 avoids many of the ambiguities and other problems introduced by popular nonquantitative methods such as risk matrices. All we need to do is identify your risks, state your risk tolerance and provide your initial calibrated estimates for an annual likelihood and impact for each risk. For now, we are going to deliberately avoid many additional modeling issues and focus on the goal of replacing nonquantitative methods.

Modeling should be an interactive process with the SMEs, and, I find, some interactive processes are better than others. Many analysts start with a brainstorming session to identify all the things that could go wrong. I, too, start with this, but I find that it reaches a point of diminishing returns fairly quickly. At about three hours, it is time to take a break from that process and move on to something else. Following are some ideas to keep that process going.

John Schuyler (from chapter 9) says, “The biggest improvement I've seen in my thirty years is the peer review. Everything goes through this rigorous filter before it goes to management for decision-making.” This is wise at several levels. First, it is always a good idea to check assumptions in models by showing them to someone who isn't immersed in the model. Second, spreadsheet errors are a virtual pandemic in decision analysis, and spreadsheet-based risk analysis tools are no exception. Research has shown that the extent of errors in spreadsheet calculations is probably far beyond what most managers would like to believe.¹⁰

SIMPLE RISK MANAGEMENT

We've talked about introducing the very basics of quantitative risk analysis. Now we need to turn that basic risk analysis into a basic risk management framework. When you've completed your initial list of risks, you will want to compare your LEC to the risk tolerance curve. This tells you whether your current risk is acceptable, but it is not the whole story.

You also need to determine which risk mitigations to employ to reduce risk further. If a mitigation reduces a particular risk by about 50 percent but costs $200,000, is it worth it? As mentioned in chapter 4, this requires knowing our return on mitigation (RoM). RoM is similar to a return on investment but for risk mitigations. To compute this we need to work out a monetized risk so that we can monetize the reduction of risk. Then we could use RoM together with the LEC and the risk tolerance curve as shown in Exhibit 11.2.

To mitigate a risk is to moderate or alleviate a risk—to lessen it in some way. Higher risks may be deliberately accepted for bigger opportunities but even in those cases decision-makers will not want to accept more risk than is necessary. It is common in risk management circles to think of a choice among four basic alternatives for managing a given risk:

EXHIBIT 11.2 LEC vs. Risk Tolerance

Risk Mitigation Options

There are positive RoM options and sufficient budget
No positive RoM options or budget is insufficient

LEC vs. Risk Tolerance
All of the LEC is below the loss exceedance tolerance.
Consider more mitigations to go even further below the risk tolerance curve if the return exceeds return on other uses of resources.
No mitigations are necessary.

All or part of the LEC is above loss exceedance tolerance.
Implement mitigations in order of the highest RoM first until the entire LEC is below risk tolerance, until there are no positive ROM options or no more budget (see other cells).
Three approaches:

Have you thought about all possible mitigations?

Is risk tolerance unrealistically low?

Is it possible to increase the budget or decrease the required RoM?

Avoid: We can choose not to take an action that would create an exposure of some kind. We can avoid the merger, the new technology investment, the subprime mortgage market, and so on. This effectively makes that particular risk zero but might increase risks in other areas (e.g., the lack of taking risks in R&D investments might make a firm less competitive).

Reduce: The manager goes ahead with the investment or other endeavors that have some risks but takes steps to lessen them. The manager can decide to invest in the new chemical plant but implement better fire-safety systems to address a major safety risk.

Transfer: The manager can give the risk to someone else. Insurance is the best example of this. The manager can buy insurance without necessarily taking other steps to lessen the risk of the event (e.g., buying fire insurance instead of investing in advanced fire-prevention systems). Risk can also be transferred to customers or other stakeholders by contract (e.g., a contract that states, “The customer agrees that the company is not responsible for …”).

Retain: This is the default choice for any risk management. You simply accept the risk as it is.

I, and some risk managers I know, find the boundaries between these a little murky. A transfer of risk is a reduction or avoidance of risk to the person transferring it away. A reduction in risk is really the avoidance of particular risks that are components of a larger risk. The ultimate objective of risk management should be, after all, the reduction of the total risk to the firm for a given expected return, whether through the transfer or avoidance of risks or the reduction of specific risks. If total risk is merely retained, then it may be no different from not managing risks at all.

Risk Mitigation

Y. S. Kong was the treasurer and chief strategic planner at the HAVI Group in Illinois, a consortium of major distribution service companies operating in forty countries. Y. S. prefers to categorize risk management activities by specific risk mitigation actions he calls risk filters. “We have four sequential ‘risk filters’: transference, operational, insurance, and retention,” explains Y. S. The first preference is to transfer risks to customers or suppliers through their contracts. The second filter—operational—is to address risks through better systems, procedures, roles, and so on. The third filter is to insure the risk (technically, this is also transferring risks). Finally, the retention of risk is not so much a filter, but where the other risks land if they don't get filtered out earlier. Even so, Y. S. as the treasurer is tasked with ensuring they have an adequate asset position to absorb any risk that ends up in this final bucket.

In the following list, I added a couple of items to Y. S.'s list and expanded on each of them to make it as general as possible. Unlike HAVI's risk filters, the order of this list does not imply a prescribed priority. Note that this is a long, but still partial, list of risk mitigation alternatives:

Selection processes for major exposures: This is the analysis of decisions that create new sources of potential losses to ensure that the risk being taken is justified by the expected reward. For example:

Risk/return analysis of major investments technology, new products, and so on

Selection of loan risks for banks; accounts receivable risks for other types of firms

Insurance: This comes in dozens of specialized categories, but here are a few of the many general groups:

Insurance against loss of specific property and other assets, including fire, flood, and so on

Various liabilities, including product liability

Insurance for particular trades or transportation of goods, such as marine insurance or the launch of a communications satellite

Life insurance for key officers

Reinsurance, generally purchased by insurance companies, to help risks that may be concentrated in certain areas (e.g., hurricane insurance in Florida, earthquake insurance in California, etc.)

Contractual risk transfer: Business contracts include various clauses such as “X agrees the company is not responsible for Y,” including contracts with suppliers, customers, employees, partners, or other stakeholders.

Operational risk reduction: This includes everything a firm might do internally through management initiatives to reduce risks, including the following:

Safety procedures

Training

Security procedures and systems

Emergency/contingency planning

Investments in redundant and/or high-reliability processes, such as multiple IT operations sites, new security systems, and so on

Organizational structures or roles defining clear responsibilities for and authority over certain types of risks (a shift safety officer, a chief information security officer, etc.)

Liquid asset position: This is the approach to addressing the retention of risk but still attempting to absorb some consequences by using liquid reserves (i.e., cash, some inventory, etc.) to ensure losses would not be ruinous to the firm.

Compliance remediation: This is not so much its own category of risk mitigation because it can involve any combination of the previously mentioned items. But it is worth mentioning simply because it is a key driver for so much of current risk mitigation. This is, in part, a matter of “crossing the t's and dotting the i's” in the growing volume of regulatory requirements.

Legal structure: This is the classic example of limiting liability of owners by creating a corporation. But risk mitigation can take this further even for existing firms by compartmentalizing various risks into separate corporate entities as subsidiaries, or for even more effective insulation from legal liability, as completely independent spin-offs.

Activism: This is probably the rarest form of risk mitigation because it is practical for relatively few firms, but it is important. Successful efforts to limit liabilities for companies in certain industries have been won by advocating new legislation. Examples are the Private Securities Litigation Reform Act of 1995, which limits damage claims against securities firms; Michigan's 1996 FDA Defense law, which limits product liability for drugs that were approved by the FDA; and the Digital Millennium Copyright Act of 1998, which limits the liability of firms that provide a conduit for the transmission of data from damages that may be caused by the sources of the data.

As always, an informed risk mitigation starts with an identification and then some kind of assessment of risks. Once a risk manager knows what the risks are, steps can be taken to address them in some way. It might seem that some extremely obvious risks can be managed without much of an assessment effort (e.g., implementing full backup and recovery at a data center that doesn't have it, installing security systems at a major jewelry store, etc.). But in most environments, there are numerous risks, each with one or more potential risk mitigation strategies and a limited number of resources. We have to assess not only the initial risks but also how much the risk would change if various precautions were taken. Then those risk mitigation efforts, once chosen, have to be monitored in the same fashion and the risk management cycle can begin again (see exhibit 11.3). Notice that the assessment of risks appears prior to and as part of the selection of risk mitigation methods.

Now, getting this far should be an improvement over unaided gut feel and a big improvement over methods such as the risk matrix or qualitative scoring methods. Of course, this approach still makes many and big, simplifying assumptions. In chapter 12, we will review some issues worth considering when you are ready to add more realism to the model.

EXHIBIT 11.3 A (Simplified) Risk Management Cycle

NOTES

 1. P. E. Meehl, “Causes and Effects of My Disturbing Little Book,” Journal of Personality Assessment 50, no. 3 (1986): 370–75.

 2. D. MacGregor and J. S. Armstrong, “Judgmental Decomposition: When Does It Work?” International Journal of Forecasting 10, no. 4 (December 1994): 495–506.

 3. D. Bearden, C. Freaner, R. Bitten, and D. Emmons, “An Assessment of the Inherent Optimism in Early Conceptual Designs and Its Effect on Cost and Schedule Growth,” SSCAG/SCAF/EACE Joint International Conference, Noordwijk, The Netherlands, May 15–16, 2008.

 4. A. Hoerl and H. Fallin, “Reliability of Subjective Evaluations in a High Incentive Situation,” Journal of the Royal Statistical Society 137, no. 2 (1974): 227–30.

 5. S. Lichtenstein and L. Phillips, “Calibration of Probabilities: The State of the Art to 1980,” in D. Kahneman, P. Slovic, and A. Tversky, ed., Judgment under Uncertainty: Heuristics and Biases (New York: Cambridge University Press, 1982).

 6. D. Kahneman, P. Slovic, and A. Tversky, Judgment under Uncertainty: Heuristics and Biases (New York: Cambridge University Press, 1982).

 7. Daniel Kahneman, Thinking, Fast and Slow (New York: Farrar, Straus and Giroux, 2011), 248.

 8. Bertrand Russell, The Problems of Philosophy (New York: Henry Holt; London: Williams and Norgate, 1912).

 9. G. Klein, “Performing a Project Premortem,” Harvard Business Review 36, no. 2 (September 2007):103–04.

10. T.S.H. Teo and M. Tan, “Quantitative and Qualitative Errors in Spreadsheet Development,” Proceedings of the Thirtieth Hawaii International Conference on Systems Sciences, 1997; R. Panko and R. Sprangue, “Hitting the Wall: Errors in Developing and Code Inspecting: A ‘Simple’ Spreadsheet Model,” Decision Support Systems 22, no. 4 (April 1998): 337–53.

CHAPTER 12
Improving the Model

The test of all knowledge is experiment. Experiment is the sole judge of scientific truth.

—RICHARD FEYNMAN, FEYNMAN LECTURES ON PHYSICS

When I conduct our webinar and seminar training, I like to divide the content into takeaway and aspirational. The former are methods the attendees should be able to immediately apply by the end of the training without further assistance. The basic one-for-one substitution described in chapters 4 and 11 is the takeaway method. This is the one of the simplest quantitative risk analysis methods possible. It involves just eliciting quantitatively explicit estimates of the likelihood and impact of events, the appetite for risk, and the effects of controls. Only the simplest empirical methods have been introduced and most estimates will rely on calibrated experts. This is the starting point from which we will improve incrementally as you see fit.

This chapter will provide a high-level introduction of just some of the aspirational issues of quantitative risk management. Depending on your needs and your comfort level with these techniques, you may want to introduce these ideas soon. The objective here is to teach you at least enough that you know these methods exist so you can aspire to add them and more in the future. The ideas we will introduce now are as follows:

Additional empirical inputs

More realistic detail in the model

Further improvements to expert estimates

More tools for Monte Carlo simulation

Empirical tests of the model itself

EMPIRICAL INPUTS

The survey of Monte Carlo modelers (see chapter 10) found that of the seventy-two models I reviewed, only three (4 percent) actually conducted some original empirical measurement to reduce uncertainty about a particular variable in a model. This is far short of what it should be.

Should more measurements have been attempted? Would such efforts have been justified? Which specific measurements are justified? Those questions can be answered. As previously discussed, there is a method for computing the value of additional measurements and we have been applying that routinely on many models.

Of the well-over 150 models I've completed up to this point, only three have shown that further measurement was not needed. In other words, I'm finding that additional empirical measurement is easily justified at least 97 percent of the time, not 4 percent of the time. Clearly, the lack of empirical methods is a key weakness of many quantitative models. Here, we will quickly discuss the concept behind computing the value of information and some key ideas for conducting further measurements for risk analysis.

The Value of Information

As discussed in chapter 10, the expected value of perfect information (EVPI) for some uncertain decisions is equal to the expected opportunity loss (EOL) of the decision. This means that the most you should be willing to pay for uncertainty reduction about a decision is the cost of being wrong times the chance of being wrong.

The EVPI is handy to know, but we don't usually get perfect information. So we could estimate the expected value of information (EVI). This is the EVPI without the perfect. This is equal to how much the EOL will be reduced by a measurement. I won't go into further detail here other than to direct the curious reader to the www.howtomeasureanything.com/riskmanagement site for an example.

OVERVIEW OF INFORMATIONAL VALUE

Where

EOL = Chance of being wrong × Cost of being wrong

Expected value of perfect information (EVPI) = EOLBefore Info

(EOLAfter Info is zero if information is perfect)

The systematic application of this is why I refer to the method I developed as applied information economics. The process is fairly simple to summarize. Just get your Monte Carlo tool ready, calibrate your estimators, and follow these five steps:

Define the problem and the alternatives.

Model what you know now (based on calibrated estimates and/or available historical data).

Compute the value of additional information on each uncertainty in the model.

If further measurement is justified, conduct empirical measurements for high-information-value uncertainties and repeat step 3. Otherwise, go to step 5.

Optimize the decision.

This is very different from what I see many modelers do. In step 2, they almost never calibrate, so that is one big difference. Then they hardly ever execute steps 3 and 4. And the results of these steps are what guides so much of my analysis that I don't know what I would do without them. It is for lack of conducting these steps that I find that analysts, managers, and SMEs of all stripes will consistently underestimate both the extent of their current uncertainty and the value of reducing that uncertainty. They would also likely be unaware of the consequences of the measurement inversion described in chapter 10. This means that because they don't have the value of information to guide what should be measured, if they did measure something, it is likely to be the wrong thing.

The reasons for underestimating uncertainty and its effects on decisions are found in the research we discussed previously. JDM researchers observed the extent of our overconfidence in estimates of our uncertainty. And Daniel Kahneman observes of decision-makers that when they get new information, they forget how much they learned. They forget the extent of their prior uncertainty and think that the new information was no big surprise (i.e., “I knew it all along”). Researchers have also found that decision-makers will usually underestimate how much can be inferred from a given amount of information.

I once had a related conversation with a very experienced operations research expert, who had said he had extensive experience with both Monte Carlo models and large law enforcement agencies. We were discussing how to measure the percentage of traffic stops that inadvertently released someone with a warrant for his or her arrest under some other jurisdiction. They needed to quantify a way to justify investments in building information technology that would enable easier communication among all participating law enforcement agencies.

