EXTREME
RISK MANAGEMENT
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EXTREME
RISK MANAGEMENT
REVOLUTIONARY APPROACHES TO EVALUATING AND MEASURING RISK
CHRISTINA RAY
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-175956-4 MHID: 0-07-175956-5 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-170059-7, MHID: 0-07-170059-5. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative please e-mail us at
[email protected]. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that neither the author nor the publisher is engaged in rendering legal, accounting, securities trading, or other professional services. If legal advice or other expert assistance is required, the services of a competent professional person should be sought. —From a Declaration of Principles Jointly Adopted by a Committee of the American Bar Association and a Committee of Publishers and Associations TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGrawHill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.
CONTENTS
Preface
vii
Chapter 1
Plausibility versus Probability: Two Worldviews
1
Chapter 2
The Evolution of Modern Analytics
8
Chapter 3
Natural Selection on Wall Street
23
Chapter 4
A Review: Risk Management Metrics, Models, and Best Practice
32
Chapter 5
Systemic Risk and Systems Thinking
61
Chapter 6
Belief Systems and the Inadvertent Conspiracy: The Global Capital Markets as System 81 Chapter 7
Analytic Tradecraft and Model Risk
94
Chapter 8
The Future as Forecast: Probability, Likelihood, and Uncertainty 117 v
vi
Contents
Chapter 9
An Alternative Path to Actionable Intelligence
144
Chapter 10
Solutions: Moving toward a Connectivist Approach
153
Chapter 11
An Introduction to Causality: Theory, Models, and Inference 165 Chapter 12
Bayesian Inference Networks: Estimating Vulnerability, Consequences, and Likelihood 175 Chapter 13
Securities Valuation, Risk Measurement, and Risk Inference Networks 189 Chapter 14
Risk Fusion and Supermodels: A Framework for Enterprise Risk Management 206 Chapter 15
Inferring Causality from Historical Market Behavior Chapter 16
Sensemaking for Warnings: Reverse-Engineering Market Intelligence 230 Chapter 17
The United States as Enterprise: Implications for National Policy and Security 245 Notes
263
Index
279
216
PREFACE
Shortly after September 11, 2001, I was struck by the stories in the press alleging insider trading in the stocks of the airlines involved in the attack. Dr. William Hery, research professor at the Polytechnic Institute of NYU, and I posited the ability to reverse-engineer actionable market intelligence, or MARKINT, that might be useful in counterterrorism from publicly available market information and prices. One of the earliest supporters of MARKINT was Randolph Tauss, director of corporate strategy at Omnis, Inc., who, while a senior government program manager, enthusiastically adopted the concept. Since then, my scope and interests have widened. Over the last eight years, I have come to see the intelligence community and the financial community as having essentially similar issues with respect to the measurement and mitigation of extreme risk. However, I’ve also seen that the members of each community are largely unaware of the applicability of the other’s work to their own problems. The financial community is generally unaware of the mathematical sophistication that has been operational in the defense community for a number of years in the form of network-centric operations within the Department of Defense. Similarly, in spite of new emphasis on open-source intelligence, or OSINT (as opposed to intelligence gathered by sensors or clandestine operations), the national security community is largely unaware of the wealth of information and analytical models available in the financial community that might be retasked to its purposes. Fortunately, this is changing. The financial crisis of 2007–2008 has been a driver of analytical change, and the missions of the financial and intelligence communities have never before been so aligned. Recently, vii
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Dennis Blair, the new director of national intelligence (DNI), said that the “primary near-term security concern of the United States is the global economic crisis and its geopolitical implications.” The President’s Daily Brief (the PDB) has been joined by the daily Economic Intelligence Brief (the “Butterfly Brief”), both of which are classified intelligence community products. The CIA is now publicly advertising employment opportunities for ex-Wall Streeters. At the same time, failures in risk management protocols and models by top-tier institutions such as Lehman Brothers and Bear Stearns have spurred a search for alternatives. And recognition of the causal chains that led to the crisis has led some theorists to move from backward-looking statistical models to forward-looking causal inference models. Fortunately, the financial community is just now starting to take a systems view of the elements and interconnections of the causal network that is the global markets in an effort to explain and anticipate “black swan” events (i.e., undirected, unpredicted, and rare events) and “tipping points” (i.e., points at which a previously rare phenomenon becomes dramatically more common), popularized by Nassim Taleb and Malcolm Gladwell, respectively. This book contains much of what I’ve learned by having a foot in each world. It is meant to be a modern Art of War for those who are involved in the pseudo-warfare of trading in the global capital markets. Appropriately, I’ve been immeasurably assisted by experts from each world. From the financial community, I would like to thank Dr. Robert Mark, the founder of Black Diamond Risk Enterprises and one of the premier experts in the world on risk management and corporate governance. Bob generously suggested some additions on the subject of systemic risk and current best practice in risk management and contributed examples of typical risk reports. And from the government community, I would also like to thank Dr. Paul Edward Lehner, consulting scientist at the Center for Integrated Intelligence Systems of The MITRE Corporation. Paul provided me with extraordinarily insightful comments (and an education in cuttingedge developments in mathematical psychology) as well as a unique perspective of the complementary analytical techniques used by the private and public sectors. I’m also very appreciative to Bryan Ware (CEO), Dr. David Daniels (chief scientist), and Linwood Hudson (VP product development) of Digital Sandbox, Inc., of McLean, Virginia, who provided me with examples of risk inference networks used for purposes of national security.
Preface
ix
My thanks also to Professor James Moffat, who allowed me to reproduce his fascinating summary of complexity concepts as they apply to information-age military forces, and to Dr. Julien Diard of the Laboratoire de Psychologie et NeuroCognition, Université Pierre Mendès France, who allowed me to do the same with his comprehensive hierarchy of probabilistic modeling formalisms. And last but not least, my appreciation to Quantum 4D, Inc., and Palisades Corporation, who generously provided me with network analysis and visualization tools with which to create working examples of concepts from this book.
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CHAPTER 1
Plausibility versus Probability: Two Worldviews
Over the last three decades or so, sophisticated financial modeling has been almost exclusively statistical in nature. The ready availability of massive amounts of historical market data has fueled the creation of valuation and risk measurement models built on concepts such as association, correlation, and likelihood. All these models create implicit forecasts, that is, estimates of expected and possible future scenarios for a security or a portfolio of securities. Most often, these forecasts are based on the assumption that the future market behavior is well represented by the past. However, this stochastic approach implies a worldview that ignores causality in favor of correlation. In this world, it doesn’t matter whether gold prices increased because interest rates decreased or vice versa. It also doesn’t matter whether the prices of a utility stock and an airline stock are directly related in some fashion or whether, instead, they are both driven by a common dependence on fuel prices. This world is a supremely efficient world as well: all prices reflect new information immediately, and that information is transmitted instantaneously around the globe. However, intuition belies these notions. Traders and portfolio managers know that events drive prices. Catalysts such as the release of an economic indicator or an earnings report drive prices, and chain reactions precipitated by an important event can take a finite amount of time to propagate. Such statistical models were often sufficient in the past, when the volume and complexity of derivative instruments were far lower than they are today. But now, the value and risk of popular instruments such as options on credit derivatives and complex asset-backed securities increasingly depend on the modeling of low-probability, high-consequence events. If the models used are not adequate for the task of anticipating such high-consequence events, massive losses and market disruptions can 1
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occur. Certainly the financial disruptions that began in 2007–2008 are abundant evidence of such failures. But as the old saying goes, “Correlation is not causation.” The alternative to a statistical model is a causal model that explicitly creates an alternative worldview, one in which cause and effect are modeled in logical or temporal order. This alternative world is one in which plausibility rather than probability is modeled. The consequences and likelihood of events that have never before occurred but that can be reasonably anticipated (as a consequence of other events) are included in the quantitative models. Such modeling is the forte of the intelligence community and those responsible for national security, who must create metrics and construct solutions for threats that have never before occurred. Plausibility can be determined from a mixture of expert opinion, hard facts, and historical experience. Although the structure of any causal model may be guided by the insights of human experts, it need not be strictly an expert system. Instead, through a process of causal inference, past history can be used to validate and inform the model. A causal model is not necessarily deterministic; it can allow for uncertainty. Ideally, causal inference facilitates the integration of substantive knowledge with statistical data to refine the former and interpret the latter. Such causal models are used in other disciplines, most notably epidemiology and decision science. They are little used in finance, with the notable exception of the measurement of operational risk (i.e., the risk of loss due to human error). Causal models are nearly absent from1 quantitative modeling for purposes of instrument valuation or market and credit risk measurement. The preference that quantitative analysts have for “frequentist” or probabilistic models over causal models over the last three decades is understandable for a number of reasons. First, such models are relatively easy to create and implement, using financial theories (such as modern portfolio theory) that are already well accepted and in the public domain. Also, until recently, neither the mathematical language nor the technical tools that might facilitate the creation of causal models existed. Although the financial community commenced serious quantitative modeling in the 1970s, it wasn’t until the mid-1980s that much substantive work was done on causal models, even within the academic community. Thus, the creation of rigorous theory, methodologies, and a language of causality that might have facilitated such model building did not exist at the time the financial community was choosing its path. Perhaps more
Plausibility versus Probability: Two Worldviews
3
important, even if such models had been created, the data required to inform them were usually insufficiently granular, synchronized, and properly organized for use in a causal inference process. However, now, in the words of Judea Pearl, a leader in this field, “Put simply, causality has been mathematized.” At the same time, certain technological innovations have made causal inference practical in the financial arena. Consider one of the key questions in causal inference: How can one distinguish between mere correlation and cause and effect? When the sun rises and the cock crows, was one of these two events the catalyst for the other, or were they both the consequence of a third event? One of the best methods of validating causal relationships is via experimentation. We can wake up the cock at 3 a.m. and see if this causes the sun to rise. Or an experiment can be designed to eliminate all variables but one: for example, in medical trials, the effect of the drug on a patient. To produce valid results, such an experiment would probably contain key features used in causal modeling, such as randomization (e.g., patients are randomly selected to receive an experimental drug or a placebo) and elimination of exogenous factors (e.g., variations in age or sex). Fortunately, in finance, the capital markets are a laboratory that continuously provides us with natural experiments. Thus, rather than using historical market prices in statistical analyses, we can use them in causal inference models. Every day, traders receive information about catalytic events that move markets and are able to observe the synchronous or subsequent effects of those catalysts. Technological advances now make the observation of these natural experiments both possible and practical. Formerly, end-of-day data were relatively useless for determining causation because so many important events occur during the course of a trading day. Just as in a medical trial, when there are multiple variables, reliable causal inferences are exceedingly difficult to make. Only in the last few years has commercial software become available that is capable of capturing event data and synchronizing those data with real-time market data of the highest granularity. This synchronized information gives us the means to learn from one controlled experiment at a time, even if the experiments last just seconds. Although many events occur in the course of a trading day, few of them occur simultaneously, where simultaneous is defined as occurring within the same very small window of time. For example, we might capture the earliest moment at which an earnings report became public or a report on crude oil inventory was released. If we then examine the real-time
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behavior of stock or oil prices in the seconds to minutes after the release, we can form opinions about how such an event drives prices. Besides potentially providing better estimates of value and risk, causal models may be more intuitive and understandable by risk managers and portfolio managers than statistical models are. For example, the language of causality is a natural language for risk management. Examples of causal concepts are influence, ignorability, disturbance, effect, confounding, intervention, and explanation. The graphic representations that substitute for mathematical equations lend themselves well to financial applications. As Pearl points out, there is no analog in algebra or statistics to the causal operator “given that I do,” that is, the effect of a deliberate action on the outcome of the analysis. However, these representations lend themselves well to programming. Computer code does allow such operators; the statement A ⫽ B is a substitution rather than a statement about an inviolate relationship between A and B. Similarly, hedge positions can be considered “interventions” that can block certain paths: those that lead to undesirable outcomes, such as very large losses. Such a hedge might be a security that is already in a portfolio or, alternatively, an exogenous variable that drives changes in one or more securities in the portfolio. Further, the identification of hierarchically organized causes lends itself very naturally to the identification of systematic and specific risks as required by the Basel II accord. Such methods may provide results that are far superior to those provided by statistical methodologies such as principal component analysis,2 the results of which can be degraded by spurious correlations without expert intervention. Causal models also provide a natural framework for the estimation of two key risk measures for which no industry-standard methods yet exist: economic capital (the amount of capital required to ensure the continued existence of the enterprise to a very high degree of confidence) and enterprise risk (the risk to an enterprise from all sources of risk). In such models, expert opinion can be integrated with historical behavior to systematically generate all plausible future scenarios, estimate their likelihood, and measure their consequences. All else being equal, a causal approach is preferable to a statistical approach for several reasons. First, a causal approach allows a more general solution. A statistical solution can be simulated, albeit inefficiently, using a causal network that includes an error component. However, the reverse is not true. Second, causal networks do not require extensive historical data for all the securities and instruments in a portfolio. Causal models can be used
Plausibility versus Probability: Two Worldviews
5
even when history is not a reliable indicator of the future—for example, when a shift in risk regime has occurred or when new risk factors such as changing regulatory policy are expected to have a significant impact. Causal networks can also be allowed to have a specific order in which events occur or a temporal component suitable for high-frequency trading and real-time risk management. Forecasts of consequential behavior produced in sufficient time to execute a trade can be used in automated, algorithmic trading. Further, observed market behavior that is time dependent (e.g., volatility clusters and jump diffusion processes) might be more easily explained in terms of causal models than it is by statistical models. Also, instead of relying on solutions such as GARCH3 methods or stochastic volatility models4 to calibrate observations to history, such observations might be explained in terms of the observable, noninstantaneous effects of traders’ and portfolio managers’ behavior.5 A causal approach can use all available information to inform the model, not just historical pricing data. In the terminology of the intelligence community, this is the use of “all source intelligence.” For example, additional fundamental information might be used to inform (or override) certain causal relationships. The sensitivity of an airline to the price of fuel might be independently modeled by a fundamental equity analyst and then compared to the relationship inferred by the causal model. Or if a publicly traded home builder has never before hedged its interest-rate exposure but has just started such a program, the past dependence of the company’s stock price on interest rates might be overridden. A causal approach is far more dynamic than a statistical approach because it allows the introduction of prior knowledge. A forecast of one-day risk is substantially different one second after the release of the monthly unemployment statistics from what it was one second before that release, based on knowledge of both market expectations and the actual news. In the language of causal modeling, these are the prior and posterior distributions. Most important of all, a causal structure provides far more transparency than do statistical parameters. The graphical language of causal modeling reveals the fundamental relationships assumed by experts and inferred from data and lends itself to the use of visualization tools that enhance clarity and aid human cognition. The process of building such a model also removes some of the intellectual barriers between the front office and the middle office and between technical analysis and fundamental analysis. Causal relationships that can be understood and vetted by human experts with multiple areas of expertise are far more likely to be repeated in the future. Clearly, causal models are somewhat more difficult to implement and to inform than are statistical models. However, when they are used for
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certain purposes, such as valuing complex derivative instruments, estimating extreme or real-time portfolio risk, or designing an optimal hedging strategy, they are well worth the effort. For example, one of their major advantages is the ability to perform discrete-time and discrete-outcome modeling. Although common statistical methodologies such as copula approaches are mathematically elegant, they often implicitly eliminate the granularity, asymmetry, and noncontinuous behavior that are interesting features (and opportunities for profit) of real markets. By doing so, they may substantially over- or underestimate value or risk, particularly for instruments with a narrow payoff window, such as nth-to-default tranches in collateralized debt obligations,6 or in strategies such as calendar or price spreads in options. What a causal approach lacks in computational elegance it may make up for in accuracy. Consider a situation in which Treasury bond traders are split 50/50 on whether the Treasury will announce an auction of 30-year bonds. This is a binary event: it will occur, or it will not; the yield curve will flatten or steepen. A realistic forecast of changes in 30-year bond yields just after the announcement is likely to be bimodal because there is no neutral event. The benefit of a causal model is its ability to generate many plausible scenarios in a systematic fashion. The likelihood of some of these scenarios may be higher than in a random-walk world; that of others may be lower. Markets may have “hot spots” and “cold spots”: scenarios in which a convergence of certain chain reactions is likely to have major market repercussions or, conversely, scenarios that are virtually impossible. This alternative forecast of the future, in which the distributions of possible outcomes can be granular, be asymmetrical, and have extreme outcomes, has profound implications for financial engineering, portfolio management, risk management, and even decision science. Clearly, a set of possible future scenarios substantially different from those created using continuous, normally distributed variables, suggests radically different results for all kinds of estimates. Specifically, valuation models, particularly those for securities or complex derivative instruments, will produce results that are substantially different from the results of standard models that assume normality, symmetry, and outcomes that are in line with historical experience. Portfolio optimization and performance attribution models are similarly affected. The interactions between the securities in the portfolio may be poorly described by statistical measures such as correlation, and an ideal portfolio (i.e., one with an optimum risk-return profile) constructed using such
Plausibility versus Probability: Two Worldviews
7
scenarios might look quite different from one constructed using more traditional methods. Most important, risk measurement models based on causal methods may estimate risk to have a magnitude that is either far greater or far less— as well as less continuous—than that estimated using traditional stochastic models. Certain outcomes that were formerly assumed to be virtually impossible must now be considered, whereas others are now less likely than before. At the heart of all risk measurement (and in fact all financial engineering) is the ability to generate all plausible alternative scenarios and estimate their likelihood. The sensitivity of a portfolio, an enterprise, or even the global capital markets themselves to the most extreme of these scenarios provides a systematic method for generating stress tests (i.e., measures of the consequences of a particular scenario) and ensuring the continued existence of the system as we know it. The use of causal methods also provides solutions; they can be used to mitigate as well as measure risk. They provide a method for inserting circuit breakers into a portfolio or a banking system to subvert the most catastrophic outcomes. For example, a portfolio manager might purchase far out-of-the-money calls on crude oil to hedge the risk of large declines in the price of airline and hospitality stocks, or a regulator might modify capital requirements or position-limit rules. The ultimate goal of enterprise risk management is as a quantitative decision-making tool. Ultimately, the use of causal methods facilitates the highest-level goal of risk management: decision making by senior management. An understanding of the possible future paths that might trigger tipping points and lead to catastrophic outcomes can assist C-suite executives in optimizing their business strategies on a risk-adjusted basis. SUMMARY In this chapter, we contrasted frequentist and causal approaches to risk management and their utility in measuring and mitigating extreme risk and optimizing decision making. WHAT’S NEXT In the next chapter, we will relate key milestones in the evolution of risk management philosophy and describe the most recent and revolutionary innovations in quantitative decision making.