After I explained my approach, he said, “But we don't have enough data to measure that.” I responded, “But you don't know what data you need or how much.” I went on to explain that his assumption that there isn't enough data should really be the result of a specific calculation. Furthermore, he would probably be surprised at how little additional data would be needed to reduce uncertainty about this highly uncertain variable.

I've heard this argument often from a variety of people and then subsequently disproved it by measuring the very item they thought could not be measured. It happened so often I had to write How to Measure Anything: Finding the Value of Intangibles in Business, just to explain all the fallacies I ran into and what the solutions were. Here are a couple of key concepts from that book that risk managers should keep in mind:

The definition of measurement is uncertainty reduction based on observation.

It is a fallacy that when a variable is highly uncertain, we need a lot of data to reduce the uncertainty. The fact is that when there is a lot of uncertainty, less data are needed to yield a large reduction in uncertainty.

When information value is high, the existing amount of data is irrelevant because gathering more observations is justified.

As mentioned, the often-observed measurement inversion means you probably need completely different data than you think, anyway.

Updating Uncertainty with Bayes' Theorem

In risk analysis, it is often important to assess the likelihood of relatively uncommon but extremely costly events. The rarity of such events—called catastrophes or disasters—is part of the problem in determining their likelihood. The fact that they are rare might make it seem problematic for statistical analysis. But there are solutions even in these cases. For example, the previously mentioned Bayes' theorem is a simple but powerful mathematical tool and should be a basic tool for risk analysts to evaluate such situations. From what I can tell it is used much less frequently by quantitative modelers than it should be.

Bayes' theorem is a way to update prior knowledge with new information. We know from calibration training that we can always express our prior state of uncertainty for just about anything. What seems to surprise many people is how little additional data we need to update prior knowledge to an extent that would be of value.

BAYES' THEOREM

Where:

P(A|B) = The probability of A given B

P(A), P(NOT A) = Probability of A and NOT A, respectively

P(B) = Probability of B = P(B|A)P(A) + P(B|NOT A)P(NOT A)

P(B|A) = Probability of B given A

One area of risk analysis in which we don't get many data points is in the failure rates of new vehicles in aerospace. If we are developing a new rocket, we don't know what the rate of failure might be—that is, the percentage of times the rocket blows up or otherwise fails to get a payload into orbit. If we could launch it a million times, we would have a very precise and accurate value for the failure rate. Obviously, we can't do that because, as with many problems in business, the cost per sample is just too high.

Suppose your existing risk analysis (calibrated experts) determined that a new rocket design had an 80 percent chance of working properly and a 20 percent chance of failure. But you have another battery of tests on components that could reduce your uncertainty. These tests have their own imperfections, of course, so passing them is still no guarantee of success. We know that in the past, other systems that failed in the maiden test flight had also failed this component testing method 95 percent of the time. Systems that succeeded on the launch pad had passed the component testing 90 percent of the time. If you get a good test result on the new rocket, what is the chance of success on the first flight? Follow this using the notation introduced in the previous chapter:

In other words, a good test means we can go from 80 percent certainty of launch success to 98.6 percent certainty. We started out with the probability of a good test result given a good rocket and we get the probability of a good rocket given a good test. That is why this is called an inversion using Bayes' theorem, or a Bayesian inversion.

Now, suppose we don't even get this test. (How did we get all the data for past failures with the test, anyway?) All we get is each actual launch as a test for the next one. And suppose we were extremely uncertain about this underlying failure rate. In fact, let's say that all we know is that the underlying failure rate (what we could measure very accurately if we launched it a million times) is somewhere between 0 percent and 100 percent. Given this extremely high uncertainty, each launch starting with the first launch tells us something about this failure rate.

Our starting uncertainty gives every percentile increment in our range equal likelihood. An 8–9 percent base failure rate is a 1 percent chance, a 98–99 percent failure rate is a 1 percent chance, and so on for every other value between 0 and 100 percent. Of course, we can easily work out the chance of a failure on a given launch if the base failure rate is 77 percent—it's just 77 percent. What we need now is a Bayesian inversion so we can compute the chance of a given base rate given some actual observations. I show a spreadsheet at www.howtomeasureanything.com that does this Bayesian inversion for ranges. In exhibit 12.1, you can see what the distribution of possible base failure rates looks like after just a few launches.

Exhibit 12.1 shows our estimate of the baseline failure rates as a probability density function (pdf). The area under each of these curves has to add up to 1, and the higher probabilities are where the curve is highest. Even though our distribution started out uniform (the flat dashed line), where every baseline failure rate was equally likely, even the first launch told us something. After the first launch, the pdf shifted to the left.

EXHIBIT 12.1 Application of Robust Bayesian Method to Launch Failure Rates

Here's why. If the failure rate were really 99 percent, it would have been unlikely, but not impossible, for the first launch to be a success. If the rate were 95 percent, it would have still been unlikely to have a successful launch on the first try, but a little more likely than if it were 99 percent. At the other end of the range, an actual failure rate of 2 percent would have made a success on the first launch very likely.

We know the chance of launch failure given a particular failure rate. We just applied a Bayesian inversion to get the failure rate given the actual launches and failures. It involves simply dividing up the ranges into increments and computing a Bayesian inversion for each small increment in the range. Then we can see how the distribution changes for each observed launch.

Even after just a few launches, we can compute the chance of seeing that result given a particular failure probability. There are two ways to compute this. One is to compute the probability of seeing a given number of failures given an assumed failure rate and then use a Bayesian inversion to compute the probability of that failure rate given the observed failures.

We compute the first part of this with a calculation in statistics called the binomial distribution. In Excel the binomial distribution is written simply as =binomdist(S,T,P,C), where S = number of successes, T = number of trials (launches), P = probability of a success, and C is an indicator telling Excel whether you want it to tell you the cumulative probability (the chance of every number of successes up to that one) or just the individual probability of that result (we set it to the latter). After five launches we had one failure. If the baseline probability were 50 percent, I would find that one failure after five launches would have a 15.6 percent chance of occurrence. If the baseline failure were 70 percent, this result would have only a 3 percent chance of occurrence. As with the first launch, the Bayesian inversion is applied here to each possible percentile increment in our original range.

BINOMIAL PROBABILITY IN EXCEL

The Excel Formula for the probability of a given number of successes after a given number of trials:

Where S = number of successes, T = number of trials, P = probability of a success, and C = 0 if you want the probability for that specific number of successes or C = 1 if you want the probability of that number of successes or less.

Because this starts out with the assumption of maximum possible uncertainty (a failure rate anywhere between 0 and 100 percent), this is called a robust Bayesian method. So, when we have a lot of uncertainty, it doesn't really take many data points to improve it—sometimes just one.

A Probability of Probabilities: The Beta Distribution

There is an even simpler way to do this using a method we briefly mentioned already: the beta distribution. In the previous chapter we showed how using just the mean of the beta distribution can estimate the chance that the next marble drawn from an urn would be red given the previously observed draws. Recall from chapter 11 that this is what Laplace called the rule of succession. It works even if there are very few draws or if you have many draws but no observed red marbles yet. This approach could serve as a baseline for a widely variety of events where data is scarce.

Now, suppose that instead of estimating the chance that the next draw is a red marble, we want to estimate a population proportion of red marbles given a few draws. The beta distribution uses two parameters with rather opaque names: alpha and beta. But you could think of them as hits and misses. We can also use alpha or beta to represent our prior uncertainty. For example, if we set alpha and beta to 1 and 1, respectively, the beta distribution would have a shape equal to the uniform distribution from 0 percent to 100 percent, where all values in between are equally likely. Again, this is the robust prior or uninformative prior in which we pretend we know absolutely nothing about the true population proportion. That is, all we know is that a population proportion has to be somewhere between 0 percent and 100 percent but other than that we have no idea what it could be. Then if we start sampling from some population, we add hits to alpha and misses to beta.

Suppose we are sampling marbles from an urn and we think of a red marble as a hit and green marbles as a miss. Also, let's say we start with the robust prior for the proportion of marbles that are red—it could be anything between 0 percent and 100 percent with equal probability. As we sample, each red marble adds one to our alpha and each green adds one to our beta. If we wanted to show a 90 percent confidence interval of a population proportion using a beta distribution, we would write the following in Excel:

If we sampled just four marbles and only one of those were red, the 90 percent confidence interval for the proportion of red marbles in the urn is 7.6 percent to 65.7 percent. If after sampling twelve marbles only two were red, our 90 percent confidence interval narrows to just 6 percent to 41 percent.

It can be shown that the beta distribution will produce the same answer as the method using the binomial with the Bayesian inversion. You can see this example in chapter 12 spreadsheet on the website.

Using Near Misses to Assess Bigger Impacts

For the truly disastrous events, we might need to find a way to use even more data than the disasters themselves. We might want to use near misses, similar to what Robin Dillon-Merrill researched (see chapter 8). Near misses tend to be much more plentiful than actual disasters and, because at least some disasters are caused by the same events that caused the near miss, we can learn something from them. Near misses could be defined in a number of ways, but I will use the term very broadly. A near miss is an event in which the conditional probability of a disaster given the near miss is higher than the conditional probability of a disaster without a near miss. In other words, P(disaster|with near miss) > P(disaster|without near miss).

For example, the failure of a safety inspection of an airplane could have bearing on the odds that a disaster would happen if corrective actions were not taken. Other indicator events could be an alarm that sounds at a nuclear power plant, a middle-aged person experiencing chest pains, a driver getting reckless-driving tickets, or component failures during the launch of the Space Shuttle (e.g., O-rings burning through or foam striking the Orbiter during launch). Each of these could be a necessary, but usually not sufficient, factor in the occurrence of a catastrophe of some kind. An increase in the occurrence of near misses would indicate an increased risk of catastrophe, even though there are insufficient samples of catastrophes to detect an increase based on the number of catastrophes alone.

As in the case of the overall failure of a system, each observation of a near miss or lack thereof tells us something about the rate of near misses. Also, each time a disaster does or does not occur when near misses do or do not occur tells us something about the conditional probability of the disaster given the near miss. To analyze this, I applied a fairly simple robust Bayesian inversion to both the failure rate of the system and the probability of the near miss. When I applied this to the Space Shuttle, I confirmed Dillon-Merrill's findings that it was not rational for NASA managers to perceive a near miss to be evidence of resilience. Remember, when they saw a near miss followed by the safe return of the crew, they concluded that the system must be more robust than they thought.

EXHIBIT 12.2 Conditional Robust Bayesian Method: Chance of Shuttle Disaster after Each Observed Near Miss (e.g., Falling Foam, O-Rings Burning Through) with an Otherwise Successful Launch

Exhibit 12.2 shows the probability of a failure on each launch given that every previous launch was a success but a near miss occurred on every launch (as was the case with the foam falling off the external tank). I started with the prior knowledge stated by some engineers that they should expect one launch failure in fifty launches. (This is more pessimistic than what Feynman found in his interviews.) I took this 2 percent failure rate as merely the expected value in a range of possible baseline failure rates. I also started out with maximum initial uncertainty about the rate of the near misses. Finally, I limited the disaster result to those situations when the event that allowed the near miss to occur was a necessary precondition for the disaster. In other words, the examined near miss was the only cause of catastrophe. These assumptions are actually more forgiving to NASA management.

The chart shows the probability of a failure on the first launch (starting out at 2 percent) and then updates it on each observed near miss with an otherwise successful flight. As I stated previously, I started with the realization that the real failure rate could be much higher or lower. For the first ten flights, the adjusted probability of a failure increases, even under these extremely forgiving assumptions. Although the flight was a success, the frequency of the observed near misses makes low-baseline near-miss rates less and less likely (i.e., it would be unlikely to see so many near misses if the chance of a near miss per launch were only 3 percent, for example). In fact, it takes about fifty flights for the number of observed successful flights to bring the adjusted probability of failure back to what it was.

But, again, this is too forgiving. The fact is that until they observed these near misses they acted as if they had no idea they could occur. Their assumed rate of these near misses was effectively 0 percent—and that was conclusively disproved on the first observation.

The use of Bayesian methods is not reserved for special situations. I consider them a tool of first resort for most measurement problems. The fact is that almost all real-world measurement problems are Bayesian. That is, you knew something about the quantity before (a calibrated estimate, if nothing else), and new information updates that prior knowledge. It is used in clinical testing for life-saving drugs for the same reason it applies to most catastrophic risks—it is a way to get the most uncertainty reduction out of just a few observations.

The development of methods for dealing with near misses will greatly expand the data we have available for evaluating various disasters. For many disasters, Bayesian analysis of near misses is going to be the only realistic source of measurement.

ADDING DETAIL TO THE MODEL

In chapter 11 we discussed how decomposition and a little bit of Monte Carlo simulation helps estimates. Bear in mind that we could always add more decomposition detail to a model. Models will never be a perfectly accurate representation of what is being modeled. If they were, we wouldn't call them models; we would call them reality. So the objective of improving a model is not infinite detail but only to find marginal improvements that make the model incrementally more realistic and less wrong. As long as the value of being less wrong (the information value) exceeds the cost of the additional complexity, then it is justified. Otherwise, it is not.

In the one-for-one substitution model, we can think of decompositions in three dimensions: vertical, horizontal, and Z. This classification of decompositions is convenient given the structure of a spreadsheet, and they naturally allow for different levels of effort and complexity.

Vertical Decomposition

This is the simplest decomposition. It involves only replacing a single row with more rows. For example, if we have a risk that a data breach is 90 percent likely per year and that the impact is $1,000 to $100 million, we may be putting too much under the umbrella of a single row in the model. Such a wide range probably includes frequent but very small events versus infrequent but serious events. In this case, we may want to represent this risk with more than a single row. Perhaps we differentiate the events by those that involve a legal penalty in one row and those that do not in another. We might say that data breaches resulting in a legal penalty have a likelihood of 5 percent per year with a range of $2 million to $100 million. Smaller events happen almost every year but their impact is, say, $1,000 to $500,000. All we did for this decomposition was add new data. No new calculations are required.

Horizontal Decomposition

If you were starting with the one-for-one substitution model, a horizontal decomposition involves adding new columns and new calculations. For example, you might compute the impact as a function of several other factors. One type of impact might be related to disruption of operations. For that impact, you might decompose the calculation as follows:

Furthermore, cost per hour could be further decomposed as revenue per hour, profit margin, and unrecoverable revenue. In a similar way, you could decompose the cost of a data breach as being a function of the number of records compromised and a cost per record including legal liabilities.

When adding new variables such as these, you will need to add the following:

Input columns. For continuous values you need to add an upper and lower bound. Examples of this would be to capture estimates of hours of duration, cost per hour, and so on. If you are adding probabilities of discrete events (remember, we already have one discrete probability regarding whether the event occurs at all) you just need a single column. Examples of this include the probability that, if an event occurs, legal liabilities might be experienced.

Additional PRNG columns. For each new variable you add, you need to add another PRNG column. That column needs its own variable ID.

Simulated loss column modification. Your simulated loss calculation needs to be updated to include the calculation from the decomposed values (e.g., the disruption example shown above).

Expected loss column. This is the quick way to compute your ROI. But, remember, you can't just compute this based on the averages of all the inputs. You have to take the average of the values in the simulation.