CHAPTER 2
The Evolution of Modern Analytics
The recent journey toward the current state of quantitative finance owes as much to philosophy as it does to mathematics. It has been said that a human can’t visualize a number of objects greater than five without breaking them into smaller groups, such as two sets of three or three sets of two. For more complicated problems, humans have always had to create an abstraction or model of how things work. As eloquently described by Peter Bernstein in Against the Gods: The Remarkable Story of Risk1 scientists of the seventeenth and eighteenth centuries considered the problem of decision making under uncertainty. Some of the greatest mathematicians in history (including Isaac Newton) were tasked by their patrons with solving gaming problems, with profit as the motive. Such problems provided the perfect thought experiment, involving as they did both chance and preferences. In a sense, they forced the evolution of the financial markets, since those who used these insights to inform their decisions prospered, whereas those who did not became extinct. This process of financial natural selection continues today. It’s a short leap from the gaming table to the trading room. Broker-dealers and hedge funds that were able to adequately manage risk survived and prospered during the financial crisis of 2008, whereas those that were not (including Bear Stearns, Lehman Brothers, and AIG) did not. Along the evolutionary path are two historical milestones that were separated by more than 200 years but are suddenly receiving more attention from the mainstream of economic thought nearly simultaneously. DANIEL BERNOULLI AND A NEW THEORY ON THE MEASUREMENT OF RISK In 1954, spurred by a spate of recent references to this work, the journal Econometrica2 published the first English translation from the original 8
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Latin of Daniel Bernoulli’s 1738 Specimen theoriae novae de mensura sortis, or Exposition of a New Theory on the Measurement of Risk.3 Bernoulli is far more famous as a physicist for his contributions to fluid mechanics, including the basic principles that allow aircraft to fly. Exposition was considered an exceedingly minor scientific contribution until its rediscovery by economists, evolutionary biologists, computer scientists, and others in the second half of the twentieth century. Although Dr. Louise Sommer, the translator, explicitly attempted to retain the article’s eighteenth-century flavor, the concepts and language of the article are astoundingly up to date. This amazingly concise and complete piece of work not only discussed basic probability theory but also put forth the concepts of individual preferences and utility functions, which together form the foundation of a framework for cutting-edge topics such as quantitative decision support4 and enterprise risk management (ERM). For example, in discussing optimum wagering decisions, Bernoulli rejected the notion that the expected outcome (based on probabilities) should always be maximized and introduced sophisticated concepts such as risk premia5 and utility functions:6 Somehow a very poor fellow obtains a lottery ticket that will yield with equal probability either nothing or twenty thousand ducats. Will this man evaluate his chance of winning at ten thousand ducats? Would he not be ill-advised to sell this lottery ticket for nine thousand ducats? To me it seems that the answer is in the negative. On the other hand, I am inclined to believe that a rich man would be ill-advised to refuse to buy the lottery ticket for nine thousand ducats. If I am not wrong then it seems clear that all men cannot use the same rule to evaluate the gamble.
Bernoulli went on to more formally introduce key concepts such as quantitative measurement of risk, diversification, hedging, and, perhaps most important, the concept of maximizing utility rather than expected return: Thus it becomes evident that no valid measurement of the value of a risk can be obtained without consideration being given to its utility, that is to say, the utility of whatever gain accrues to the individual or, conversely, how much profit is required to yield a given utility . . . the determination of the value of an item must not be based upon its price, but rather the utility it yields.
Long before the advent of behavioral economics, Bernoulli proposed the famous St. Petersburg Paradox, first suggested to him by his distinguished cousin Nicholas Bernoulli. In this simple but elegant thought
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experiment, he presages preference theory by introducing the topic of human preferences in valuation decisions. In this experiment, a casino offers a gambler the opportunity to enter a game in which a coin is tossed repeatedly. The pot starts at one ducat but doubles each time heads appears on the toss. The game ends when tails appears, and the gambler realizes whatever is in the pot at that time, that is, 2k⫺1 ducats if tails appears on the kth toss. The question is, what should the gambler be willing to pay to enter this game? The series has an expected value of infinity, since there is always some finite—albeit minuscule—probability of an infinite number of coin tosses. Bernoulli recognized that there was a disconnect between what one might expect the gambler to pay and the expected value of infinity for the payout. Theoretically, the gambler should be willing to enter the game at any finite buy-in amount, but this is clearly a counterintuitive result (some have suggested that the mean amount that gamblers are willing to pay is as little as 25 ducats). A number of solutions to resolve this paradox have been suggested, but they tend toward the practical: no casino would offer a game that could lead to an infinite expected loss or has the resources to pay off on the most lucrative payouts (an implicit acknowledgement of credit risk), or gamblers tend to underestimate the probability of the most extreme outcomes. Bernoulli’s more insightful solution was to introduce the concept of a marginal utility function, in which he suggested that the utility to the gambler of each possible ducat earned is not equal. For example, the value to the gambler of the first ducat he earns is greater than that of one additional ducat added to a payoff of, say, 1,024 ducats (after 11 tosses). Depending on the nature of the function (Bernoulli suggested a logarithmic form7), the series can be made to converge to an intuitively acceptable value by weighting each successive outcome by its diminishing utility. Bernoulli presaged behavioral economics by recognizing that the price at which a particular bet might trade might be quite different from its theoretical value, excluding preferences; in the case of the St. Petersburg Paradox, it would trade at around 25 ducats instead of infinity. Instead of calculating the expected value, he calculated the expected utility. Bernoulli explicitly recognized that the price at which a bet might trade is a function of both objective measures of its worth and investors’ net preferences. In Exposition, Bernoulli addressed nearly every important issue having to do with portfolio diversification, optimum portfolio construction,
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risk measurement, capital adequacy, and decision making under uncertainty. He presages risk metrics such as value at risk (VaR),8 which are designed to constrain the worst outcomes possible, and capital requirements, and he even dealt with issues such as optimal hedging and the efficient frontier described by Markowitz 200 years later. However, probably his greatest philosophical insight was that Decision theory ⫽ probability theory ⫹ utility theory In Exposition, Bernoulli also considers the case of Caius, a Petersburg merchant who is deciding whether to insure commodities purchased in Amsterdam and transported by sea. The risk is high—he assumes that 5 of 100 ships sailing from Amsterdam will be lost—and the price of insurance is correspondingly high. “The question is, therefore, how much wealth must Caius possess apart from the goods under consideration in order that it be sensible for him to abstain from insuring them?” Bernoulli also asks the opposite question (i.e., from the viewpoint of the seller of insurance rather than that of the buyer): “What minimum fortune should be possessed by the man who offers to provide this insurance in order for him to be rational in doing so?” His answer is this: “This is the rule: that it is advisable to divide goods which are exposed to some danger into several portions rather than to risk them all together.” Bernoulli demonstrates that another merchant, Sempronius, would be best advised to diversify his investments among multiple ships. “In this way the value of Sempronius’ prospects of success will grow more favorable the smaller the proportion committed to one ship. However, his expectation will never rise in value above 7200 ducats. This counsel will be equally serviceable for those who invest their fortunes in foreign bills of exchange and other hazardous enterprises.”9 The power of Bernoulli’s logic is demonstrated by the fact that it has been adapted by other disciplines. For example, in evolutionary biology, the geographical dispersion of a species via migration increases the probability that the species will continue to exist in spite of the fact that some price was paid during migration. If a species remained in place at a location with uncertain environmental conditions, it would eventually die off. This is equivalent to a species hedging its evolutionary bets via diversification. As brilliant as his insights were, Bernoulli’s computational problems were trivial. His case studies dealt with discrete events: a coin toss results in either heads or tails; a ship does or does not survive a winter storm. There was little uncertainty regarding the odds of each event, as well: the probability of heads is 50 percent; the nature of winter storms at sea and
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the failure rate of eighteenth-century ships were relatively stable. Further, there was zero or weak correlation between the discrete events: the coin has no memory, and each ship’s fate was assumed to be independent of the others’. LOUIS BACHELIER AND BROWNIAN MOTION Almost two centuries later, the French mathematician Louis Bachelier expanded on Bernoulli’s work on the role of chance. Although little known in finance, Bachelier contributed both the philosophical and the mathematical foundations for modern quantitative finance. In July 2000 and on the occasion of the hundredth anniversary of the publication of Bachelier’s Ph.D. dissertation, the authors of a tribute to Bachelier in the journal Mathematical Finance10 declared, “The date March 29, 1900, should be considered as the birthdate of mathematical finance. On that day, a French postgraduate student, Louis Bachelier, successfully defended at the Sorbonne his thesis Theorie de la Speculation (The Theory of Speculation).” Anecdotally, the instructor who reviewed Bachelier’s dissertation was the famous mathematician, physicist, and philosopher Jules Henri Poincaré, the first to describe a chaotic deterministic system in physics that laid the groundwork for modern chaos theory. This dissertation contains a number of advanced financial concepts. Because Bachelier had responsibility for his family’s business (wine merchants), he had practical experience with French financial instruments, including forward contracts and options. Bachelier considered the evolution of stock prices over time to follow a Markov process, that is, a memoryless process in which the future depends on the current state of the system, not on its past. Bachelier stated, “The expectation of the speculator is zero.” This simple statement, along with his description of the Brownian motion that is an element of nearly every stochastic model in finance, presages an explicit representation of the efficient market hypothesis posited by Eugene Fama in his doctoral dissertation more than 60 years later. Bachelier demonstrated that a Gaussian (normal) distribution with variance that increases linearly with time correctly represents the results of a Markov process.11 Stunningly, Bachelier also presages the BlackScholes option-pricing model of the 1970s (inspired by a heat flow equation in physics) when he also observes that this family of distribution functions satisfies the heat equation: like heat, the probability diffuses or “radiates.”
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The Black-Scholes partial differential equation (PDE), from which the famous option-pricing formula for European-style12 options is derived, is dSt = mStdt + sStd Wt where St is the price of the underlying stock, m is the mean return, s is the standard deviation of returns of the stock, and Wt represents Brownian (random) motion (also called a Weiner process). This formula contains two components: one deterministic, in that the price is expected to trend over time along the mean expected return, and one stochastic, in which Wt represents all sources of uncertainty in price movement over time. Bachelier’s contribution to this concept has recently received new attention. As Courtault and his associates state in their centenary tribute, “It is worth noting that in spite of the fact that in modern English textbooks Brownian motion is traditionally referred to as the Wiener process, the original terminology suggested by W. Feller in his famous treatise An Introduction to Probability Theory and Its Applications (1957) was the Wiener–Bachelier process.” Bachelier’s work on Brownian motion also predates Einstein’s work on the subject. In his dissertation, Bachelier even applied his theories to the problem of option pricing, including that of American-style13 path-dependent options. This exceedingly practical contribution was unusual for a rigorously mathematical work. In it, he calculated the probability that a stock price controlled by Brownian motion does not exceed some threshold (the strike price) and identifies the least upper bound of the Brownian motion. The tribute continues: “Bachelier considered that his principal achievement was the systematic use of the concept of continuity in probabilistic modeling: the continuous distributions are the fundamental objects correctly describing the very nature of many random phenomena and not just mathematical inventions simplifying a work with discrete distributions.” Bachelier’s Theorie seemed destined for oblivion until it received fresh attention during the golden age of finance of the 1950s and 1960s. Economist (and later Nobel Prize winner) Paul Samuelson started to circulate the piece among his colleagues. Its appeal was instantaneous, and Samuelson and others took great interest in its implications. But Wall Street didn’t catch up with him until decades later, when stochastic calculus and some of its specific applications (for example, the copula function, which allowed the computation of joint marginal probability distributions) were required for increasingly complex valuation and risk management problems.
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FAMA AND THE EFFICIENT MARKET HYPOTHESIS One of the most powerful concepts in twentieth-century economic thought was the efficient market hypothesis (EMH). EMH posits that all markets for traded assets are informationally efficient; that is, the price of each security reflects all public information known about that security at any point in time, and prices correct instantly as news becomes known or other events occur. Like Einstein’s mythical dice, market prices are therefore memoryless, and changes to them can be represented by a random process. EMH implies that markets in the aggregate are rational; that is, although individual investors may over- or underreact to new information, on average they will correctly assess the effect of that information on price, and their diverse opinions are randomly distributed. EMH therefore anticipates the “wisdom of crowds” popularized many years later, which serves as the philosophical foundation for prediction markets. EMH was formalized and expanded by Eugene Fama (also within his Ph.D. dissertation, originally published in 1965) at the University of Chicago. In an article titled “Efficient Capital Markets: A Review of Theory and Empirical Work,”14 Fama identified three forms of efficient markets: weak-form, semistrong-form, and strong-form efficiency. Each of these had implications for mathematical finance and the suitability of stochastic methods for forecasting and risk measurement. In weak-form efficiency, Fama proposed that there is no serial correlation between successive prices in a time series. This implies that patterns in prices (for example, those identified in technical analysis15) that can be exploited for predictive value cannot exist. In weak-form efficiency, only fundamental analysis (e.g., projections of a company’s earnings and market share) can provide an opportunity to profit systematically over the long run. Extraordinary events such as market crashes are permitted in the weak form, being considered rare but statistically possible. In semistrongform efficiency, even fundamental analysis will not allow an opportunity for profit. In strong-form efficiency, market prices are assumed to reflect all information known to any market participant, either public or private, so that even insiders or those with expert knowledge have no edge. When legal and regulatory impediments to insider trading are strictly enforced, strong-form efficiency is deemed to be impossible. EMH provided the philosophical foundation for the use of stochastic methods in mathematical finance. Clearly, this is philosophically consistent with Bachelier’s earlier assumption of both a memoryless Markov
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process (in that all information from the past is included in the current market price) and a speculator’s expectation of profit being zero. Besides being philosophically attractive, EMH was exceedingly convenient. An assumption of instantaneous efficiency hugely simplified the task of modeling price movements in a mathematical fashion. Analysts could assume that all price observations were automatically synchronized. If one calculated, say, a correlation coefficient between the time series of two stocks, that statistic could be assumed to measure at least in part whether the two securities were related in a causal fashion, that is, were mutually dependent, as in a supplier-customer relationship, or were both dependent on the same exogenous drivers. In contrast to macroeconomic models, in which it might take time for the effects of a driver to be felt, no inconvenient leads or lags need be assumed. Some assumption of rational processes by investors is subtly implied as well, along with justified choices such as the assumption that daily returns (rather than just changes in price) are normally distributed. These choices were also operationally convenient; in the days of batch processing, any models that minimized computer run time (especially ones expressed as closed-form solutions that did not require iteration) were favored by financial institutions.
SAMUELSON AND THE MATHEMATIZATION OF ECONOMICS In addition to spurring innovation in market theories such as EMH, Paul Samuelson is best known for his pioneering work in creating meta-theories of economics—that is, in his own words, “a general theory of economic theories.” Samuelson’s classic Foundations of Economic Analysis16 was first published in 1947, also as a product of his doctoral dissertation at Harvard in 1941. In it, he applied mathematical rigor to economics. The front page of Foundations quotes the American physicist Willard Gibbs’s motto, “Mathematics is a language.” Perhaps Samuelson’s knowledge of thermodynamics assisted him in visualizing complex systems. Samuelson formalized the study of systems such as those of economies, describing the change in an equilibrium state as a function of the variables on which it depends, just as the gas in a container reacts to a change in temperature. Samuelson’s work helped make economics operational; that is, he formalized qualitative theories so that the variables that defined them could be measured via real-world observation. For example, Samuelson’s
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work described in mathematical terms the effect on a system in equilibrium of a change in one of its variables. Such “operationalization,” in turn, allowed econometricians to build quantitative models to explain or forecast economic conditions. HARRY MARKOWITZ AND MODERN PORTFOLIO THEORY In 1952, just two years before the new translation of Bernoulli, Dr. Harry Markowitz introduced portfolio theory in his paper “Portfolio Selection” in the Journal of Finance.”17 The topic, today called modern portfolio theory (MPT), was both highly novel and extraordinarily mathematical for the times. While defending his Ph.D. dissertation at the University of Chicago three years later, Markowitz has said that Milton Friedman jokingly argued that portfolio theory was not economics.18 Markowitz’s work moved Bernoulli’s work from the casino and the high seas to Wall Street. MPT dealt with formal and rigorously mathematical expansions of Bernoulli’s basic concepts. Like Bernoulli, Markowitz explicitly addressed the gap between intuitively correct behavior, such as the diversification practiced by the Medicis, and contemporaneous portfolio construction methods. Previously, portfolio managers had often constructed portfolios in a bottom-up fashion: when they identified new securities with favorable risk-reward characteristics, they added them to their portfolios irrespective of those portfolios’ prior composition. Although they might attempt to manage risk by limiting concentration in one or more individual stocks or industry sectors, they used no mathematical means to optimize the composition of a portfolio. Markowitz mathematized diversification; he proposed a formal framework for a top-down approach in which the optimal portfolio was constructed by first abstracting each security into quantitative measures of individual and combined risk (that is, its expected return, standard deviation, and correlation with every other security that might be included in the portfolio) and then identifying the portfolio that maximized return for each possible value of risk. For example, an ideal portfolio might consist of two securities, each with a favorable return, but negatively correlated so that their risks canceled. Such a portfolio is considered the theoretical ideal in “pairs trading” in equities, in which long and short positions in stocks of related industries are paired so that returns are additive but risk cancels out. Markowitz’s key insight was that all optimally constructed portfolios sit on the “efficient frontier” of risk versus reward, as shown in Figure 2-1 for a two-stock portfolio.19
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Return
Stock B
Stock A
Risk (Standard Deviation of Returns)
Figure 2-1 The Efficient Frontier for Two Stocks
This graph illustrates the efficient frontier for a universe of two stocks: A and B. The x axis reflects risk, expressed as the standard deviation of daily returns, and the y axis reflects reward, expressed as return. Security B is assumed to have both more risk and more reward than the more stable Security A. The curve reflects the efficient frontier for each possible portfolio composition, starting with 100 percent A (the lowest point) and going to 100 percent B (the highest point). Any portfolio with a return below the line for a given level of risk is suboptimal, and any portfolio with a return above the line is impossible. The investor is forced to accept a higher level of risk in order to increase return or accept a lower return to decrease risk. There is no right answer for the optimal portfolio construction; as Bernoulli pointed out, it depends on the investor’s appetite for risk. MPT produces a range of values rather than one perfect portfolio, and the investor’s utility function with respect to risk determines the portfolio that is right for her. That is, the maximum amount of risk that an investor is willing to take determines where on the curve her optimal portfolio falls. Essentially, MPT maximizes investor utility. Markowitz gave credit for MPT to A. D. Roy, who in July 1952 independently formalized the same equation as Markowitz. Years later, Markowitz graciously wrote, “On the basis of Markowitz (1952), I am often called the father of modern portfolio theory (MPT), but Roy (1952) can claim an equal share of this honor.” Roy went one step further than Markowitz: whereas Markowitz left the decision as to the amount of risk to the investor, Roy, like Bernoulli, also attempted to suggest an appropriate utility function. He advised choosing the single point on the efficient frontier that maximized (mP - d)/sP, where d is a “disaster level” in terms of return.
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Hi. 283.69
280
INDU Index - Hist Vol(100D) (R) 7.3241 INDU Index - Price (L) 283.69
Hi. 17.6274
18.00 16.00
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200
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Low. 161.60
1948
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Figure 2-2 INDU Prices and Historical 100-Day Volatility: January 1, 1948, to
December 31, 1952 Source: Bloomberg, L.P.