Z Decompositions

Some decompositions will involve turning one row in the original risk register into an entirely separate model, perhaps another tab on the same spreadsheet. The estimates usually directly input into the risk register are now pulled from another model. For example, we may create a detailed model of a data breach due to third-party/vendor errors. This may include a number of inputs and calculations that would be unique to that set of risks. The new worksheet could list all vendors in a table. The table could include columns with information for each vendor, such as what type of services they provide, how long they have been an approved vendor, what systems and data they have access to, their internal staff vetting procedures and so on. That information could then be used to compute a risk of the breach event for each vendor individually. The output of this model is supplied to the original risk register. The simulated losses that would usually be computed on the risk register page are just the total losses from this new model.

The Z decomposition is essentially a new model for a very specific type of risk. This is a more advanced solution, but my staff and I frequently find the need to do just this.

Just a Few More Distributions

In the simple one-for-one substitution model, we only worried about two kinds of distributions: binary and lognormal. What we are calling the binary distribution (what mathematicians and statisticians may also call the Boolean or Bernoulli distribution) only produces a 0 or 1. Recall from chapter 4 that this is to determine whether or not the event occurred. If the event occurred then we use a lognormal distribution to determine the size of the impact, expressed as a monetary loss. We use the lognormal because it naturally fits fairly well to various losses. Similar to a lognormal, losses can't be negative or zero (if the loss was zero we say the loss event didn't happen). It also has a long upper tail that can go far beyond the upper bound of a 90 percent confidence interval.

But we may have information that indicates that the lognormal isn't the best fit. When that is the case, then we might consider adding one of the following. Note that the random generators for these distributions are on the book website. (See exhibit 12.3 for illustrations of these distribution types.)

Normal: A normal (or Gaussian) distribution is a bell-shaped curve that is symmetrically distributed about the mean. Many natural phenomenon follow this distribution, but in some applications it will underestimate the probability of extreme events. This is useful when we have reason to believe that the distribution is symmetrical. That is, a value is just as likely to be above the middle of the stated confidence interval as below. Also, in this distribution values are more likely to be in the middle. But, unlike the lognormal, nothing keeps this distribution from producing zero or negative values. If you use a normal distribution with a 90 percent confidence interval of 1 to 10, it is possible to produce a negative value (in this case 2.2 percent). If that is intended, then perhaps this distribution is the answer. It is also the distribution you would usually use if you are estimating the mean of a population based on a sample greater than thirty.

Triangular: For a triangular distribution, the UB and LB represent absolute limits. There is no chance that a value could be generated outside of these bounds. In addition to the UB and LB, this distribution also has a mode that can vary to any value between the UB and LB. This is sometimes useful as a substitute for a lognormal, when you want to set absolute limits on what the values can be but you want to skew the output in a way similar to the lognormal. It is useful in any situation when you know of absolute limits but the most likely value might not be in the middle, such as the normal distribution.

EXHIBIT 12.3 Examples of Various Distribution Types

Beta: As we already saw in this chapter, Beta distributions are very useful in a measurement problem that is fairly common in risk assessment. It is also extremely versatile for generating a whole class of useful values. They can be used to generate values between 0 and 1 but some values are more likely than others. This result can also be used in other formulas to generate any range of values you like. They are particularly useful when modeling the frequency of an event, especially when the frequency is estimated based on random samples of a population or historical observations. In this distribution it is not quite as easy as in other distributions to determine the parameters based only on upper and lower bounds. The only solution is iteratively trying different alpha and beta values until you get the 90 percent CI you want. If alpha and beta are each greater than 1 and equal to each other, then it will be symmetrical, where values near .5 are the most likely and less likely further away from .5. The larger you make both alpha and beta, the narrower the distribution. If you make alpha larger than beta, the distribution will skew to the left, and if you make beta larger, it skews to the right.

Power law: The power law is a useful distribution for describing phenomena with extreme, catastrophic possibilities—even more than lognormal. The fat tail of the power law distribution enables us to acknowledge the common small event, while still accounting for more extreme possibilities. In fact, sometimes this type of distribution may not always have a defined mean because the tail goes out so far. Be careful of producing unintended extreme results. To keep this from producing unrealistic results, you might prefer to use the truncated power law below. We show this distribution in a simple form that requires that you enter alpha and beta iteratively until you get the 90 percent CI you want.

Poisson: A Poisson distribution tells you how likely a number of occurrences in a period would be, given the average number of occurrences per period. Imagine you have one hundred marbles and each marble is randomly distributed to one of eighty urns, which start out empty. After the marbles are distributed, some urns—28.6 percent—will still have no marbles, 35.8 percent will have one marble, 22.4 percent will have two, 9.3 percent will have three, and so on. This distribution is useful because an event that could happen in a year could happen more than once, too. When the annual likelihood exceeds 50 percent, the chance of happening twice or more exceeds 9 percent.

Student t-distribution and log t distribution: The t-distribution, also known as the student-t distribution, after the inventor of the distribution, William Sealy Gossett, used student as a pseudonym when he published papers on it. The t-distribution is often used when we are estimating the mean of a population based on very small samples. A t-distribution has much fatter tails than a normal distribution. If a sample is somewhere less than thirty and as small as two, a t-distribution is a better representation of the error of the estimate of the mean than a normal distribution. The t-distribution can also be used to generate random variables with the same properties. If you want a symmetrical distribution similar to the normal but want more the extreme outcomes to be more extreme, the t-distribution may be a good fit.

Hybrid and truncated distributions: Sometimes you have specific knowledge about a situation that gives you a reason to modify or combine the distributions previously mentioned. For example, a catastrophic impact of an event in a corporation can't have financial losses to the corporation itself greater than the total market value of the firm. Losses may usually follow a lognormal or power law distribution but they may need to be limited to some maximum possible loss. Also, when distributions are created from historical data, more than one distribution may be patched together to create a distribution that fits the observed data better. This is sometimes done in the financial world to more accurately describe market behavior where there are fat tails. I call these Frankendistributions.

Correlations and Dependencies Between Events

In addition to further decomposition and the use of better-fitting distributions, there are a few slightly more advanced concepts you may want to eventually employ. For example, if some events make other events more likely or exacerbate their impact, you may want to model that explicitly. One way this is done is to build correlations between events. This can be done using a correlation coefficient between two variables. For example, your sales are probably correlated to your stock prices. An example at www.howtomeasureanything.com/riskmanagement shows how this can be done.

But unless you have lots of historical data, you probably will have a hard time estimating a correlation. Correlations are not entirely intuitive metrics that calibrated estimators can approximate. You may be better off building these relationships explicitly as we first described in chapter 10. For example, in a major data breach, the legal liabilities and the cost of fraud detection for customers will be correlated, but that is because they are both partly functions of the number of records breached. If you decompose those costs, and they each use the same estimate for number of records breached, they will be correlated.

Furthermore, some events may actually cause other events, leading to cascade failures. These, too, can be explicitly modeled in the logic of a simulation. We can simply make it so that the probability of event A increases if event B occurred. Wildfires caused by downed power lines in California in 2018, for example, involved simultaneous problems exacerbated the impact of having to fight fires as well as dealing with a large population without power. Including correlations and dependencies between events will cause more extreme losses to be much more likely.

ADVANCED METHODS FOR IMPROVING EXPERT'S SUBJECTIVE ESTIMATES

In chapter 11 we discussed how calibration training can improve the subjective estimates of subject matter experts. Most experts will start out extremely overconfident, but with training they can learn to overcome that. Observations will confirm that the experts will be right 90 percent of the time they say they are 90 percent confident.

There is more we can add to the expert's estimates. First, experts are not just overconfident, but highly inconsistent. Second, we may need to consider how to aggregate experts because not all experts are equally good.

Reducing Expert Inconsistency

In chapter 7, we described the work of a researcher in the 1950s, Egon Brunswik, who showed that experts are highly inconsistent in their estimates. For example, if they are estimating the chance of project failures based on descriptive data for each project (duration, project type, project manager experience, etc.) they will give different estimates for duplicates of the same project. If the duplicates are shown far apart enough in the list—say one is the eleventh project and the other is the ninety-second, experts who forget they already answered will usually give at least a slightly different answer the second time. We also explained that Brunswik showed how we can remove this inconsistency by building a model that predicts what the expert's judgment will be and that, by using this model, the estimates improve.

A simple way to reduce inconsistency is to average together multiple experts. JDM researchers Bob Clemen and Robert Winkler found that a simple average of forecasts can be better calibrated than any individual.¹ This reduces the effect of a single inconsistent individual, but it doesn't eliminate inconsistency for the group, especially if there are only a few experts.

Another solution is to build a model to try to predict the subjective estimates of the experts. It may seem nonintuitive, but Brunswik showed how such a model of expert judgment is better than the expert from whom the data came, simply by making the estimates more consistent. You might recall from chapter 7 that Brunswik referred to this as his lens method.

Similar to most other methods discussed in this chapter, we will treat the lens method as an aspirational goal and skim over the details. But if you feel comfortable with statistical regressions, you can apply the lens method just by following these steps. We've modified it somewhat from Brunswik's original approach to account for some other methods we've learned about since Brunswik first developed this approach (e.g., calibration of probabilities).

Identify the experts who will participate and calibrate them.

Ask them to identify a list of factors relevant to the particular item they will be estimating, but keep it down to ten or fewer factors.

Generate a set of scenarios using a combination of values for each of the factors just identified—they can be based on real examples or purely hypothetical. Use at least thirty scenarios for each of the judges you survey. If the experts are willing to sit for it, one hundred or more scenarios will be better.

Ask the experts to provide the relevant estimate for each scenario described.

Average the estimates of the experts together.

Perform a logistic regression analysis using the average of expert estimates as the dependent variable and the inputs provided to the experts as the independent variable.

The best fit formula for the logistic regression becomes the lens model.

Performance Weights

In chapter 4 and in the lens model, we assume we are simply averaging the estimates of multiple experts. This approach alone (even without the lens method) usually does reduce some inconsistency. There are benefits to this approach but there is a better way.

A mathematician focusing on decision analysis who has researched this in detail is Roger Cooke.² He conducted multiple studies, replicated by others, that showed that performance-weighted expert estimates were better than equally weighted expert estimates.³ and applied these methods to several types of assessments including risk assessments of critical infrastructures.⁴

Cooke and his colleagues would develop topic-specific calibration questions. Unlike the generic trivia calibration question examples we showed previously, this enabled Cooke to simultaneously measure not only the calibration for confidence of the expert but also to assess the general knowledge of the expert in that field. Consider, for example, two equally well calibrated experts but one provides ranges half as wide as the other. Because both experts were calibrated, both experts provided ranges that contained the answer 90 percent of the time. But because the latter expert provides narrower 90 percent confidence interval, she is assessed to have more knowledge than the other expert and, therefore, less uncertainty.

Cooke uses both calibration performance and the assessment of knowledge to compute a weight for each expert. My staff and I have the opportunity to use the performance-weighted methods with clients. What I find most interesting is how most experts end up with a performance weight of at or near zero with just a few—or maybe one—getting the majority weighting for the group.

I find this astonishing. Can it really be true that we can ignore half or more of experts' opinions in fields as diverse as operational risks, engineering estimates, terrorism risks, and more? Apparently so. This is consistent with the research of Philip Tetlock (see chapter 9). Even though Tetlock uses different scoring methods he still finds that a few “superforecasters” outperform the others by large margins.⁵ You might improve risk models a lot by finding the superforecasters in your team.

OTHER MONTE CARLO TOOLS

There are plenty of good Monte Carlo tools to pick from (see exhibit 12.4). The total number of users for all of the various Monte Carlo software tools is in the tens of thousands and chances are that somebody is already applying one of these tools to problems very similar to yours.

You probably already have a license for Excel and that will be good enough for starting out. But as you start developing more elaborate decompositions and using more advanced methods, you may find some other tools more suitable. Some of the tools listed in exhibit 12.4 are actually add-ins for Excel that add a lot more functionality. Others are entirely separate software packages, and some may be more suited to enterprise solutions. There are players in this field coming and going on a regular basis so treat this as a tentative list for starting your research.

EXHIBIT 12.4 Some Available Monte Carlo Tools

Tool | Made by | Description
Excel | Microsoft (Free supporting templates by HDR) | Sufficient for the vast majority of users; HDR has developed free downloadable templates that use the HDR pseudo random number generator (PRNG) www.howtomeasureanything.com/riskmanagement
SIPMath | Sam Savage, Probabilitymanagement.org | An intuitive and free set of Excel add-ins from the Savage's nonprofit that promotes standards in simulation tools; these tools use the Hubbard PRNG
RiskLens | RiskLens | Developed primarily for cybersecurity with a decomposition already developed for that use
Risk Solver Engine | Frontline Systems Incline Village, NV | Unique Excel-based development platform to perform interactive Monte Carlo simulation at unprecedented speed; support SIP and SLURP formats for probability management
Analytica | Lumina Decision Systems, Los Gatos, CA | Uses an extremely intuitive graphical interface that enables complex systems to be modeled as a kind of flowchart of interactions; has a significant presence in government and environmental policy analysis
R and RStudio | Open source, supported by R Foundation for Statistical Computing | Not just Monte Carlo; R is a popular open source stats programming language with a large user group; most users of R will use RStudio as a more intuitive interface; requires a bit more technical knowledge
Crystal Ball | Oracle (Previously Decisioneering, Inc.) Denver, CO | Excel-based; a wide variety of distributions; a fairly sophisticated tool; broad user base and technical support
@Risk | Palisade Corporation, Ithaca, NY | Excel-based tool; main competitor to Crystal Ball; many users and much technical support
SAS | SAS Corporation, Raleigh, NC | Goes well beyond the Monte Carlo; extremely sophisticated package used by many professional statisticians
SPSS | SPSS Inc., Chicago, IL | Goes far beyond the Monte Carlo; tends to be more popular among academics
Mathematica | Wolfram Research, Champaign, IL | Extremely powerful tool that does much more than Monte Carlo; used primarily by scientists and mathematicians, but has applications in many fields
Pelican | Vose Software, Ghent, Belgium | A Monte Carlo-based Enterprise Risk Management and risk governance tool

SELF-EXAMINATIONS FOR MODELERS

Too often, a model of reality takes on a reality of its own. The users of the model are likely eventually to adopt it as the truth. The philosophers Plato (an idealist) and Benedict de Spinoza (a rationalist) were similar in that respect. That is, they believed that all knowledge had to come from their models (reason) alone—that everything we know could have been deduced without observation. In a way, they believed, the need to resort to observation merely shows the weaknesses and flaws in our ability to reason.

The philosopher David Hume, by contrast, was an empiricist. Empiricists doubt even the most rigorous, rational models and prefer to get their hands dirty with observation and real-world facts. They insist that reason alone would be insufficient for the basis of our knowledge even if our ability to reason were perfect. In fact, empiricists say that much of what we call reason could not have been known without observation first. But the best combination appears to be skill in theory and in observation. The Nobel Prize–winning physicists Enrico Fermi and Richard Feynman were competent theorists as well as consummate observers. They had a knack for checking just about any claim with observations much simpler than one might expect were necessary.

However, I would say that most modelers, whether they really thought about this or not, are closer to Plato and Spinoza than Hume. They believe that because they are using a sophisticated sounding method such as Monte Carlo that the model should work. They and their clients may feel more confident in their decisions having gone through this process. But because we know about the analysis placebo effect (described in previous chapters) we also know that their confidence in the method is an unreliable indicator of effectiveness.