It’s interesting to note that to Roy, a disastrous scenario was one in which the return was insufficiently high rather than one in which the portfolio lost value. This is in spite of the fact that the stock market of the few years previous to the publication of his work had been reasonably volatile, as shown in weekly returns and historical volatility20 for the Dow Jones Industrial Average in Figure 2-2.21 There are some additional interesting implications of MPT. For one, the addition of risk-free assets that are funded by borrowing (i.e., adding leverage) can create a return that is above the original efficient frontier. However, there are also a number of issues with the theory. For example, risk is expressed in terms of the standard deviation of returns, which is not a natural unit for risk preference. (Most people would prefer some loss limit, whereas a high standard deviation where profit is concerned is a good thing.) Markowitz later suggested some alternative expressions of risk, such as expected value of loss and probability of loss, foreshadowing future risk metrics such as value at risk and extreme value theory (EVT),22 and suggested, like Bernoulli and Roy, an alternative form for utility. For a number of reasons, MPT was of mainly theoretical interest until the 1970s. First, portfolio optimization using such methods is a computationally intensive process. The size of the correlation matrix can be very large for all but the simplest portfolios: if N is the number of possible stock choices, the matrix is of size N ⫻ N. There were practical considerations as well. For example, return often trumped risk in the optimization process: a stock with outstanding
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performance would tend to dominate the recommended portfolio. In those early days, return considerations appeared to outshine risk considerations. Given the state of computer technology in 1952 and the computational demands of MPT, it’s no surprise that it wasn’t until decades later that Markowitz’s work was appreciated by the mainstream financial community. Markowitz recognized this impediment and attempted to address it. Although he is far better known for MPT than he is for his work in the field of operations research in the 1950s and 1960s, he also developed numerical methods and computer languages (i.e., SIMSCRIPT, a computer language specifically designed to facilitate simulations) that could speed certain calculations. His theoretical work, together with an expression of a utility function and the means to perform the necessary calculations, would operationalize automated decision support in the field of portfolio selection.
WILLIAM SHARPE AND SPECIFIC AND SYSTEMATIC RISK In 1964, economist William Sharpe expanded on Markowitz’s work by introducing the concepts of systematic risk and specific risk. Awarded the Nobel Prize in Economics for his work on the capital asset pricing model (CAPM), his work dealt in part with how much of a risk premia investors require to take on market risk and to what extent an enterprise should seek to hedge its own risks.23 Systematic risk is risk that is caused by movement of the markets as a whole (e.g., as a result of recessions or high interest rates), whereas specific risk is risk that is related to the individual characteristics of the securities (e.g., industry sector factors or management quality for a particular company). Specific risk can be reduced by diversification (i.e., by ensuring that highly correlated securities don’t constitute an inordinate share of the portfolio), but systematic risk cannot. According to Sharpe, an enterprise should seek only to eliminate systematic risk (often referred to as beta), since investors can reduce their exposure to specific risk via diversification. In 1966, Sharpe proposed the metric that is now famous as the Sharpe ratio and is routinely reported by every asset manager. This ratio characterizes the risk-reward profile of a portfolio manager by penalizing the manager for volatility of returns24: Portfolio return - risk-free rate Portfolio volatility
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Dissent about EMH, Kahneman, and the Growth of Behavioral Finance The efficient market hypothesis remained mainstream opinion until the 1990s in spite of the fact that actual price behavior was not consistent with its most basic premises, at least for strong-form efficiency. For several decades, economists and analysts have been well aware that distributions of historical returns exhibit fat tails.25 Depending on the asset class, these distributions might skew to the left or to the right.26 There are a variety of reasons for such skewness. Recently, economist Burton Malkiel (author of the classic finance book A Random Walk Down Wall Street27) pointed out that in emerging markets such as China’s, evidence of price manipulation as well as its statistical artifacts, such as serial correlation and nonrandom movement, can be observed. Practitioners have also long been aware of this nonrandom behavior. For example, as early as 1987 (after the Black Monday crash), risk managers at the Options Clearing Corporation (OCC)28 considered which type of distribution might best estimate future market movements and therefore determine how much margin they should collect to protect the exchange. They chose to use a Lévy distribution rather than a Gaussian distribution. In part, they selected a Lévy distribution (Figure 2-3) because it can be expressed analytically (like a Gaussian) and therefore calculated
1
c = 0.5 c=1 c=2
0.8
0.6
0.4
0.2
0 0
0.5
1
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x
Figure 2-3 Lévy Probability Density Function Note: c is a scale parameter in the Lévy distribution.
2
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quickly. Also, it’s not so overly sensitive to new data (e.g., market shocks) that it creates its own market turmoil by precipitating sudden, large calls for additional margin. Such calls might exacerbate a crisis (and the exchanges’ own risk) if the OCC’s calculations were too responsive to recent history. There is some theoretical as well as empirical justification for such a choice. Mathematician Benoît Mandelbrot, the father of fractal theory, suggested that daily returns are well represented by a distribution with infinite variance and converge to a log-Lévy distribution. But if the markets are not efficient, what other nonrandom drivers might explain observed market behavior? Behavioral economists, who had previously been dismissed as having more to do with psychology than with finance, were suddenly taken seriously. Like Bernoulli, they posited that humans are subject to various preferences and biases in their decision making. Because markets are, after all, composed of humans, their behavior and biases will extend to their investment choices. Theoretically, such factors would not contradict EMH if they were randomly distributed and averaged out, along with all the other drivers of individual actions. However, these economists found evidence of nonrandom biases. Behavioral economists have identified a number of cognitive biases in humans, that is, a tendency to make errors in judgment or to prefer certain outcomes in a manner that is inconsistent with rational choice theory. Psychologists Amos Tversky and Daniel Kahneman29 and others related a number of types of biases, starting in the early 1970s. Some of those that are most relevant to market choices included innumeracy, in which individuals were unable to reason intuitively when faced with large-scale problems; confirmation bias, in which humans interpret new information in such a manner as to confirm a preexisting opinion; and illusory correlations, in which humans see causality where none exists. Some behavioral economists have provided empirical evidence of such biases outside the market environment. For example, psychologist Peter Wason demonstrated hyperbolic discounting, in which humans prefer smaller, immediate payouts to larger, distant ones, but prefer the larger payout if the two payouts are both in the future—albeit at the same distance in time from one another. Some economists feel that behavioral finance is not inconsistent with EMH. In fact, some hedge funds consider any systematic biases resulting from human behavior to be trading opportunities because both rational and irrational biases can be arbitraged away for a profit. One of the major purposes of the capital markets is risk transference, and those who prefer the left side of the efficient frontier (i.e., the risk
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adverse who will accept a lower return in exchange for lower risk) can exchange positions with those who prefer the right. If the size of the funds that engage in such arbitrage is sufficiently large compared to the biases, even behavioral effects can be traded away. SUMMARY In this chapter, we related the scientific innovations that gave birth to the fields of financial engineering and mathematical finance and the early consideration of modern topics such as securities valuation, risk management, and portfolio optimization. We further described the continuing bias toward a frequentist approach in problems having to do with wagering or its modern equivalents, tempered by recent emphasis on the role of investor preferences and utility functions. We also described how, by the middle of the twentieth century, economic theory had been mathematized. A frequentist approach, in which estimates of probability inform decision making under uncertainty, has dominated recent advances and provided a road map to quantitative risk management and portfolio optimization. WHAT’S NEXT In the next chapter, we will describe how Wall Street took economic theory and made it operational, thereby facilitating the extraordinary growth of the financial sector in the last three decades.