Constantly testing your model by seeing how well it matches history is absolutely essential. This requires tracking and/or backtesting of models. Tracking is simply recording forecasts and comparing them with eventual outcomes. Look at a set of project cost estimates produced by a model. How well did they match reality? Backtesting is similar to tracking except that with backtesting the real-world events used to test the model may have predated when the model was built. In other words, you test the model against data you already had. For the same model which estimates project costs, you don't have to wait until current projects are done. You can look at past models. These tests are necessary to have any confidence in modeling at all. However, even though this testing is not difficult to implement, the survey of models in chapter 10 showed it is rarely done. There is simply very little incentive for analysts or management to go back and check models against reality.

Tracking: Documenting forecasts in your model (including variables forecasted within the model) so they can be compared to real outcomes when they occur

Backtesting: Running models to compare them to existing historical data

We know from the research mentioned in the previous chapters that there is evidence that statistical models, decomposition, and the use of Monte Carlos improve estimates. But we know this not because the users merely felt better about their estimates. We know it because estimates were compared to actual outcomes in a large number of trials.

In that spirit, I try to routinely go back and check forecasts against reality. Of all the variables in all the models I've forecasted, I can easily get real data to compare to forecasts for only a small percentage, but it still adds up to more than two hundred variables in which we had initially estimated outcomes and confirmed outcomes to compare them to.

We can validate forecasts of binary probabilities in the same way we validated the results of true/false calibration tests in the previous chapter. That is, of all the times we said some event was about 10 percent likely, it should have occurred about 10 percent of the time. To validate ranges, we can apply a test that is just a bit more detailed than the test we used to validate 90 percent confidence intervals. To get a little bit more data out of the actual observations, I separated all the original range forecasts into multiple buckets:

50 percent should be in the interquartile range (the middle half of a distribution).

5 percent should be above the upper bound of a 90 percent CI.

5 percent should be below the lower bound of a 90 percent CI.

20 percent should be above the interquartile but below the upper bound of a 90 percent CI.

20 percent should be below the interquartile but above the lower bound of a 90 percent CI.

The buckets are arbitrary and I could have defined a very different set. But, as with the true/false tests, things should be about as frequent as we estimate. In this case, the actual data should fall in these sections of a range about as often as would be implied by the forecasts. And ranges don't have to be all the same type. Some separation of buckets can always be done for any distribution of a range, no matter what its shape. No matter how I define a distribution, only 5 percent of the data should be above the 95 percentile of the forecast.

When I go back and look, I find that, within a statistically allowable error, the forecasts of most types of data were distributed as we expected. For those, the forecasting methods were working. However, in 2001, just as I was reaching thirty projects in my database, I was also finding that there were certain variables the calibrated estimators still didn't forecast well, even though they had shown their ability to assess probabilities in the calibration tests. The two areas where I found that even calibrated persons failed to perform well were the estimation of catastrophic project failures and business volumes.

In the case of project cancellations (stopping a project after beginning it), the assessed probabilities were far too low to account for the observed rate of cancellations. Calibrated estimators never gave a chance of cancellation to be above 10 percent and the average estimate is 5 percent. But observation of those same projects after they got started showed that the cancellation rate was six out of thirty, or 20 percent. According to the binomial distribution we discussed previously, it would be extremely unlikely, if there were only a 5 percent chance of cancellation per project, to see six cancellations out of thirty (less than one in one thousand). One of the cancellations was a project that was thought to have no chance of cancellation, which, of course, should be impossible.

I saw a similar inability for people not directly involved with tracking business volumes to forecast them well. For many of the operational investments I was assessing for companies, the return on investment had to be partly a function of sales. For example, if an insurance company was trying to increase the efficiency of new policy processing, the value had to be, in part, related to how many new policies were sold. At first, we would ask IT managers to estimate this and, if the information value justified it, we would do more research. Again, I found that too many of the actual observations of business volumes were ending up in the extremes of the original forecast.

The good news is that because of this tracking and testing, I found that the historical data for project cancellations and changes in business volumes was more reliable than the calibrated estimators—even if the data came from the industry and not that particular firm. And now we know better than to ask managers to estimate business volumes if tracking them is not in their own area of expertise. Furthermore, for every other kind of forecast I was asking estimators to make (e.g., project duration, productivity improvements, technology adoption rates, etc.), the calibrated estimator did as well as expected—about 90 percent of the observations fell within the originally stated 90 percent CI.

Using historical data to validate models and track forecasts to compare them to actual outcomes is fairly simple. Don't worry that you can't get all the data. Get what you can. Even though I had limited data, I still learned something useful from tracking results. Here are four things to keep in mind (if these items sound a little like what we saw previously, it is because the same principles apply):

Don't assume that because each model was unique, you can't assess outcomes in some aggregate fashion. All forecasts of any type can still be assessed by comparing the chance you gave the event to the outcomes. For example, you can look at the 5 percent lower tails of all your forecasts of any kind and see whether about 5 percent landed there. Also, don't commit the Mount St. Helens fallacy (from chapter 10). Just because there are unique aspects of two different systems doesn't mean that we can't learn something from one about the other. No matter how specialized your problem may be, your reference class is larger than that problem.

Don't worry about not having enough data to track because you only have a few models. Almost every variable in your model is a forecast that can be checked against observation, whether that forecast was based on other historical data or calibrated estimates. Even a single, typical model will have several forecasts you can attempt to track. Ten models use and produce just ten forecasts—there may be hundreds of individual variables.

Don't worry about the fact that there are some data you can't easily get—because there are data you can easily get. If you don't know whether the forecast of some productivity improvement was accurate without doing a big study of operations, don't worry. You can easily check the actual project duration or widgets produced.

Don't presume that the few data points will tell you nothing. Laplace's rule of succession is just one example in which you can still make valid inferences from a small amount of data. At least get the data, then determine how much can be learned from it. In the case of the IT project that had a 0 percent chance of cancellation, I proved the original estimators wrong with one data point of a failure. If you find that events that were estimated to have less than a 1 percent chance of occurrence happened three times out of just ten forecasts, then you have all the data you need to indicate that the event is probably more likely than 1 percent.

Change your time scales. There is a habit among some analysts to look at five years of data as if that were a magic number. But, as 2008 proved, events that happen only once every several decades can be much more impactful. Consider an event that has only a 5 percent chance of occurrence in one year. In a five-year period, it still only has a 23 percent chance of occurrence but will have an 87 percent chance sometime during the typical forty-year working career. Even showing management the chance of an event occurring in a decade as opposed to a year puts impactful events in a better perspective.

If you use history, use meta-history. Meta-history is simply the larger reference class than the history of the immediate topic of consideration, that is, the set of similar histories of events. For example, if you are looking at the history of the price volatility of a stock, ask yourself, “Historically, how often has this history predicted an outcome within a given range?” It is common for financial analysts to use the volatility of the previous five years of a stock to estimate the volatility for the next quarter. If we look at each day in the history of Dow Jones, how well do the previous five years match the volatility of the following quarter? We would find that it varies by a factor of about two—the volatility of the next quarter could be anywhere between half as much and twice as much as the previous five years. Likewise, as we found in chapter 10, don't just accept a historical correlation between two variables as immutable fact without asking how often previously correlated variables change their correlation.

The first thing you have to know is yourself. A man who knows himself can step outside himself and watch his own reactions like an observer.

—ADAM SMITH [pseudonym], The Money Game

NOTES

 1. R.T. Clemen and R. L. Winkler, “Combining Economic Forecasts,” Journal of Business & Economic Statistics 4, no. 1 (January 1986): 39–46.

 2. Roger Cooke, Max Mendel, Wim Thijs, “Calibration and Information in Expert Resolution: A Classical Approach,” Automatica 24, no. 1 (1988): 87–94.

 3. M. P. Wiper, S. French, and R. Cooke, “Hypothesis-Based Calibration Scores Author(s),” Journal of the Royal Statistical Society, Series D (The Statistician) 43, no. 2 (2011): 231–36, https://www.jstor.org/stable/2348340; Roger M. Cooke, Experts in Uncertainty: Opinion and Subjective Probability in Science (New York: Oxford University Press, 1991).

 4. R. M. Cooke and L.H.J. Goossens, “Expert Judgement Elicitation for Risk Assessments of Critical Infrastructures,” Journal of Risk Research 7 (2004): 643–56.

 5. Philip E. Tetlock and Dan Gardner, Superforecasting: The Art and Science of Prediction (New York: Crown Publishers, 2015).

CHAPTER 13
The Risk Community: Intra- and Extra-organizational Issues of Risk Management

Take calculated risks. That is quite different from being rash.

—GEORGE PATTON

Prediction is very difficult, especially about the future.

—NIELS BOHR, NOBEL PRIZE–WINNING PHYSICIST

Most of this book is primarily focused on methods for the analysis of risks and decisions. That is certainly a key to answering how to fix risk management. The continued use of risk assessment methods that are no better than astrology would make any improvement in risk management impossible. But if you were to implement better methods for measuring risks, then you would have much better guidance for managing risks.

To achieve an improvement, however, your organization has to have a way to deal with barriers that are not part of the quantitative methods themselves. You need to break organizational silos, have good quality procedures, and incentivize good analysis and good decisions.

The management side of the issue requires some larger-scale solutions that involve collaboration within the firm and may eventually need to go beyond the borders of the firm. Fixing risk management will involve a level of commitment from your organization that goes beyond superficial measures, such as declaring that you have a formal risk process or even appointing a risk czar.

We will wrap up this book with a few important notes about organizing the team, managing the model, incentivizing the desired performance, and developing solutions beyond the individual organization. We will also add some practical observations from a real-world user of the methods in this book.

GETTING ORGANIZED

Sam Savage sees the organizational management and quality control issues to be at least as important as the risk assessment methods he and I both promote. According to Savage, “The big failure of risk management is the lack of consolidating individual risk models and the lack of being able to audit them.” Christopher “Kip” Bohn of Aon agrees: “There's a huge silo effect at organizations. Nobody takes the big view of risk at organizations and therefore risk mitigation capital is not spent effectively.” Without addressing issues such as these, the sophistication of the risk analysis method would be irrelevant.

Who's in Charge?

Let me reiterate a previous clarification of risk management and consider the role of chief risk officer (CRO). As I mentioned previously, risk analysis is only part of decision analysis, and analysis is only part of any kind of management—risk management or otherwise. As chapter 6 pointed out, the position of some is that risks should include uncertain benefits as well as losses, but risk analysis with benefits is already called decision analysis. Some analysts such as myself have just been calling it a risk/return analysis, where risk is only half the problem. As stated previously, using the word risk for both sides of uncertainty is confused.

Don't we really want analysis of all uncertainties, including risks, done in a systematic way that supports the objectives of the organization? The best choice of all big decisions is one that follows a trade-off between risk and benefits—the risk/return analysis. Whatever title this person should have, someone should be given responsibility for the overall assessment of uncertainties of all types in the firm. Accounting doesn't deal with quantitative probabilistic uncertainties at all. Even the CFO would be too narrowly focused because we need to address uncertainties under the COO, the CIO, marketing, and everywhere else.

It sounds like we should consider using a broader term such as chief decision analysis officer (CDAO) or Sam Savage's recommended term chief probability officer (CPO). But, I have to admit, CRO is a much better cover-your-ass designation. Putting someone in charge of risk makes it sound more like management is taking the bull by the horns than would be putting someone in charge of probabilistic modeling in general. The CPO may be less confused about his or her role in the firm but, as Savage sees it, “Risk management has already poisoned the well,” and there may be no going back. So let's proceed from here.

Whoever it is, this individual should be given charge of the following:

Define and document roles: In addition to a CRO, you will need to have one or more analysts, depending on the size of the organization. The models we discussed in chapters 4 and 11 are meant to be simple but if you want to go further with methods described in chapter 12, then you may want some people with dedicated training in the decision sciences. Also, you may want to consider identifying a risk committee to represent management from different parts of the organization. This group would participate in defining risk tolerance as well as agreeing to related procedures for maintaining the risk model.

Determine training requirements: Any individuals providing subjective estimates for the model should go through calibration training. The risk committee and other stakeholders should have at least some familiarization with the quantitative approach. The CRO and supporting analysts should, of course, at least have familiarity with the methods in this book and, better yet, be able to investigate the more advanced methods mentioned in the previous chapter.

Document procedures to manage the model: Someone needs to manage the initial development and continuous evolution of a simulation of all of the organization's key uncertainties (including opportunities as well as risks). This is not a divergent set of separate risk models for different problems.

Track and improve forecasts: As discussed in chapter 12, the performance of models should themselves be measured. Someone needs to set up and monitor all forecasting efforts in the firm so that future assessments of uncertainty gradually improve. This person will be in charge of designing and overseeing the system for tracking individual predictions, reporting actual results, and incentivizing better forecasting.

Selling Better Risk Management to Stakeholders

In chapter 4 we suggested a way to clarify how much risk is acceptable using the simple loss exceedance tolerance curve. In addition to clarifying a key requirement for risk management, defining the organization's tolerance for risk helps to improve the executives' acceptance of these methods by directing involving them in an important part of it.

This is done in a single workshop with the appropriate level of upper management. In some cases, pilot tolerance curves are created in advance of meeting with upper management. We spend about twenty or thirty minutes explaining the reasons why we are building a quantitative model and why we need an unambiguous statement of risk tolerance. Among the topics discussed with decision-makers are why we need better methods and the advantages of quantitative methods. We cover (just in a PowerPoint slide or two) the problems with the risk matrix and the estimation improvements from using quantitative methods. We explain how this method is actually more consistent with other financial methods.

I often hear how I should expect more resistance from management than I actually observe once I have the meeting. Contrary to some warnings, I have found that management is appreciative of the reasons why we need to use different methods and very accommodating for the discussion regarding how much risk they are willing to take. They appreciate that this is a first attempt and does not have to be written in stone. They start discussing how often the curve needs to be updated. They realize that if the first presentation shows that management's first curve was unrealistically risk averse, they may decide to modify it further. But have some initial refinements, once per year would probably be the most frequent. Once every few years is probably more appropriate for something that should be a stable enterprise-level strategic policy such as the loss exceedance tolerance curve.

Using the arguments from previous chapters of this book is useful. Show management why some solutions are better than others and that some really are a best practice. In short, the selling may be easier than you think. They are eager for solutions and you just have to be armed with the right evidence.

MANAGING THE MODEL

The idea of a model that reaches across organizational silos to combine several models seems daunting. But it can just start with some seed models and each new risk/return analysis made for the firm. Or it can start as a top-down design of the entire model for the organization. The technological home of this model could be any of the Monte Carlo tools previously described.

The idea is that if two different areas of the firm are assessing a risk/return model that considers, for example, uncertainty about revenue, then both can be using the same model for revenue forecasts. The uncertainty about revenue should come from marketing (or whoever is closest to the issue), and it shouldn't be reinvented by every modeler who needs to simulate the same thing. Likewise, individual analysts working on models for the risks and returns of big technology investments, new products, and supply chains should not be reinventing models for the weather, the stock market, and currency exchange rates if these uncertainties affect all the models.

We need a single repository for analysis of decisions under uncertainty in the organization. I'll call this the Global Probability Model (GPM). Exhibit 13.1 shows how the GPM can evolve based on ongoing modeling efforts and external events. The right side of the process is, in effect, the applied information economics (AIE) method I developed in the 1990s. This originally focused on major, specific decisions that involved a high degree of uncertainty, risks, and intangibles. I show a two-way interaction between the individual modeling effort and the evolving GPM. Each time a new decision requires additional modeling, that model becomes part of the GPM.