CHAPTER 3
Natural Selection on Wall Street
THE ASCENT OF THE QUANT Over the last three decades, growth in the financial sector has been driven in large part by rapid advances in mathematical finance and financial engineering. Such innovation is the bedrock on which new products, businesses, and strategies rest. Without the existence of mathematical models and the means to implement them, the growth of trading in entirely new types of securities—such as the multi trillion dollar credit derivatives market that is just a few years old—would not be have been possible. These advances have allowed participants to model increasingly complex and derivative instruments, better measure risk and performance, and optimize the use of an enterprise’s risk capital. This is the case because, in spite of the usefulness of these instruments as hedging vehicles, speculative trading in them for profit is still the dominant motive for most enterprises. Complex trading strategies employing such instruments (whose intrinsic risks are often multiplied many times by employing large amounts of leverage) cannot be initiated, monitored, or managed without state-of-the-art analytic tools on the trading desk and off. Such trading has been so lucrative that it has helped spawn the massive hedge fund industry, whose members forgo all the more mundane activities of a securities dealer or a bank. Instead, a hedge fund can concentrate on whatever proprietary strategy its principals deem most likely to produce exceptional returns. Also, the so-called quantitative trading strategies, in which the role of the human as decision maker is diminished (other than as the developer of the algorithms), have been popular with investors and successful in attracting new money. Parallel improvements in technology have facilitated this evolutionary path. The complex mathematical routines are computer-intensive, and supercomputers or their technical equivalent are sometimes required to meet the demands of analysts, traders, and risk managers. Furthermore, the computers themselves now trade; nearly 75 percent of all trading activity 23
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on the New York Stock Exchange today is computer-generated. So-called algo traders use mathematical algorithms to identify opportunities that last milliseconds, all without human intervention. The communications technology used by their executing brokers is so advanced that it is constrained only by the speed of light. Even lower-frequency traders and trading management are able to monitor global markets in real time on portals that provide them with a wealth of information, including trading opportunities, performance statistics, and risk metrics. They’re supported by a wealth of commercial offthe-shelf services that inform and supplement proprietary models. Historical data are readily available (Bloomberg L.P. alone has 1.2 million economic and financial time series available to its subscribers), and live exchange feeds available at very high (millisecond) frequencies have facilitated increasingly sophisticated models and strategies. In light of this intersection of attractive theory and the means to implement it, it was natural for the financial community to gravitate toward stochastic methods to create forecasting models. Thus, starting with the original “rocket scientists” in the late 1970s, quantitative analysts with doctorates in physics or computer science modeled future price behavior based only on past price behavior in increasingly sophisticated ways. Academics and practitioners both contributed to a burst of new theory, and the gap between innovation and implementation became exceedingly short. This is still the case, except that these quants have taken their place on front-office trading desks as well. Anecdotally, at the University of California at Berkeley, fully 25 percent of the applicants for a master’s degree in financial engineering already have a Ph.D. in physics. However, to rely on stochastic models, one must assume that the processes by which securities prices are established have both a deterministic (predicable) component and a random component. The deterministic component, which is subject to both known and unknown drivers, may be so complex that it’s virtually impossible to model. As in other areas in which stochastic models are used (e.g., meteorology), there are often so many interacting drivers in play at one time that attempting to separating them is exceedingly difficult even if they are deterministic at a microscopic scale. Therefore, trailblazing “quants” ignored the economic fundamentals that drove changes in market price. Instead, they concerned themselves only with the best means of expressing typical market behavior in rigorous mathematical equations, using only historical pricing data. These equations could be used to estimate both the value of a specific security or
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instrument and the uncertainly in that estimate over a particular future time horizon. Theoretically, such analysis could be done without even knowing the identity of each of the historical time series; they might as well be series A and B rather than IBM and Bank of America. In fact, practically the only concession to the fact that the historical data were market data was the assumption that returns1 (rather than some other metric) are normally distributed. Thirty or more years ago, this was an eminently reasonable choice because of the difficulty of collecting diverse fundamental data and modeling the market’s reactions to them. Perhaps more important, it was also an eminently practical choice. While best practice was in its embryonic state, only end-of-day prices were readily available for most securities and instruments. Furthermore, only end-of-day data could be synchronized with data from other sources2—a requirement when parameters such as correlation coefficients that measured relative behavior were being calculated. In addition, at such a low frequency, prices and events could not be synchronized. Many events might affect the price of a security over a 24-hour period—the day might include an economic news release, an earnings report, and a corporate action as well as noise and more mundane market flows. The linkage between events and the market reaction to those events might be separated by hours—certainly a long enough period to lose the association between cause and effect. Therefore, for good and practical reasons, quantitative analysts deliberately avoided the explicit modeling of causal relationships between a driver and a security or between changes in the price of one security and that of another. Instead, they modeled the behavior of one security relative to another in the form of a correlation coefficient. However, something was lost in the process. Quants do not need to understand economics or financial analysis; they don’t need to know that higher oil prices will hurt an airline. Instead, they can observe the correlation between airline and oil prices. A simple causal relationship (e.g., one cause, one effect) might create apparent correlation. Conversely, a more complex causal relationship (e.g., two causes, different effects) might obscure real correlation. A correlation coefficient calculated at a low daily frequency cannot distinguish among situations in which (1) news relevant to only one security triggered changes in another related security (e.g., one in the same industry), (2) the same news triggered changes in both securities simultaneously (e.g., an economic news release), or (3) multiple events drove
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prices in a complex manner. If such estimates of correlation are flawed because they fail to reflect causality, they will provide poor estimates of future portfolio risk. Nevertheless, analysts had some theoretical justification for ignoring causality in favor of correlation. Recall that the efficient market hypothesis postulates that, at any point in time, the market price of any security reflects all the information known about that security. Barring artificial constraints such as laws against insider trading, the fact that any nonpublic knowledge provides an opportunity for profit dictates that transactions designed to benefit from that information will move each security’s price to its proper level. However, in a stochastic modeling process, even the most expert analysts acknowledge the uncertainty with respect to results. Explicit modeling of the nature and magnitude of such uncertainty gave rise to quantitative risk measurement, in which risk managers reported metrics such as value at risk (a measure of short-term risk) or economic capital (a measure of the amount of capital required by the enterprise). Early on, analysts gradually recognized that simple statistical assumptions such as stable volatilities, normal distributions of returns, and independence of daily returns did not adequately represent actual market behavior to the degree of precision required when money was on the line. Many academic studies dating back to the 1960s observed that distributions in nearly all markets generally had fat tails, or higher-than-normal probabilities of very large and very small outcomes. Although most initial models used the Gaussian (normal) distribution as the starting point, theorists soon created alternative representations of the random component of the stochastic process. For example, a jumpdiffusion process was postulated for how prices moved over time (occasionally “jumping” and then diffusing that jump). These alternative representations were required to better price derivative securities (particularly those with some optionality) and measure risk. Over time, analysts developed new theoretical models that allowed for such observed behavior, such as extreme value theory (EVT), which explicitly attempts to model fat-tailed distributions, and generalized autoregressive conditional heteroskedasticity (GARCH), which models stochastic volatility. Such models were used to value increasingly complex instruments as well as to measure market risk. For a long time, the party continued. Technical innovation kept pace with financial innovation, and the most quantitative and technologically proficient shops, such as Goldman Sachs and Morgan Stanley, made money year after year.
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There was a kind of inadvertent conspiracy with respect to best practice. Although the top-tier firms all closely guarded their own proprietary models and the manner in which they calculated the parameters (e.g., variance and covariance) that informed those models, nearly all firms used models with the same underlying assumptions regarding price behavior. Without such relative unanimity, liquidity would have been much reduced: if firm A values a security at 80 and firm B values it at 90, no trade will occur, whereas if there is a quarter-point spread, it might. However, sometimes these methods were pushed beyond their original utility. As old innovations became commoditized and new and more complex variations were created, financial engineers were called upon to produce increasingly specific forecasts. For example, in the 1980s, they were called upon to project mortgage prepayment rates3 by geographical region for use in pricing mortgage-backed securities,4 and in the 2000s, they were called upon to project the recovery rates5 in the case of a bankruptcy for pricing credit default swaps.6 Analysts needed to express their uncertainty about their estimates in statistical terms, for example, to price securities with embedded optionality or to measure risk. Often, a single, complex derivative security might include a number of such sensitivities or might be ultrasensitive to one or more risk factors (for example, in the case of “first-to-default” tranches of a collateralized mortgage obligation [CMO]). It might even be pathdependent, for example, in the case of “down-and-out” options, in which a price movement below a specific threshold terminates the option before expiration. The terms for complex securities increased as well, requiring that forecasts of possible future scenarios be extended far into the future. Generally, most firms’ protocols called for using the last two or three years of data in calculating model parameters. (Data older than that are often considered unrepresentative of the future). However, using data from an immature market (e.g., using historical default probabilities and recovery experiences for purposes of pricing loans or credit default swaps) to price swaps with 10 years or more to expiration strained the “past represents future” assumption. Sometimes, specific exposures could be hedged in the open market. For example, sensitivity to short-term rates could be laid off in the Chicago Mercantile Exchange’s Eurodollar futures contract. However, such hedging only increased the gross size of the portfolio and added additional credit risk (if the counterparty to the hedge transactions failed to meet its contractual obligations) in place of the original market risk.
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Because many of the new structured securities “traded by appointment,” some of the largest dealers were required to keep these positions on their firms’ books for extended periods until they could be sold to institutional investors. Others held them willingly because they assumed that the positions would profit over time. For example, at the time of the AIG bailout, it was reported that AIG Financial Products held about $500 billion of credit default swaps on its books, which would have reaped large profits if there had been fewer credit defaults than expected. Firms that were heavily involved in securitization were highly vulnerable to model risk, that is, the risk that the quantitative models produced flawed forecasts. In general, a firm realizes most of the profit on a new securitization when the new issue is distributed to institutional investors. However, if the securities were held in the firm’s portfolio, their value could only be estimated (using the same quantitative models, albeit calibrated to trading activity) rather than directly observed. Thus, until the position was laid off, the firm continued to own the risk that reality would deviate from the original forecasts. THE WORLD BEFORE The stochastic methods that are widely used in the financial community require an assumption of system stability; that is, although there will always be random motion and even occasional shocks, there will be no event that is so far away from historical experience that the system won’t survive and most enterprises live to trade another day. Extreme events such as the crash of 1987 and the demise of LongTerm Capital Management (LTCM) in 1998 came close to triggering systemic failure; without timely bank intervention, one or more of the commodities exchanges might have closed their doors. However, in large part because of intervention by the Treasury and regulators, the casualties after each event were relatively limited, and so the lessons learned may have been more theoretical than tangible. Outside such special cases and within the normal ebb and flow of daily trading, ordinary risk had not proved to be much of a problem. Most firms prospered, even during interim spikes in volatility, because their day-to-day activities generated substantial profits. However, these firms were at risk from their own down-and-out scenario: an extreme event from which they might not recover. For example, a Russian financial crisis may have been the nominal trigger for LTCM’s sudden demise (Figure 3-1), but the amount of leverage that LTCM
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5,000 LTCM DJIA U.S. Treasury 4,000
3,000
2,000
1,000
3/
1/ 1 7/ 994 1/ 1 11 994 /1 /1 3/ 994 1/ 1 7/ 995 1/ 1 11 995 /1 /1 3/ 995 1/ 1 7/ 996 1/ 1 11 996 /1 /1 3/ 996 1/ 1 7/ 997 1/ 1 11 997 /1 /1 3/ 997 1/ 1 7/ 998 1/ 19 98
0
Figure 3-1 Assets under Management of Long-Term Capital Management
(billions of dollars) Source: Wikipedia Commons
employed, along with flawed risk management protocols, created its vulnerability to such an event. WHEN THE WORLD CHANGED During the peak of the U.S. credit crisis in November 2008, the negotiations between the Federal Reserve, the Treasury, and the large brokerdealers shone a spotlight on the fragility of valuation and risk management protocols. As former Lehman Chairman Dick Fuld said after the Lehman board voted unanimously to file for bankruptcy, “I guess this is good-bye.” It was reported that AIG CEO Hank Paulson had, on impulse, designated a $700 billion price tag for the Troubled Assets Relief Program (TARP) because it was about half the size of the $1.7 trillion mortgage-backed securities market worldwide.