EXHIBIT 13.1 Evolving Global Probability Model

I also show interactions that represent other sources of updating the GPM besides a single modeling effort in one part of the organization. Other modeling efforts (possibly from other organizations) can be included in the GPM. Also, external events and new sources of risks can drive additions to the GPM even without supporting specific decisions. The GPM itself also becomes one of the ways of identifying new risks for the organization.

Sam Savage has developed a solution that nicely facilitates this sharing that a GPM requires. Savage created the technology for keeping scenario libraries. The libraries are a database of one hundred thousand scenarios each for a variety of problems. They include variables that already have correlations with variables such as holiday sales and the cost of part-time labor or energy costs and steel costs. He calls these stochastic information packets (SIPs) and stochastic library units with relationships preserved (SLURPS).

This approach of keeping standard scenario libraries enables an audit trail that is not usually feasible with Monte Carlo tools. These are part of what Savage refers to as certified distributions, which are validated for particular uses. His goal is a level of quality control and standardization that has not previously existed. This is not a product but a standard that Savage has championed. Crystal Ball and Risk Solver already support this standard, and Savage is seeking more participants among the Monte Carlo software firms.

Perhaps the enterprise applications already used by an organization can contribute significantly to a GPM. There may soon be a way to include probabilistic modeling in all the major applications of the firm. Jim Franklin, who previously ran the Crystal Ball division at Oracle, explains that Oracle is integrating Monte Carlo simulation tools in all of its major enterprise applications: “Anywhere in the enterprise where Oracle has a static input, they will have an option of a stochastic input. Think of CRM with pipeline forecasting and being probabilistic.” Several other enterprise applications produce forecasts of some sort for planning, budgeting, and so forth. Right now, these forecasts are deterministic, but they could be part of a Crystal Ball simulation.

This might seem overwhelming, but it is no harder than starting any Monte Carlo–based decision-making process. I've done stochastic analysis of risks in a variety of organizations (including some not very large) on a variety of decision problems. The only difference here is that I would try to keep each model and add it together with other models. Following are a few items to keep in mind for developing any simulation that are also important in developing a GPM.

Start by standardizing a few model components that should not be reinvented each time you need to assess the risks and returns of some new decision. Some items that can be standardized early might include the sales of your firm (or other measures of output if it is a not-for-profit or government agency) and how they might be tied to other economic indicators. Likewise, you should consider standardizing routine risks, such as weather, accidents, or network and power outages.

Then use these risks as part of your next big risk return analysis—for example, investments in a manufacturing facility. The model developed in that analysis then becomes part of the GPM. This continues with each new decision being analyzed, which, for most firms of moderate size or bigger, should be frequent. This could happen in conjunction with top-down design methods independent of individual decisions. But several of the same model development methods that would be used on individual risk/return analyses should apply to top-down modeling.

Modeling should be an interactive process with the subject matter experts (SMEs), and, I find, some interactive processes are better than others. Many analysts start with a brainstorming session to identify all the things that could go wrong. I, too, start with this but I find that it reaches a point of diminishing returns fairly quickly unless we try a variety of methods. Following are some ideas to keep that process going (including a little useful repetition from previous chapters):

Pretend you are in the future looking back at a failure: Remember to use Gary Klein's “premortem” approach, as previously described. Start with the assumption that a major disaster did happen and describe how it happened.¹

Look to risks from others: Rick Julien, previously with the management consulting firm Crowe Horwath, proposed a way to look to other firms for ideas for generating a list of risks. For all the firms in your industry that are publicly traded you should look up their Form 10-K, the annual financial report. In section 9 of this form, firms must disclose to the public the risks they see. Julien finds this to be a constructive addition to thinking of risks that his clients might not have otherwise thought of. I would also recommend looking up the reported risks of your key suppliers and even customers. I might even suggest sampling Forms 10-K from companies in related industries that are not competitors (other service industries, other durable goods manufacturers, etc.).

Include everyone: Your organization has numerous experts on all sorts of specific risks, and chances are that many of them aren't in management. Some effort should be made to survey representatives of just about every job level in the firm.

Ask business insurance consultants about potential risks: Sometimes consultants' advice might be narrow, but it tends to be practical. Some risk management firms, such as Aon and Protiviti, approach the problem from a fairly broad point of view, and they are often quantitatively proficient in topics of risk analysis and risk management.

Do peer reviews: John Schuyler (from chapter 9) says, “The biggest improvement I've seen in my thirty years is the peer review. Everything goes through this rigorous filter before it goes to management for decision-making.” This is wise on several levels. First, it is always a good idea to check assumptions in models by showing them to someone who isn't immersed in the model. Second, spreadsheet errors are a virtual pandemic in decision analysis, and spreadsheet-based risk analysis tools are no exception. Research has shown that the extent of errors in spreadsheet calculations is probably far beyond what most managers would like to believe.²

Use a dynamic online source: Go to www.howtomeasureanything.com/riskmanagement for growing lists of risk categories and their considerations. There is a discussion group that will be expanding a list of risks. This will enable the readers of this book to be up-to-date regardless of what has happened since this book was purchased. I'll also include links to other good sources and free downloads of tools on the book's website.

INCENTIVES FOR A CALIBRATED CULTURE

A calibrated culture is one in which managers and SMEs know that predictions will be documented and reported and that good predictions will be incentivized. It is also one in which actions that change risks are considered in compensation plans as much as actions that improve one quarter's profit.

To make a calibrated culture, you will have to do more than taking your estimators through a calibration process. You need to track predictions and report results (i.e., show whether the predictions turned out right), incentivize performance for forecasting, and, more important, generally behave in a way that is in the longer-term best interest of the organization.

A Metric for the Performance of a Forecaster

One method for generating incentives is the use of the Brier score, originally developed in 1950 for weather forecasters.³ The Brier score is a way to evaluate the results of predictions both by how often the estimators were right and by the probability they estimated for getting a correct answer. Getting a forecast right should be worth more if the forecaster was 90 percent sure than if she was 50 percent sure. And if the forecaster was 99 percent certain and she turns out to be wrong, there should be a bigger penalty than for being wrong if she said she was only 60 percent certain.

The Brier score is proven to be what decision theory researchers call a proper scoring method in that it is impossible to game; that is, it is impossible to get a better score by using a trick strategy other than giving the best calibrated answer for each prediction. An example of a method that can be gamed is our simplified calibration test of 90 percent confidence intervals. You could get a perfectly calibrated score by giving an absurdly wide range for 90 percent of the questions and a tiny range for the other 10 percent—resulting in a “perfect” score of 90 percent correct. But a Brier score would penalize that behavior.

Brier scores are averaged for a number of predictions for individual forecasted items and the lower the score the better (similar to golf). A perfect Brier score is, in fact, zero, and that can be obtained only by being 100 percent confident on each forecast and getting all of them right. The worst average score is 1, which is obtained by being 100 percent confident on each forecast and getting each one wrong. The score is calculated as follows:

Where:

T = 1 if a particular forecast turns out to be true and T = 0 if not

P(T) = the probability, according to the forecaster, that T will be true

Average Brier score = the average of item Brier scores for all of the forecast items of a given forecaster

Consider a forecast by an expert that this month there would be no injuries on the factory floor that required medical attention. If the forecaster were 90 percent confident that the statement “There will be no injuries next month” was true, then P(T) = .9. If the forecaster believed it was false with 80 percent confidence, then the chance it is true is believed to be 20 percent (P(T) = .2). If the former prediction was made (P(T) = .9) and it turns out to be true, then T = 1 and the item Brier score is (.9—1)² = .01. The average of several items Brier scores is shown in exhibit 13.2.

Here are a few other items to keep in mind for incentivizing the calibrated culture:

Brier scores can be computed for ranges just by decomposing ranges into a set of individual true/false predictions. For example, a range for the cost of a new building could be stated as a percent confidence it is over one amount, another percent confidence it is above another amount, and so on.

EXHIBIT 13.2 Brier's Core Example for Forecasters

This Year the Following Events Will Happen | Assessed Probability Event Will Be True = P(T) | Event Was True (T = 1) or Event Was False (T = 0) | Item Brier Score = (P(T) − T)²
New product will be available | 0.95   | 1 | 0.0025
Labor strike | 0.25 | 0 | 0.0625
Key competitors merge | 0.5  | 0 | 0.25  
COO will retire | 0.6  | 1 | 0.16  
Illinois factory will have layoffs | 0.4  | 1 | 0.36  
|  | Average Brier Score | 0.167 

Some predictions, such as the completion date of a project, will be easily confirmed once the event occurs. Some predictions might be verifiable only with deliberate measures. For example, a forecast that a productivity improvement from a new technology will exceed 10 percent might require a deliberate survey. It might not be economically feasible to measure all such forecasts. But a random sample of forecasts could be measured in this way so that forecasters know that any prediction they make has at least a chance of being verified. They cannot know, of course, which predictions will be used in the score. Predictions such as these that happen not to get measured would be excluded from the score.

You might want to consider compensating forecasters for volume as well. You could convert item Brier scores so that the best score is 1 (just subtract the result of the item Brier score in the calculation from and add them up instead of averaging them). This means that the score will be high not only for being well calibrated but also for the number of predictions made. For this, you might want to limit predictions to a particular list.

You might also want to consider different bonus structures for more important forecasts. For example, forecasting the successful completion of a major project could be more important than forecasting the successful completion of a small project.

Market-based Incentives?

As shown in chapter 12, simply averaging together multiple SME forecasts can show improvements. We also showed that techniques such as the lens method and Cooke's performance weighting can provide further improvements.

One tool that has been proposed for incentivizing good forecasts is prediction markets. Prediction markets enable individuals to buy and sell options on given claims. For example, if you are trying to forecast whether two competitors will merge, ask your SMEs to participate in an online market for options that pay $1 if the event occurs. The bid prices for these options historically show that they are a very good indicator of the probability the forecasted event will occur. For example, if the option for the merger of the competitors is selling at $0.65, then the market is estimating there is a 65 percent probability that the option will be worth $1 (which happens only if the merger occurs). The option is worth nothing if the event does not occur.

There have been multiple websites and tools that support this. They trade options on events such as who will win an election. Predictit.com is one such site. I would mention one or two more but they seem to come and go so, if you are interested, just do your online research first. Organizations can also create their own internal markets. Several firms currently sell software for this and already there is a large and growing community of users. Prediction markets have gotten a lot of attention in some circles but I would temper the hype with a couple of observations.

First, the complexity of dynamic trading may not be required to perform well. My firm has had the opportunity to test different versions of prediction markets with clients. In one case we tested a simple version with a pharmaceutical company. Instead of handling real-time trades on a 24/7 basis, we simply took sell-price and buy-price orders by email and settled up the orders once a week on a spreadsheet. This simple approach performed about as well as more complicated solutions.

Second, Phil Tetlock, mentioned previously, measured prediction markets relative to other forecasting methods. Based on measures of relative accuracy Tetlock concluded that prediction markets were 20 percent more accurate than ordinary teams of forecasters, but he also concluded that teams of superforecasters beat prediction markets by 15 percent to 30 percent.⁴

Incentivizing the Right Behavior

But perhaps the biggest issue for creating the calibrated culture is not incentives for forecasts, but incentives for better decision-making for the firm, including better risk management. If we measure risks in a quantitatively meaningful way, then management bonuses could be based as much on risks as near-term profits. Fund managers who earn high profits only by taking highly leveraged positions that expose the entire firm to ruin would have the increased risk—as computed by the GPM—considered in the calculation of their bonuses.

Most risk analysts I talk to who have any relationship to the financial market, banking, or insurance have all pointed their finger to inefficient incentives as a common cause for many of the problems the market saw in 2008. “Incentives are a main culprit,” says Andrew Freeman, a risk expert with McKinsey & Company, “Without proper incentives, risk management becomes boxes that management just ticks off to feel more comfortable.” Usually, bonuses can be taken without regard to whether risk exposure was increased or decreased under the direction of management. Once the bonuses are calculated and paid, they are never garnished in the future if catastrophes occurred as a result of the risky positions that executives took.

If investors, boards, and regulators want a solution to this, they will have to start measuring risk while the executive is still there and before bonuses are paid. The risk can be considered in a number of ways for this purpose. For one, consider the idea of using the certain monetary equivalent (CME) discussed in chapter 6. Recall that this is an exact monetary amount—either a gain or a loss—the firm would consider equivalent to some uncertain range of possible outcomes. Now, suppose a manager makes a $5 million profit for one division. But the GPM says that the future losses from the decision expose the firm to a 25 percent chance of losing $500,000 to $4 million. What is the risk-adjusted profit on which the manager's bonus should be based? A bonus based on the calculated CME of the board or other appropriate executive level would be more appropriate.

The board could also decide to defer part of the bonus and make it contingent on future gains and losses, possibly even after the manager retires. If the manager prefers a lump sum now, the amount would have to reflect this uncertainty. If the manager had an option of selling those future contingent bonuses, then presumably the buyer would price the future contingent bonuses with those same considerations in mind. Of course, this calculation would be based on an analysis conducted by an independent individual or other entity.

Incentivizing better forecasts as well as better management of future risks is critical. Without this, no level of sophistication of risk analysis or modeling will be of any use.

EXTRAORGANIZATIONAL ISSUES: SOLUTIONS BEYOND YOUR OFFICE BUILDING

Some of the really big issues in risk management can't be solved by individual firms. Some of the most critical issues can be resolved only by better guidance from standards organizations, new professional associations, and, in some cases, changes in law. But you can be an advocate and get involved in the solution.

Growing the Profession

Of all the professions in risk management, that of the actuary is the only one that is actually a legally recognized profession. Becoming an actuary requires a demonstration of proficiency through several standardized tests. It also means adopting a code of professional ethics enforced by some licensing body. When actuaries sign their name to the Statement of Actuarial Opinion of an insurance company, they put their license on the line. As with doctors and lawyers, if they lose their license, they cannot just get another job next door. The industry of modelers of uncertainties outside of insurance could benefit greatly from this level of professional standards.

Standards organizations, government affiliated and otherwise, have always been a key part of what makes a profession a profession. But standards organizations such as PMI, NIST, and others are all guilty of explicitly promoting the ineffectual methods previously debunked. The scoring methods developed by these institutions should be disposed of altogether. These organizations should stay out of the business of designing risk analysis methods until they begin to involve people with quantitative decision analysis backgrounds in their standards-development process. Professionals should take charge of the direction their profession evolves by insisting the standards move in this direction.

Improving the Regulatory Environment

It may not seem in the organization's interest to lobby for laws but there is an argument for it even from the point of view of self-interest. Organizations are part of an ecosystem in which the risks affect more than one body. Firms are connected not just through regulators at the national and state levels but also through vendors, customers, and local governments. Their risks are related to yours. Regulations should be thought of as a risk mitigation for all the parties in a system.

Unfortunately, many laws and regulations are so vague about what counts as proper risk analysis that any of the approaches debunked previously in this book would suffice to meet the requirements. Sarbanes-Oxley wrote a one-page guideline on risk assessment that mentioned nothing about what would qualify as a proper method. The FASB allows so much subjective interpretation of which contingent losses should even be reported that the entire guidance on this is meaningless.

The vague laws leave the impression that managing risks is simply about addressing risk management in some way, any way—it matters not what or how. In these cases, it appears that whoever was thinking about risk management added it as an afterthought or simply developed the entire approach in isolation from all the quantitative research in the field. Including specific requirements about quantitative models of risks is the only way to keep risk regulation and risk management from being purely superficial. Regulatory bodies should likewise get on board with GPMs and develop unambiguous (i.e., quantitative) requirements regarding risks.

Growing the Society

Whether they are necessarily regulatory in nature, another key aspect of being a profession is the role of professional societies. In this case, a professional society may have an important role of facilitating collaboration. This can be one of many societies that exist now in decision-making or it could be a new one for this purpose. I don't see yet where one has risen to that role—I hope to be corrected on that soon.

Societies of professionals in modeling should combine and share components of models that affect multiple firms. Some societies could develop GPM models that span multiple firms in one industry so that cascade failures among firms can be assessed. For this we may not be able to depend on regulatory bodies because, unfortunately, the regulatory bodies have done little to consolidate disparate risk analysis efforts. Basel III, for example, seems to have different people working on different parts of risk management without much consideration for either the effectiveness of the methods or the issues of common mode failures among the different pillars.

However, modeling of interorganizational risks is already being done by some firms that perform risk analysis in finance and banking. Dennis William Cox of Risk Reward Limited is a statistical economist who has been modeling cascade failures among investment banks for years. He had told me in February 2008 that he was concerned about the cascade failure effects in investment banking, including specifically the exposure of Lehman Brothers (eight months prior to their collapse). Collaboration of modeling efforts would enable organizations whose risks affect each other to make much more realistic models of their own risks and risks in their industry.

PRACTICAL OBSERVATIONS FROM TRUSTMARK

I've mentioned that none of this is pure theory. Everything I've discussed has been employed in real-life environments. Perhaps it is not surprising that one example of a firm that has taken solid steps to improve operational risk management is Trustmark Mutual Holding Company (Trustmark) in Lake Forest, Illinois. Trustmark offers a variety of employee benefits to employers of all sizes.

In 2018, Trustmark hired my firm, Hubbard Decision Research (HDR), to assist in implementing an enterprise risk management (ERM) solution. We started the process by creating a high-level risk model for the organization using a tool similar to the one-for-one substitution. We then developed more detailed models in specific areas using many of the methods described in chapter 12.

What follows are observations about this process directly from John Hester, Trustmark's Vice President of Internal Audit. First, to explain the reason for adopting the new method, Hester explains:

Our prior assessment approach was deterministic. We would identify relevant risks and then determine a likelihood of the risk event occurring along with a dollar impact amount. We'd then multiply the likelihood by the impact to obtain our expected value.

We'd often be challenged in trying to determine what the “right” impact should be. We knew that the impact could vary depending on the particular scenario one might use for the risk event, but our approach required that we choose just one number.

Over time, our board became dissatisfied with the heat maps that we would share with them because the risks were all single points. Board members would have their own views on where the points should be. None of these points of view were wrong. They just underscored the fact that risk assessment isn't about one point, but risk distributions.

Hester goes on to comment about how the new approach compared to what they were doing before. There are areas where he sees a lot of difference but in terms of basic inputs, it doesn't have to be such a big difference.

Under the hood there are a lot of differences between the two approaches, with use of probability distributions and Monte Carlo simulations as the key differences. These are relevant for those of us on the core ERM team who deal with the model details.

However, when I think about this question as a typical subject matter expert who will contribute risk inputs to something like our high-level risk model, the differences aren't as great. For example, we're still developing likelihoods and impacts for each risk, but now we've been calibrated and we provide impact ranges rather than points. Supplying a range is no more difficult than a point. I think calibration is the key difference for most of our user population.

He offers some practical advice about the importance of acceptance from decision-makers and the team's success in achieving that.

I think the number one best practice is to get buy-in from top management prior to trying to roll out a new method. Early on in our work our board was made aware of what we were planning. They took an interest and supported where we were trying to go. I think without their support, and that of our Enterprise Leadership Team (ELT), our efforts would not be successful.

Our board is very interested in the new approach. They have seen examples and risks depicted as loss exceedance curves really resonate with them. They took to the LECs very quickly.

Our CEO and enterprise leadership team are very keen about the LECs as well. An opportunity for us going forward will be making probabilistic risk assessment a process (used for business decision-making) rather than just an event (for annual reporting to the board).

Finally, Hester understands the ultimate goal is of this method or any other related to risk management.

The biggest benefit that I expect Trustmark will experience is the ability to make better risk management decisions. We now have the capability to understand the risks across our enterprise and measure the value of corrective actions before we implement them.

FINAL THOUGHTS ON QUANTITATIVE MODELS AND BETTER DECISIONS

Ultimately, we should be heading toward ever-evolving and constantly tested models that support not just risk management but decision-making in general. These models are managed by people with this key specialty and have a highly visible role within the organization. The models and the data they use, when possible, are from shared sources. Collaborations across firms and industries reduce individual risk by reducing the risk for the system.

I mentioned previously that finding firms that tracked the performance of their models was difficult, but I found some. It was even harder to find research that showed how quantitative models actually contributed to overall performance of the firm. Thompson Terry, a modeler who works at Palisade Corporation (the makers of the @Risk Monte Carlo tool), recently offered some anecdotal evidence of the effectiveness of better quantitative modeling. He pointed out that Goldman Sachs, Morgan Stanley, and Deutsche Bank were all @Risk users and they all survived the 2008 financial crisis. He then pointed out that Merrill Lynch, Bear Stearns, and Lehman Brothers were not customers. This is interesting, but obviously not conclusive.

I did find one piece of research that measured a real strategic advantage for users of more advanced quantitative methods. Fiona MacMillan is a quantitative methods researcher who wrote her PhD thesis on a survey of oil exploration firms and their use of quantitative methods. She later coauthored a paper on it in the journal Society of Petroleum Engineers. It showed a strong correlation among several measures of financial performance and the maturity of the firm in the use of more quantitative risk analysis methods.⁵ She was also able to show that the improvements in financial performance occurred just after they began to adopt more quantitative methods.⁶ This is about as good as evidence gets in this field because so few other firms use quantitative methods at all.

Most of the users of quantitative methods in MacMillan's study probably were not even using many of the methods I discuss in this book: calibration, incentives for forecasting, global risk models, and so on. Still, the findings indicate what the potential could be for all firms.

This book has reviewed the measured performance of decision-making methods such as intuition, ordinal scales, risk matrices, and certain quantitative methods, even if they still employ subjective components. It should be clear by now that the last of these wins out.

Remember from chapter 1 that, for many firms, the single biggest risk is how they assess risk. Of course, risk management is just part of the larger issue of decision-making and, in a similar manner, we can also say our single most important decision is how we make decisions. Our decision-making methods—including risk management—should have a measurable benefit. In fact, it should have a demonstrably positive return on investment. Knowing this would seem to be central to what Kahneman referred to as quality control of decisions.

Thinking about uncertainties and risks in a quantitative way had obvious benefits long before so many studies have demonstrated the benefits empirically. What makes any important decision challenging is the fact that it is made under a state of uncertainty when some of the outcomes include losses and—if it is considered a big decision—it is because the potential losses for making the wrong choice is large. Recall this is what we mean by risk in the first place. It should be obvious that thinking clearly about such decisions should be considered an important area of interest. Even two centuries ago, Laplace would already refer to thinking quantitatively about risk as a science and commented on its influence in so many human endeavors:

It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.⁷

NOTES

 1. G. Klein, “Performing a Project Premortem,” Harvard Business Review (September 2007).

 2. T.S.H. Teo and M. Tan, “Quantitative and Qualitative Errors in Spreadsheet Development,” Proceedings of the Thirtieth Hawaii International Conference on Systems Sciences, 1997; R. R. Panko and R. Sprangue, “Hitting the Wall: Errors in Developing and Code Inspecting; A ‘Simple’ Spreadsheet Model,” Decision Support Systems 22, no. 4 (April 1998): 337–53.

 3. G. W. Brier, “Verification of Forecasts Expressed in Terms of Probability,” Monthly Weather Review 75 (1950): 1–3.

 4. Philip E. Tetlock and Dan Gardner, Superforecasting: The Art and Science of Prediction (New York: Crown Publishing, 2015).

 5. G. S. Simpson, F. E. Lamb, J. H. Finch, and N. C. Dinnie, “The Application of Probabilistic and Qualitative Methods to Asset Management Decision Making,” Society of Petroleum Engineers (2000).

 6. W. Bailey, B. Couet, F. Lamb, G. Simpson, and P. Rose, “Taking Calculated Risks,” Oilfield Review (Autumn 2000).

 7. Pierre-Simon Laplace, Théorie Analytique des Probabilitiés (Paris: Courcier, 1812).

APPENDIX
Additional Calibration Tests and Answers

CALIBRATION TEST FOR RANGES: A

No. | Question | Lower Bound (95% Chance Value Is Higher) | Upper Bound (95% Chance Value Is Lower)
1 | How many feet tall is the Hoover Dam? |  |
2 | How many inches long is a $20 bill? |  |
3 | What percentage of aluminum is recycled in the United States? |  |
4 | When was Elvis Presley born? |  |
5 | What percentage of the atmosphere is oxygen by weight? |  |
6 | What is the latitude of New Orleans? [Hint: Latitude is 0 degrees at the equator and 90 degrees at the North Pole.] |  |
7 | In 1913, the United States military owned how many airplanes? |  |
8 | The first European printing press was invented in what year? |  |
9 | What percentage of all electricity consumed in US households was used by kitchen appliances in 2001? |  |
10 | How many miles tall is Mount Everest? |  |
11 | How long is Iraq's border with Iran in kilometers? |  |
12 | How many miles long is the Nile? |  |
13 | In what year was Harvard founded? |  |
14 | What is the wingspan (in feet) of a Boeing 747 jumbo jet? |  |
15 | How many soldiers were in a Roman legion? |  |
16 | What is the average temperature of the abyssal zone (where the oceans are more than 6,500 feet deep) in degrees F? |  |
17 | How many feet long is the Space Shuttle Orbiter (excluding the external tank)? |  |
18 | In what year did Jules Verne publish 20,000 Leagues Under the Sea? |  |
19 | How wide is the goal in field hockey (in feet)? |  |
20 | The Roman Coliseum held how many spectators? |  |

No. | Answers to Calibration Test for Ranges: A
1 | 726 feet
2 | 63/16ths (6.1417) inches
3 | 45 percent
4 | 1935
5 | 21 percent
6 | 29.95
7 | 23
8 | 1450
9 | 26.7 percent
10 | 5.5 miles
11 | 1,458 kilometers
12 | 4,160 miles
13 | 1636
14 | 196 feet
15 | 6,000
16 | 39 F
17 | 122 feet
18 | 1870
19 | 12 feet
20 | 50,000

CALIBRATION TEST FOR RANGES: B

No. | Question | Lower Bound (95% Chance Value Is Higher) | Upper Bound (95% Chance Value Is Lower)
1 | The first probe to land on Mars, Viking 1, landed there in what year? |  |
2 | How old was the youngest person to fly into space? |  |
3 | How many meters tall is the Sears Tower? |  |
4 | What was the maximum altitude of the Breitling Orbiter 3, the first balloon to circumnavigate the globe, in miles? |  |
5 | On average, what percentage of the total software development project effort is spent in design? |  |
6 | How many people were permanently evacuated after the Chernobyl nuclear power plant accident? |  |
7 | How many feet long were the largest airships? |  |
8 | How many miles is the flying distance from San Francisco to Honolulu? |  |
9 | The fastest bird, the falcon, can fly at a speed of how many miles per hour in a dive? |  |
10 | In what year was the double helix structure of DNA discovered? |  |
11 | How many yards wide is a football field? |  |
12 | What was the percentage growth in internet hosts from 1996 to 1997? |  |
13 | How many calories are in 8 ounces of orange juice? |  |
14 | How fast would you have to travel at sea level to break the sound barrier (in mph)? |  |
15 | How many years was Nelson Mandela in prison? |  |
16 | What is the average daily calorie intake in developed countries? |  |
17 | In 1994, how many nations were members of the United Nations? |  |
18 | The Audubon Society was formed in the United States in what year? |  |
19 | How many feet high is the world's highest waterfall (Angel Falls, Venezuela)? |  |
20 | How deep beneath the sea was the Titanic found (in miles)? |  |

No. | Answers to Calibration Test for Ranges: B
1 | 1976
2 | 26
3 | 443 meters
4 | 6.9 miles
5 | 20 percent
6 | 350,000
7 | 803 feet
8 | 2,394 miles
9 | 200 mph
10 | 1953
11 | 53.3 yards
12 | 70 percent
13 | 120
14 | 760 mph
15 | 27
16 | 3,300 calories
17 | 184
18 | 1905
19 | 3,212 feet
20 | 3.36 miles

CALIBRATION TEST FOR BINARY: A

| Statement | Answer (True/False) | Confidence that You Are Correct (Circle One)
1 | The Lincoln Highway was the first paved road in the United States, and it ran from Chicago to San Francisco. |  | 50% 60% 70% 80% 90% 100%
2 | The Silk Road joined the two ancient kingdoms of China and Afghanistan. |  | 50% 60% 70% 80% 90% 100%
3 | More American homes have microwaves than telephones. |  | 50% 60% 70% 80% 90% 100%
4 | Doric is an architectural term for a shape of roof. |  | 50% 60% 70% 80% 90% 100%
5 | The World Tourism Organization predicts that Europe will still be the most popular tourist destination in 2020. |  | 50% 60% 70% 80% 90% 100%
6 | Germany was the second country to develop atomic weapons. |  | 50% 60% 70% 80% 90% 100%
7 | A hockey puck will fit in a golf hole. |  | 50% 60% 70% 80% 90% 100%
8 | The Sioux were one of the Plains Indian tribes. |  | 50% 60% 70% 80% 90% 100%
9 | To a physicist, plasma is a type of rock. |  | 50% 60% 70% 80% 90% 100%
10 | The Hundred Years' War was actually more than a century long. |  | 50% 60% 70% 80% 90% 100%
11 | Most of the fresh water on Earth is in the polar ice caps. |  | 50% 60% 70% 80% 90% 100%
12 | The Academy Awards (“Oscars”) began over a century ago. |  | 50% 60% 70% 80% 90% 100%
13 | There are fewer than two hundred billionaires in the world. |  | 50% 60% 70% 80% 90% 100%
14 | In Excel, ^ means “take to the power of.” |  | 50% 60% 70% 80% 90% 100%
15 | The average annual salary of airline captains is over $150,000. |  | 50% 60% 70% 80% 90% 100%
16 | By 1997, Bill Gates was worth more than $10 billion. |  | 50% 60% 70% 80% 90% 100%
17 | Cannons were used in European warfare by the eleventh century. |  | 50% 60% 70% 80% 90% 100%
18 | Anchorage is the capital of Alaska. |  | 50% 60% 70% 80% 90% 100%
19 | Washington, Jefferson, Lincoln, and Grant are the four presidents whose heads are sculpted into Mount Rushmore. |  | 50% 60% 70% 80% 90% 100%
20 | John Wiley & Sons is not the largest book publisher. |  | 50% 60% 70% 80% 90% 100%