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Figure 3-2 Daily Five-Year CDS Spreads for Select G-10 Sovereign Debt: Two
Years Ending November 26, 2009 Source: Bloomberg, L.P.
Model error hit home, especially for firms with leverage as high as 30:1, as was the case for Lehman before its demise. Formerly high-quality assets became toxic assets, and virtually no asset was considered safe. As shown in Figure 3-2, even the sovereign debt of the United States (i.e., U.S. Treasury securities), which is normally considered the safest asset in the world, traded as high as 100 basis points in the credit default swap (CDS) market—worse than Germany and equivalent to medium-grade corporate debt not long before.
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These events demonstrated that the greatest risk to which a financial enterprise is exposed is systemic risk; when the entire system becomes unstable, it may be too late to change one’s exposure or mitigate damage. Weeks or even months are insufficient to turn the battleship, and the fact that most institutions are in the same boat can precipitate a liquidity crisis that exacerbates the downward spiral. SUMMARY In this chapter, we discussed the fundamental assumptions about the process by which prices are established, and the reasons—fundamental, technical, and practical—for their almost universal adoption by the financial community. We also discussed their extension to increasingly risky or inappropriate uses and the financial system’s resultant sensitivity to an assumption of stability that was violated during the credit crisis of 2008. WHAT’S NEXT In the next chapter, we will describe risk management models and protocols in use by financial institutions.
CHAPTER 4
A Review: Risk Management Metrics, Models, and Best Practice
IN THE TIME BEFORE VAR In the 1970s and early 1980s, risk management was often a haphazard affair. Even in the heyday of the bond-trading masters of the universe such as Salomon Brothers and Drexel Burnham, risk measurement generally consisted of simple aggregate statistics, such as “bond-equivalent position,” in which all Treasury bill, bond, and note positions held at the end of the day were converted to their economic equivalent in terms of the most recently issued 30-year bond.1 This metric served as both a position limit and a rough indicator of market risk. Such bond-equivalent positions were not converted to dollars, nor were any probabilities attached to various sized losses (although trading managers could make such a mental mapping based on their own experience). Credit risk was virtually ignored; counterparties were assigned notional trading limits by the credit department, and as long as these limits were not exceeded, credit risk was considered to be the firm’s problem and not the trading desk’s. C-suite executives were informed by daily profit and loss statements (P&L), and if the worst days were not too bad and the general trend was higher, then risk was assumed to be under control. When most of the risk on a desk consisted of simple long and short positions in stocks, bonds, commodities, and foreign exchange, such metrics were adequate. However, as trading in derivative securities increased and more and more structured products were created, they would no longer do. For example, an option might be more sensitive to implied volatility than to the price of the underlying security, and a mortgagebacked security might be more sensitive to prepayment assumptions than to interest rates. Securities such as these had explicit or implicit optionality, 32
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33
and financial engineers began building sophisticated models that accounted for uncertainty. COMMUNICATING RISK This stochastic approach was different from that used by the firm’s financial analysts (who might forecast a company’s earnings) and economists (who might forecast GDP). Instead, risk analysts forecast a distribution of outcomes rather than the single most likely scenario. But a distribution is hard to communicate to consumers. In the early 1990s, J.P. Morgan CEO Dennis Weatherstone called for a “4:15 report” that summarized all of the firm’s risk in a single page and was available just after the close of the major U.S. equity exchanges. To meet this demand, analysts at Bankers Trust, J.P. Morgan, and others popularized value at risk, a metric that communicated the magnitude of risk in a single, meaningful number. VALUE AT RISK Value at risk (VaR) is a statistical measure of the possible loss on a portfolio. Any estimate of VaR must include a reference currency (e.g., U.S. dollars), a time horizon (usually one day), and a confidence level (usually 1 percent2). As shown in Figure 4-1, VaR measures only the left tail (that is, losses) of a distribution of potential outcomes. For example, if one-day, 1 percent VaR is $1 million, then the likelihood of a loss greater than $1 million over a one-day horizon is estimated to be only 1 percent, or 2.33 standard deviations away from the mean for the normal distribution shown.3 Although Figure 4-1 shows a normal distribution, the definition of VaR includes no assumption about how P&L is actually distributed. Figure 4-2 shows two very different distributions that might produce the same value for VaR: a lognormal distribution and a uniform discrete distribution. Note that the maximum loss is very different for each: zero for the lognormal distribution and ⫺5 for the discrete distribution. In practice, P&L distributions for all but the simplest portfolios are likely to be asymmetrical and uniquely shaped because of the presence of securities with optionality. VAR AND RISK GOVERNANCE Having a single metric such as VaR enhanced decision making by providing an objective, quantitative measure of the risk of adverse market movement. As such, it improved communication between the trading
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–23.3
+∞ 99.0%
1.0%
Normal(0,10)
1% VaR = –23.3
Minimum –∞ Maximum +∞ Mean 0.0000 Std Dev 10.0000
–40
–30
–20
–10
0
10
20
30
40
Figure 4-1 VaR for a Normal Distribution of P&L
desk and the C-suite and facilitated more informed corporate governance and better disclosure to investors. Applications using VaR soon included • Ensuring the continued existence of the enterprise by limiting risk to an amount appropriate to the firm’s capital and appetite for risk • Allocating “risk capital” (either actual cash or the ability to take risk) to various activities throughout the enterprise • Assigning VaR-based position limits to specific activities, trading desks, and/or traders • Comparing alternative trading and hedging strategies, that is, trying to approach the “efficient frontier” of risk versus return • Measuring the risk-adjusted performance of an individual trader, a profit center, or an asset manager • Allocating assets (e.g., by a fund of funds) to portfolio managers in order to optimize the fund’s risk-reward profile • Determining performance margin (used by exchanges and by dealers for OTC instruments or futures and options contracts) • Facilitating greater transparency to investors (e.g., disclosing average daily VaR in annual reports)
A Review: Risk Management Metrics, Models, and Best Practice
35 +∞
1.0 1.0%
99.0% Lognorm(10,10) 0.0000 +∞ 10.0000 10.0000
1% VaR = 1
Minimum Maximum Mean Std Dev
A –1.00
+∞
1.0%
99.0%
Discrete({},{})
1% VaR = –1
Minimum Maximum Mean Std Dev
B
–6
–4
–2
0
2
4
–5.0000 5.0000 2.9406 1.5339
6
Figure 4-2 Two Distributions of P&L with Identical Values for VaR
CLASSICAL METHODS FOR COMPUTATION OF VAR There are a number of standard methods used to estimate VaR, each with its own advantages and appropriate uses. The most common are variancecovariance estimation, historical simulation, and Monte Carlo analysis. Somewhat less common is the use of extreme value estimation, which focuses on only the most unlikely events. Note that the term VaR is sometimes incorrectly assumed to be synonymous with variance-covariance VaR.4 However, VaR is just a metric (like temperature or pressure), and use of the term implies nothing about the method used to estimate it.
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It should be noted that VaR is a measure of portfolio risk and, as such, depends on the portfolio’s particular composition. With very few exceptions (i.e., when all the securities in a portfolio are perfectly correlated), VaR is not additive; that is, the VaR of a portfolio is not the sum of the VaRs of its individual components. Variance-Covariance Estimation Variance-covariance VaR is the earliest and most computationally efficient method by which VaR might be estimated. Based on modern portfolio theory (MPT), VaR is calculated to be some multiple of the standard deviation of the portfolio’s return, based on the variance of each security in the portfolio and the intercorrelations of the securities in the portfolio.5 VaR calculated in this manner is also known as parametric VaR, analytical VaR, or closed-form VaR.6 All these terms refer to the great advantage of variance-covariance VaR: that it can be estimated speedily (e.g., by 4:15), since it can be directly calculated from a closed-form solution.7 However, variance-covariance VaR is based on the assumption that returns are normally distributed and that the relationships between securities in the portfolio are linear. It also implicitly assumes that volatility is predicable. Historical Simulation Historical simulation is a method for estimating the distribution of outcomes using only historical experience. To calculate historical VaR, a static portfolio is repriced and its P&L calculated on each of a series of historical dates, for example, each day of the last three years. The power of historical simulation is that the set of market prices used can occur because these prices have occurred before; the various prices are necessarily all internally consistent, and their relative pricing may reflect some complex dynamic (e.g., nonlinearity or causality). Like variance-covariance VaR, historical VaR is also speedy to compute and requires an assumption that the future is well represented by the past. However, unlike variance-covariance VaR, it includes no implicit assumptions about the shape of historical distributions or about the form of the relationship between assets. Monte Carlo Simulation Monte Carlo simulation is the most flexible method for the estimation of VaR. To calculate Monte Carlo VaR, a random-number generator is used to create virtually every plausible future state (typically, 10,000 or more).