No. | Answers for Calibration Test Binary: A
1 | FALSE
2 | FALSE
3 | FALSE
4 | FALSE
5 | TRUE
6 | FALSE
7 | TRUE
8 | TRUE
9 | FALSE
10 | TRUE
11 | TRUE
12 | FALSE
13 | FALSE
14 | TRUE
15 | FALSE
16 | TRUE
17 | FALSE
18 | FALSE
19 | FALSE
20 | TRUE

CALIBRATION TEST FOR BINARY: B

| Statement | Answer (True/False) | Confidence that You Are Correct (Circle One)
1 | Jupiter's “Great Red Spot” is larger than Earth. |  | 50% 60% 70% 80% 90% 100%
2 | The Brooklyn Dodgers' name was short for “trolley car dodgers.” |  | 50% 60% 70% 80% 90% 100%
3 | Hypersonic is faster than subsonic. |  | 50% 60% 70% 80% 90% 100%
4 | A polygon is three-dimensional and a polyhedron is two-dimensional. |  | 50% 60% 70% 80% 90% 100%
5 | A 1-watt electric motor produces 1 horsepower. |  | 50% 60% 70% 80% 90% 100%
6 | Chicago is more populous than Boston. |  | 50% 60% 70% 80% 90% 100%
7 | In 2005, WalMart sales dropped below $100 billion. |  | 50% 60% 70% 80% 90% 100%
8 | Post-it Notes were invented by 3M. |  | 50% 60% 70% 80% 90% 100%
9 | Alfred Nobel, whose fortune endows the Nobel Peace Prize, made his fortune in oil and explosives. |  | 50% 60% 70% 80% 90% 100%
10 | A BTU is a measure of heat. |  | 50% 60% 70% 80% 90% 100%
11 | The winner of the first Indianapolis 500 clocked an average speed of under 100 mph. |  | 50% 60% 70% 80% 90% 100%
12 | Microsoft has more employees than IBM. |  | 50% 60% 70% 80% 90% 100%
13 | Romania borders Hungary. |  | 50% 60% 70% 80% 90% 100%
14 | Idaho is larger (in area) than Iraq. |  | 50% 60% 70% 80% 90% 100%
15 | Casablanca is on the African continent. |  | 50% 60% 70% 80% 90% 100%
16 | The first manmade plastic was invented in the nineteenth century. |  | 50% 60% 70% 80% 90% 100%
17 | A chamois is an alpine animal. |  | 50% 60% 70% 80% 90% 100%
18 | The base of a pyramid is in the shape of a square. |  | 50% 60% 70% 80% 90% 100%
19 | Stonehenge is located on the main British island. |  | 50% 60% 70% 80% 90% 100%
20 | Computer processors double in power every three months or less. |  | 50% 60% 70% 80% 90% 100%

No. | Answers for Calibration Test Binary: B
1 | TRUE
2 | TRUE
3 | TRUE
4 | FALSE
5 | FALSE
6 | TRUE
7 | FALSE
8 | TRUE
9 | TRUE
10 | TRUE
11 | TRUE
12 | FALSE
13 | TRUE
14 | FALSE
15 | TRUE
16 | TRUE
17 | TRUE
18 | TRUE
19 | TRUE
20 | FALSE

Index

@Risk, 225, 316, 342

5-by-5s, 168

90 percent confidence interval questions/tests, 147e, 148e

800-30 Risk Management Guide for Information Technology Systems, 102

Activism, 289

Actuarial risk, 218–219

Actuarial science/tables, 22, 85–86, 279

Actuaries (risk management horseman), 82–86

Additive weighted scores, 165–166

Agreed-on policy statements, usage, 121

AIG, problems, 8, 85, 104

Aleatory uncertainty, 129

Algorithm aversion, 195, 198, 203

Algorithms, 194–203

Ambiguity, impact, 170–173

Amtrak, derailments/collisions, 4

Analysis, term (usage), 13

Analysis placebo, 5, 41–42, 100–102, 189

Analysts, Monte Carlo simulations (usage), 224–228

Analytic hierarchy process (AHP), 33, 54, 189–190

Analytic solutions, 262–263

Analytica, 316

Anchoring, 269, 271

Andreassen, Paul, 42

Antifragility, 205

Aon Global Risk Consulting, 25–27, 45–46, 331

Applied information economics (AIE), 228, 295, 328

Arbitrary points, usage, 72–73

Armstrong, J. Scott, 261–262

Arthur Andersen, demise, 96, 99–100

Artifacts, 155–160

Assessment, term (usage), 13

Assessors, risk aversion, 181

Auditors, usage, 99

Audits, usage, 29–30

Augliere, Reed, 175

Backtesting, 317–318

Baez, John C., 185

Barings Bank, problems, 282

Baseline failure rates, 304

Baxter International, Inc., 39–40, 229

Bayesian analysis/method/view, 131, 276–277, 300e, 305

Bayesian networks, 250

Bayesian statistics, 276–278

Bayes' theorem/inversion, 297–301

Bears, swans (contrast), 193

Bear Stearns, failure, 8

Bearden, David, 265

Behavioral economics, 95

Behavior, incentivization, 335–337

Berra, Yogi, 223

Bernoulli distribution, 308

Best-fit correlation, 246–247

Best practices, 5, 39

Beta distribution, 301–302, 309–310

Bias, 138, 140, 174

Bickel, J. Eric, 182

Big experiment, 50–52

Binary probabilities, forecast validations, 318–319

Binomial distribution, 300–301

Binomial probability, 301

Black, Fischer, 94

Black-Scholes equation, 94–95

Black swans, 203–209

Boeing 737 MAX, crashes/failures, 5–7

Bohn, Christopher, 45–46, 219, 324

Bohr, Niels, 323

Boolean distribution, 308

Box, George, 75

Bratvold, Reidar, 182

Brier core/scores, 332–334, 333e

Broomell, Stephen, 172

Brunswik, Egon, 155–156, 158, 184–185, 313–314

Buckets, range forecasts, 319

Budescu, David, 170–173, 180–182

Calibrated culture, incentives, 331–337

Calibrated estimators, usage, 319–320

Calibrated individuals, uncalibrated individuals (comparison), 145e

Calibrated probability assessment, 66–67, 212

Calibration, 226, 266, 269–272

comparison, 148e

importance, 146

test, 90 percent confidence interval questions, 147e

tests, answers, 160–161

Capital investments, 229

Cascade failure, 240–241, 283

Catastrophes, 297, 303

Catastrophic overconfidence, 142–150

Catastrophic risks, 305

Cause and effect, direct evidence, 50, 52–53

Certain monetary equivalent (CME), 122–128, 133, 336

Certified distributions, 329

Chamberlain, Thomas C., 223

Chance, misconception, 140

Chartered enterprise risk actuary (CERA) certification, 86

Checklists, usage, 29–30

Chief decision analysis officer (CDAO), 325

Chief information officers (CIOs), 228–229

Chief probability officer (CPO), 325

Chief risk officer (CRO), 217, 324, 325

Chi-square test, 238

Chomel, Auguste Francois, 163

Churchill, Winston, 86

Clemen, Bob, 171–172, 313

Close analogy fallacy, 236

Closed-form solutions, 262–263

Cognitive Neuroscience Society study, 159

Coin flip, 113, 119

Collaborative, term (usage), 230–231

Common mode failure, 5–8, 241, 243

Complementary cumulative probability function, 69

Completeness, check, 50, 54–56

Complexity index, 265

Compliance remediation, 289

Component testing, 50, 53–55

Conditional probability, 303

Conditional robust Bayesian method, 304e

Confidence interval (CI), 237–238, 263, 267

Confiscation, expropriation, nationalization, and deprivation (CEND), 220

Conjunction fallacy, 141

Consensus, building, 47, 101

Consequence (risk component), 168

Construction engineering, definition, 118–119

Contingent losses, ambiguity (FASB rules), 172

Contractual risk transfer, 288

Controlled studies, reliance, 206

Control Objectives for Information and Related Technology (CobIT), 102, 168, 185

Control self-assessment (CSA), 99

Cooke, Roger, 314–315, 334

Coopers & Lybrand, 96–98

Correlated data, examples, 245e

Correlated variable, 243

Correlation coefficient, 247e

Correlation degrees, 244

Correlations, 243–247, 311–312

Cost, measurable unit (usage), 185

Coupon insurance, 220

Covert, Ray, 264–265

Cox, Dennis William, 339

Cox, Tony, 173–176, 180–183, 190

Credit default swaps (CDSs), position, 85

Credit risk, 165

Criticality matrix, 9

Critical, term (usage), 87

Crowe Horwath, 330

Crystal Ball, 225, 316, 329

Culture. 14. 47. 331–337

Currency risk, 165–166, 247

Cyberattacks, 15

Cyber risk, 56

Cybersecurity, 13, 33, 65, 157, 209, 227

Dantzig, George, 91–92

Data, 67, 202, 272–280, 321

backup, implementation, 290

breaches, 4, 263, 272–275, 300

correlated data, examples, 245e

empirical data, usage, 76

observation, 311

obtaining, direct observation, 218

range estimation, 234

synthesis, 54

table, functions, 70–71

Dawes, Robyn, 139, 184–185

Death, cause, 141

Debiasing, 266

Decision analysis (DA), 77, 89, 123, 324

Decision-maker, 127e, 132, 296

Decision making, 40–44, 153, 214

Decision making, issues, 342–343

Decision theory/psychology, 88, 130

Decisions, quality control, 138, 343

Decomposition, 54, 262, 264, 305–307

Deductive reasoning, 279–280

Deep learning, 250

Deepwater Horizon Offshore Oil Spill, 4, 7

Defined procedure, usage, 28

DeLoach, Jim, 45–46, 99–100, 228

Deloitte, 35

Delphi technique, 42

Deming, W.E., 45, 97

Dependencies, 311–312

Deterministic, term (usage), 32

Devlin, Keith, 217

Dietvorst, Berkeley, 195–198

di Finetti, Bruno, 130, 211

Digital Millennium Copyright Act of 1998, 289

Dillon-Merrill, Robin, 151–152, 190, 303

Disaster recovery and business continuity planning (DR/BCP), 12

Disasters, 7, 297, 303

Disaster, shape, 236–243

Distributions, 237–239, 237e, 300–302, 308–311, 329

conversion, 233

lognormal distribution, 76, 263

power-law distributions, 240e, 310

types, 76, 309e

Dodd-Frank Wall Street Reform and Consumer Protection Act (2009), 24, 103

Domino effect, 283

Dow Jones Industrial Average (DJIA), 146, 241, 242e

Drucker, Peter, 21, 45, 97

Drug manufacturing, outsourcing (risk), 36–40

Drug production, outsourcing, 39–40

Dunning, David, 44

Dunning-Kruger effect, 44, 210

Duration, measurable unit (usage), 185

Dynamic online source, usage, 331

Dynamic trading, complexity, 335

Earthquake frequency/severity, power-law distributions, 240e

Economic literature, risk/probability (presence), 93e

Economist Intelligence Unit (EIU), 25, 26

Economists (risk management horseman), 82, 90–96

Emotional stimulation, NIH study, 159

Empirica Capital LLC, 207

Empirical data/inputs, usage, 76, 294–305

Empirical observation, 94

Enron, 15, 96, 172

Enterprise Leadership Team (ELT), 341

Enterprise resource planning (ERP), 51, 230

Enterprise risk management (ERM), 11, 18, 55, 227, 339–340

Equivalent bet, 267–269, 271, 276

Equivalent urn (EQU), 269

Estimates, 54, 260–262, 318

Estimation problem, observation, 261

Evans, Dylan, 176

Even-more-common common mode failure, 7

Events, 136, 219, 283, 311–312, 334

Exceedance, probability, 69

Excel, 225, 251–252, 264, 301–302, 315–316

Exercise price, 93

Expected loss column, 307

Expected opportunity loss (EOL), 248–249, 294–295

Expected value of information (EVI), 295

Expected value of perfect information (EVPI), 248–249, 294–295

Experience, features, 136–137

Experts, 64–67, 135, 208, 294, 314

algorithms, contrast, 198–203

intuition, usage, 29–30

subjective estimates, advanced methods, 312–315

Experts inconsistency, reduction, 313–314

Expiration date, 93

Exponential utility function, 125e

Exposures, selection processes, 288

Exsupero ursus fallacy (Beat the Bear), 195, 196, 200–203, 205–206, 210, 259

Extraorganizational issues, 337–339

Failure, 14–17, 298, 300, 300e, 330

Failure modes, effects and criticality analysis (FMECA), 99

Fallacy of close analogy, 236

Fear, uncertainty, and doubt (FUD), sale, 100–101

Federal Financial Institutions Examinations Council (FFIEC), 168, 185

Feedback, 137, 241, 243, 266, 271

Fermi, Enrico, 261, 263, 317

Feynman, Richard P., 35, 150–151, 293, 304, 317

Finance management, Knight (impact), 114–118

Financial Accounting Standards Board (FASB) rules, 171–172

Financial crisis (2008), 8, 96, 229

Financial models, usage, 236–243

Financial portfolio risk, 56

Financial reporting, risk valuation, 172

Fischhoff, Baruch, 139, 145, 153, 191

Fisher, Ronald A., 128, 212

Forecaster, 332–334, 333e

Forecasts, 226, 313, 318–319, 326, 333

Formal errors, 50, 54

Formal inspections indicator, 37

Fractals, usage, 207

Fractionated expertise, 149

Framing, 158

France, Clemens J., 113

Frankendistributions, 311

Franklin, Jim, 329

Freeman, Andrew, 336

Friedman, Milton, 92

Frontline Systems Incline Village, 316

Fukushima Daiichi Nuclear Disaster, 4, 7, 15, 17, 201

Gaussian probability distribution, 236, 242

General Data Protection Regulation (GDPR), 24

Global probability model (GPM), 228–230, 328e, 336–339

Goodness-of-fit tests, 238

Gossett, William Sealy, 311

Governance risk and compliance (GRC), 12

Great Recession (2008/2009), 3–4, 201

Gruenberger, Fred J., 185

Gulf Canada, 99

Hammer, Mike, 97

Health care, patient risks (evaluation), 13

Heat map, 30, 168

Heisenberg, Werner, 113

Hershey Foods Corp., 230

Hester, John, 340–341

Heuer, Dick, 173, 181

Heuristics, 138, 181

High-risk nations, credit risk insurance, 220

Hippocratic Oath, 163

Historical data, 178e, 208, 226, 312

History of histories, 208

Hoblitt, Richard, 235

Homo Economus, 94–95

Horizontal decomposition, 306–307

Howard, Ron, 89, 123, 125, 188

Hoye, Steve, 232–233, 251–252

Human errors/biases, 54, 106

Human estimates, errors, 196

Hume, David, 317

Hurricane frequency/severity, power-law distributions, 240e

Hurricane Katrina, impact, 7, 15, 201

Hybrid deterministic methods, 258

Hybrid distributions, 311

I-knew-it-all-along phenomenon, 153

Impact scale, 167e, 180e

Inconsistencies, 76, 155–160

Independence, presumption, 174, 179

Indifferent criterion independence, 187

Inductive reasoning, 279–280

Information engineering methodology, 98

Information Systems Audit and Control Association (ISACA), 102

Information Technology (IT), 116, 157e, 166, 169, 177–178

Information Technology Governance Institute (ITGI), 102

Information value, 294–295

Infrastructure, 62, 314

Initial benchmarks, data usage, 272–280

Inputs, addition, 76

Institute for Operations Research and the Management Sciences (INFORMS), 190

Institutional factors, 107

Insufficient information response, usage, 215–216

Insurance, 219, 288

Interconnections, consideration, 76

Intergovernmental Panel on Climate Change (IPCC), 170–171, 173

International Olympic Committee, insurance, 219

International Standards Organization (ISO), 24, 30, 168

Interquartile range, 319

Intervals, presumption, 174, 177–179

Intuitive approaches, sale, 101–102

Inventory management systems, reliability, 49

Inversion, Bayes' theorem (usage), 299

Investments, 13, 42

Irrational preferences/belief, 127, 141

ISO 31000, 103

Jaynes, Edwin T., 131

Jefferies, Harold, 212

Jenni, Karen, 191

Joseph, John, 247

Judgment and decision-making (JDM), 137–138, 142–143, 158, 170–171, 180–181, 269

Julien, Rick, 330

Kahneman, Daniel, 43, 126, 130, 137, 140–143, 149, 153, 158, 186, 204, 206, 269, 274, 278, 296, 343

Keynes, John Maynard, 90–91, 111–112

Klein, Gary, 43–45, 137, 269, 283, 330

Klein's premortem, 269

Knight, Frank, 90–91, 111–118, 132–133

Knutson, Brian, 159

Kolmogorov-Smirnov test (K-S test), 238

Kong, Y.S., 287

KPMG survey, 25–30, 32, 36, 46

Kruger, Justin, 44

Laplace, Pierre Simon de, 257, 278, 280, 301, 321

Launch failure, chance, 300

Lehman Brothers, 8, 339

Lewis, Michael, 198

Lichtenstein, Sarah, 139, 145, 269

Lie detection, 42

Life insurance, 288

Likelihood, 30, 169, 172

Likelihood scale, 167e, 170

Linear programming, 91–92

Liquid assets/reserves, 289

Logistic regression analysis, performance, 314

Lognormal distribution, 76, 263, 311

Log t distribution, 311

Long-term capital management (LTCM), 207, 229

Loss contingencies, recognition, 172

Loss exceedance curve (LEC), 68, 69e, 71, 122, 283–285, 341

Loss probability, 132

Loss reduction, 74

Ludic fallacy, 204–205

Lumina Decision Systems, 316

Lump sum, preference, 336

MacGregor, Donald G., 261–262

MacMillan, Fiona, 342

Maintenance, requirement (determination), 13

Management, 10, 83, 96–103

Management consulting services (MCS), 96

Mandelbrot, Benoit, 207

Manhattan Project, 68, 261, 263

Market-based incentives, 334–335

Markowitz, Harry, 91–93, 114–115

Martin, James, 97–98

Massey, Cade, 195

Mathematica, 316

Mathematical misconceptions, 209–217

Matrices, examples, 164–169

Maximum bearable risk, 133

Measurement, 248–250, 297

Meehl, Paul, 198–199, 203, 205–206, 260–261

Memory-based experience, 136

Mental math, 139–142

Merton, Robert C., 94, 207

Meta-history, usage, 322

Metropolis, Nicholas, 68, 263

Meyer, Wayne, 61

Microsoft, 316

Mission failure (predictor), complexity (usage), 265

Mitigation, return, 73–74

Modelers/modeling, 231, 285, 317–322

Modern portfolio theory (MPT), 48, 92–96, 115, 207–208

Monetary loss, subjective assignation, 65

Monte Carlo applications, 225

Monte Carlo-based methods, 250–252, 264–266

Monte Carlo model, 87–88, 179, 252, 296, 305–312, 327–331

Monte Carlo simulations, 28, 67, 71, 202, 216–217, 224–228

arithmetic, 262–264

experience, absence, 71

involvement, 32

probabilistic inputs, requirement, 266

tools, 216, 294

Monte Carlo tools, 295, 315, 316e

Morgenstern, Oscar, 88, 123–124, 186, 188

Mount St. Helens fallacy/risk analysis, 235, 247, 275, 320–321

Multi-attribute utility theory (MAUT), 33, 54, 187–189

Multi-criteria decision-making (MCDM), 33, 187, 189

Multiple objective decision analysis (MODA), 187

Multiplicative risk matrices, 165, 179

Multivariate regression, 155–156

Naive scoring methods, development, 185

NASA, 8, 264–266, 303, 304

National Institute of Standards & Technology (NIST), 24, 30, 102, 166–167, 175, 337

National Transportation Safety Board (NTSB), 7

Near misses, 303–305, 304e

Near miss interpretation paradox, 152

New York Stock Exchange (NYSE), 146

Nietzsche, Frederick, 163

NIST 800-30, 102

Nobel, Alfred, 204

Non-modelers, 231

Nonquantitative matrix, mapping, 281e

Nonrisks, filtration, 281

Normal distribution (Gaussian distribution), 237e, 236–239, 308

Normal probability distribution, 236

Numbers, trust (avoidance), 139–142

Numerical scales, usage, 30e

Observed near miss, 304e

Office building, solutions, 337–339

One-for-one substitution, 62–64, 259, 263–264, 280, 305

Operational probability, 211

Operational risk, 228, 288

Operations research (OR), 87, 91

Opportunity loss (OL), 248

Options, derivative type, 93

Options theory (OT), 48, 94–95, 207–208, 229

Oracle, 316, 329

Ordinal scales, addition/multiplication, 55

Organizational management, 324–327

Organizational Project Management Maturity Model (OPM3), 103

Outage/disruption, cost (equation), 306

Overconfidence, 76, 143, 149–154

Overestimating, consequences, 232

Palisade Corporation, 316

Pandit, Vikrim, 245

Paradigm shift, 186

Partition dependence, 174, 180–181

Past events, fear/anger (involvement), 160

Patton, George, 323

Peak end rule, 139–140

Peak energy user, impact, 240

Pearson, Karl, 156

Performance, 57–59, 314–315

Peters, Tom, 97

Phase-gate analysis, 38

Pilot tolerance curves, creation, 326

Pitch, impact, 96–103

Placebo, 41

Plato, 317

Po, Han-Hui, 172

Poisson distribution, 310–311

Political risk, 165

Positive feedback, 241

Posterior probability, 277

Post-mortem, 283

Power law, 239, 240e, 241, 310, 311

Power tie, impact, 96–103

Prediction markets, 334–355

Premortem, 283, 330

Prequantitative risk analysis, 114

President's Management Agenda (PMA), 24

Private Securities Litigation Reform Act of 1995, 289

Probabilistic functionalism, 155

Probabilistic inputs, requirement, 266

Probabilistic risk analysis (PRA), 87–88, 95–96, 105

Probability (probabilities), 93e, 128–133, 210–212, 259

binomial probability, 301

calibrated probability assessment, 66–67

calibration, 226, 266–272, 314

distribution, 248

posterior probability, 277

prior probabilities, insensitivity, 142

Probability density function (pdf), 299

Probability distributions, usage, 340

Probability of probabilities, 301–302

Probability-weighted average, 143

Productivity improvements, 320–321, 334

Product liabilities, 65, 288

Professional societies, growth, 338–339

Project duration, 320

Project failure risk, example, 120e

Project management, 65, 114–118, 227

Project Management Body of Knowledge (PMBoK), 102, 116, 118, 168, 185

Project Management Institute (PMI), 102, 116, 118, 132, 337

Project management professionals (PMPs), certification, 116

Project portfolio management (PPM), 11

Project portfolios, 13

Project Risk Analysis & Management Guide (PRAM Guide), 116–117

Project risk management (PRM), 11

Prospect theory, 126

Protiviti, 25–28, 45–46, 99, 228, 331

Proven technical proficiency, 37

Pseudo random number generator (PRNG), 69–70, 264, 307

Psychological diagnosis, 41–42

Qualitative procedure, quantitative procedure (contrast), 27–28

Qualitative risk matrix model, 245

Qualitative scales, behavioral research, 54

Quality control, 106–107

Quantitative analysts, errors, 258

Quantitative matrix, 64e

Quantitative models, 54, 202, 230–236, 341–343

Quantitative representation, nonquantitative matrix (mapping), 281e

Quantitative risk models/analysis, 223, 229, 342

R and RStudio, 316

R Foundation for Statistical Computing, 316

RAND Corporation, 88, 91–92, 185

Random deliverable generator (DRG), 97

Random sampling error, 264

Random survey (example), normal distribution (usage), 236–238

Random value, selection, 71

Range compression/forecasts, 174–177, 319

Rank reversal, absence, 187

Rasmussen, Norman C., 87

Rationalism, 317

Red Baron effect, 204

Redundant risks, filtration, 281

Reference class, 274–275, 278–280

Repetition, 266, 271

Representativeness bias, 140

Retailers, list (creation), 274

Return on control, equation, 74

Return on investment (ROI), 57, 175, 185

Return on mitigation (RoM), 285

Right question, answering, 50, 56–57

Risk, 21–24, 27e, 131–134, 280–290, 330–331

appetite/impact, 121, 173, 260

aversion, 159, 174, 181

components/representation, 168, 182

confusion/uncertainty, 106, 109, 110

defining, 8, 9, 65, 117, 131, 257, 284

economic literature, 93e

elimination/loss, 57, 119–121

event, materialization, 65

map, numerical/verbal scales (usage), 30e

matrix, 23, 30–31, 99, 136, 182–183, 250, 280, 284

paradox, 228–236

perception/preferences, 160

probability, subjective assignation, 65

quantification, 233

subjective judgments, human errors (avoidance), 106

uncertainty, contrast, 110

Risk analysis, 12–14, 230, 238–239, 257–258, 298

change, World War II (impact), 86–90

decision, support, 73–75

impossibility/problems, 200, 217–221

saving, psychologists (impact), 137–139

Risk assessment, 26–34, 54, 84, 309, 323

formal approach/methods, 27, 159

methods/guideline, 29e, 163, 229–230, 338

RiskLens, 316

Risk management, 7–16, 21, 25–26, 105–107, 285–290, 290e

apocalypse, 81

change, power tie/pitch (impact), 96–103

clarification, 324

evolution/solutions/language, 257–266

four horsemen, 81–83, 103–105, 104e

improvement, 90, 193, 258–259

measurement/methods/process/evaluations, 29, 48–52

process, 7, 47–48

profession, growth, 337–338

skepticism, 3

success-failure spectrum, 58–59

Risk Management Guide for Information Technology Systems (NIST 800-30), 166–167

Risk/return analysis/model, 287–288, 324–325, 327, 330

Risk Reward Limited, 339

Risk Solver Engine, 316, 329

Risk tolerance, 72–73, 121–128, 133, 159, 260, 325

Robust Bayesian method, 300e, 301, 304e

Robust prior, 277

Rogers Commission Report, 150

Roychowdhury, Vwani, 154

Rubin, Robert, 246

Rule of succession, 278

Rumsfeld, Donald, 133

Russell, Bertrand, 279–280

Saaty, Thomas, 189–190

Sagan, Carl, 3

Sales goal, reaching (failure/risk), 284

Sam Savage Probability Management, 316

Samples, 141–142

Sarbanes-Oxley, 338

Sarbanes-Oxley Act of 2002, 24, 172

SAS Corporation, 316

Savage, Leonard J., 89, 128, 186

Savage, Sam, 89, 186–187, 209, 251, 259, 324–325, 329

Scales, 173–178, 176e, 178e

Scenarios, set (generation), 314

Schoemaker, Paul J.H., 135

Scholes, Myron, 94, 207

Schuyler, John, 233, 285, 331

Scores, 164–169, 176e, 177, 183–186, 189–191

Scoring, 169, 177, 183–191

Security threats, protections level, 13

Self-assessments, 44–48

Sharpe Ratio, 56

Shuttle disaster, chance, 304e

Silver, Nate, 196–198, 201, 207

Simkin, Mikhail, 154

Simmons, Joseph P., 195

Simulated loss column modification, 307

Simulations, 71, 216–217

SIPMath, 316

Slovic, Paul, 139, 153

Smith, Adam, 322

Smith, Fredrick, 35

Spinoza, Benedict de, 317

Spreadsheet errors, 331

SPSS Inc., 316

Stage-gate analysis, 38

Stakeholders, risk management, 47, 326–327

Standard deviation, 273

Standard & Poor's 500 (S&P500), daily price drop, 241–242, 242e

Statement of Actuarial Opinion, 337

Statistical models, usage, 260–261

Statistical Research Group (SRG), 86

Statistical tests, misconceptions, 212–216

Stochastic information packets (SIPs), 329

Stochastic library units with relationships preserved (SLURPS), 329

Stop-gate analysis, 38, 229

Straw man quantitative model, 18, 61, 75–77

Stressed-system failure, 243

Strict uncertainty, 133

Structural model, 95

Structured approaches, sale, 101

Student t distribution, 311

Subjective estimates, 226, 312–315

Subjective judgment, 76, 136

Subjective preferences, 186–189

Subjective risks, methods (problems), 106

Subject matter experts (SMEs), 231, 266, 270–272, 285, 296, 330, 334

Substitution, checking, 280–285

Succession, 278, 321

Supercriticality, 87

Supply chains, 13, 65

Swans, bears (contrast), 193

Taleb, Nassim, 203–209, 224, 236–237, 279–280

Technology adoption rates, 320

Terry, Thompson, 342

Test group, 213

Testimonial, 48, 101

Tetlock, Philip, 199, 206, 315, 335

Thaler, Richard, 139

Thomas, Philip, 182

Thorp, Edward, 206–207

Threat (risk component), 168

Time scales, change, 321

Total risk, reduction, 287

Tracking, 317–318, 320

Training requirements, determination, 325–326

Transitivity, 187

Triangular distribution, 308–309

True/false predictions/questions, 144e, 266–267, 319, 333

Truncated distributions, 311

Trustmark Mutual Holding Company, 339–341

Twain, Mark, 209–210

Tversky, Amos, 137–138, 140–143, 158, 186, 269–270

Ulam, Stanislaw, 68, 263

Uncalibrated individuals, calibrated individuals (comparison), 145e

Uncertainty, 109–113, 132–135, 237, 258–266, 324

aleatory uncertainty, 129

exclusion, 233–234

expression, IPCC report terms (variances), 172e

math, overview, 67–71

offsetting, ambiguity (impact), 170–173

real-world problems, 209

updating, Bayes theorem (usage), 297–301

Uncertain variables, 249

Underestimating, consequences, 232

Unexpected risk, 284

Uninformative prior (robust prior), 277

Union Carbide, disaster, 282

United Airlines flight 232, crash/deaths, 6

Unknown unknowns, 133

Unquantifiable randomness, 114

Upside risk, 114

Utility, 124, 188

Value at risk (VaR), 95–96, 251

Values, combination (usage), 314

Variable, 247, 297

Variance, 114–115, 118

Vector quantity, project failure expression, 120e

Verbal scales, usage, 30e

Vertical decomposition, 306

Volatility, 115–116, 322

Voltaire, 3, 109, 193

Von Neumann, Jon, 68, 88, 89, 123–124, 186, 188, 193

Von Richthofen, Manfred (Red Baron), 154

Vulnerability (risk component), 168

Wald, Abraham, 88, 90–91

Warehouse inventory, loss, 179

War quants (risk management horseman), 82, 86–90

Weighted inputs, usage, 184

Weighted risk score, 31

Wells, H.G., 81

Winkler, Robert, 313

Wolfram Research, 316

Worst-case scenario, 32, 39, 282

Z decompositions, 307

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