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Just as in historical simulation, a static portfolio is repriced and the P&L for each state is calculated. VaR is estimated by identifying, say, the 100th worst loss (1 percent of 10,000). Unlike in historical simulation, in Monte Carlo simulation, market prices are not available for portfolio reevaluation. Instead, the modeler must rely on theoretical valuation models to estimate what the price of each security in the portfolio would be at each future state. This extra step introduces another level of uncertainty. A Monte Carlo simulation can be as simple or complex as the modeler desires; it can simulate simple Brownian motion, or it can include complex dynamics over time. For example, a sophisticated model would need to estimate volatility surfaces, yield curves, and other inputs required to price complex derivative instruments and structured products. The quality of VaR calculated using Monte Carlo estimation depends on the quality of the valuation models as well as on the parameters that control the random scenario generation. Nevertheless, in spite of the computer power required to perform so many calculations, Monte Carlo simulation is the only commonly used method that is capable of dealing with complex securities and system dynamics properly. Extreme Value Theory (EVT) Extreme value VaR (EV VaR) is a method for better estimating the most extreme outcomes for a portfolio. Extreme value theory is a branch of statistics dealing with the most extreme deviations in probability distributions. It is used in a number of disciplines to estimate the very rare and the unobserved, such as natural 100-year events (e.g., hurricanes or forest fires) and even the limits of human performance in a footrace. EVT is concerned with determining the asymptotic limits that describe the distribution of extremes. For example, EVT might be used to estimate the distribution of the maximum wave height (not the entire distribution of wave heights) based on only the maximum observed wave heights from the previous 100 years. Use of EVT to estimate VaR is appropriate when, as in finance, the distributions of returns have been observed to have fat tails. If the market dynamic that generated the fat tails is unknown, then EV VaR might be best estimated by fitting a curve to the observations beyond some quantile.8 In Figure 4-3, a curve was fitted to all observations of P&L beyond the 80 percent tail quantile, and 5 percent VaR was estimated using that fitted curve. Use of EV VaR is most appropriate when there is substantial “tail risk.” For example, Figure 4-4 shows a distribution of hourly electricity prices for a historical period and for one route on the U.S. western power grid.
1
Conditional Probability
0.8 80% Quantile Threshold = ($40MM) 0.6
0.4
0.2
0 –300
–250
–200
–150
–100
–50
P&L ($MM)
Figure 4-3 Extreme Value VaR Modeling
Probability
Horizon: 1 Day Date Range: 4/1/98–9/28/00 Volatility = 7.48 STD = 0.47 Min = 18% Max = 414%
14% 12% 10% 8% 6% 4% 2% 0% 0%
100%
200%
300%
P(t)/P(t–lag)
Figure 4-4 Distribution of Hourly Electricity Prices, 1998–2000
38
400%
0
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(Electricity, denominated in megawatts, can be purchased in as small an increment as 15 minutes of power). The price of electricity can vary widely from hour to hour and can skyrocket as a result of restricted flow on the grid, increased demand (for example, during peak seasons for electricity use), or decreased supply (resulting from an outage by a power generator). Because electricity is very difficult to store, its price responds quickly to such drivers, and the right tail of its distribution is more pronounced than that for other commodities. Note that the best-fit lognormal distribution of returns is an exceedingly poor one; it underestimates the probabilities of both moderate returns (i.e., little change) and extreme returns (over 400 percent in one day). The advantage of EV VaR is that it is more likely to estimate extreme outcomes, while its disadvantage is that it fits a curve to relatively few events that may or may not be indicative of the future. ADDITIONAL RISK METRICS VaR identifies a threshold, but not the magnitude of loss beyond the threshold. Expected shortfall (ES), also known as conditional VaR (CVaR) or expected tail loss (ETL), is an additional risk metric that estimates the magnitude of expected loss. ES estimated at the 1 percent confidence limit is the expected P&L (or return) 1 percent of the time. ES depends on the shape of the distribution beyond the confidence limit. For example, the 1 percent likely expected shortfall in the lognormal distribution of Figure 4-2 is far less than that of the uniform distribution, with its low probability but highly adverse outcomes. Another useful metric is marginal VaR, which is the sensitivity of the VaR of a portfolio to the addition of a new position. It is the difference between the VaR of the existing portfolio and that of the new portfolio, and it provides a means of determining whether the potential addition moves the portfolio closer to the efficient frontier. For example, two candidates for addition to the portfolio might have identical expected returns, but if the first is positively correlated with the old portfolio (increases VaR) while the second is negatively correlated (decreases VaR), the second choice is the better one. COMPARISON OF VAR METHODOLOGIES Clearly, depending on how P&L is actually distributed, each of these methods can create very different estimates of VaR (and of loss beyond VaR). As shown in Figure 4-5, for a fat-tailed distribution typical of
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1.60% 1.40% 1.20%
VaR Confidence Interval
VaR Based on Normal Distribution
1.00% 0.80% Historical Simulation Results
0.60% 0.40%
VaR Based on Extreme Value Distribution
0.20% 0.00%
–35%
–30%
–25%
–20%
–15%
–10%
–5%
–0%
Return
Figure 4-5 Extreme Value VaR versus Historical VaR
financial data, variance-covariance VaR (which assumes a normal distribution) may produce the lowest estimate of risk, followed in increasing order by historical simulation and EVT. PARAMETER GENERATION FOR VAR In practice, even variance-covariance VaR methodologies are not literal implementations of modern portfolio theory. For example, while MPT might have used historical variances and covariances as is to inform a variance-covariance model (tacitly assuming that volatility is constant), current implementations recognize the critical dependence of VaR on a volatility forecast. So, for example, in 1996,9 RiskMetrics used an exponentially weighted moving average (EWMA), which weighted recent data far more heavily than older data in constructing a best estimate of future volatility, and assumed that volatility grew as the square root of time (i.e., four-day volatility is twice one-day volatility). By 2006,10 with the benefit of an additional 10 years of historical data, RiskMetrics had revised its methodology to better predict volatility over longer time horizons11 and to better account for fat-tailed distributions of returns.
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Similarly, recall that parametric VaR is computationally efficient; that is, it can be directly calculated using an equation rather than via simulation. However, it becomes far less efficient when the number of securities N in a portfolio is large (it can number in the thousands or more for a financial institution), since it requires an N ⫻ N correlation matrix. Even if this computation could be done quickly, including every individual security makes the result vulnerable to spurious correlation, in which two securities are highly correlated but have no causal relationship. (Similarly, two securities that are uncorrelated can have a causal relationship, perhaps disguised by company-specific events in the past that masked their true relationship.) So, in practice, representative time series are used as proxies for specific instruments. In the 1996 version of its seminal RiskMetrics protocol, J.P. Morgan used only 480 time series, derived from the term structures of global equity indexes, currency exchange rates, commodity futures, and interest rates. Even so, this reduced set required 480 variance forecasts and 114,960 covariance forecasts.12 As risk models further evolve, some firms are using macroeconomic or other risk factors instead of market proxies in order to better explain market movements as a function of fundamental drivers. APPROPRIATE USES Table 4-1 summarizes the key assumptions of each of the classic models, as well as the key inputs. While the variance-covariance model is a parametric solution, historical VaR, Monte Carlo VaR, and extreme value VaR are all scenario-based and depend on the accuracy of the scenarios when applied to the future. This comparison provides some insight into whether a model is appropriate for a given portfolio. For example, classic variance-covariance VaR implies that the relationship between assets is linear, so that if the portfolio includes securities for which this is not true (for example, an option, with its asymmetric dependence on underlying price), this method will provide a poor estimate of VaR. MODEL DESIGN AND PARAMETER ESTIMATION In practice, VaR is recalculated at least nightly. Each firm has its own protocols for revising the parameters that inform its VaR models. However, most firms ensure that VaR is dynamic and responds relatively quickly to changing market conditions. Because traders are often assigned
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T A B L E 4-1
Summary of Classic VaR Models
VaR
Type
Assumptions
Inputs
Variancecovariance
Parametric
Historical distribution is stable, and returns are normally distributed; linear relationships between assets
Variance of each asset; covariance matrix for all assets
Historical
Scenario-based Future is well represented by the historical period used Monte Carlo Scenario-based None
Extreme value
Empirical
Historical distribution is stable, and extreme scenarios can be projected from past experience
Historical prices Modeler’s view of market dynamics; accuracy of valuation models Tail quantiles
VaR-based limits, these dynamic parameters might force traders to reduce the size of their positions in response to higher risk. The forecast parameters for VaR are usually estimated from historical data. In selecting the historical period to use, there is a trade-off between using more data (which, in a stable system, increases confidence in the results) and using less data (which makes VaR more responsive to current market conditions). Alternatively, the parameters for VaR might be calibrated to current market prices. For example, rather than using a volatility forecast derived from historical data, one might instead use the variance implied by forward-looking options contracts by out-of-the-moneyness and term.13 If the market knows best (for example, that there are some high-risk events looming on the horizon), then using the market’s implied forecast might be superior to using an empirically derived forecast. At the world-class firms, there are myriad internal protocols and variations on the classic models, all jealously guarded as valuable intellectual property. Because most large financial institutions hold thousands to hundreds of thousands of individual securities (the larger number comes from the “one-of” nature of some structured products or customized derivatives), they generally use a Monte Carlo simulation together with their proprietary valuation models to measure risk.
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CATEGORIES OF RISK Originally, VaR was used primarily to describe market risk, that is, the risk of loss in a portfolio caused by adverse market movement. But there are additional sources of risk, as well. For example, credit risk is the risk of loss as a result of the failure of a counterparty to fulfill its contractual obligations. Some of the classic VaR methods are not appropriate for simple counterparty exposure, where no profit is generated if a counterparty performs, but huge losses are possible if it doesn’t. As shown in Figure 4-6, the distribution of outcomes is far from Gaussian, and its mean is not close to zero. The standard categories of risk to which an enterprise is exposed include the following. Market Risk. The risk of loss due to adverse market movement. The four primary sources of market risk are equity risk (the risk that stock prices will change), interest-rate risk (the risk that interest rates will change), commodity risk (the risk that commodity prices will change), and currency risk (the risk that exchange rates will change). These adverse changes include both changes in the security or instrument itself and second-order changes such as a change in implied volatility, a change in the spread between related securities, or a change in the shape of the yield curve. Credit Risk. The risk of loss due to the inability of counterparties to fulfill their contractual obligations. This includes the risk that a counterparty to a transaction will fail to meet a contractual obligation (e.g., make interest 10.00% 9.00% 8.00%
Probability
7.00% 6.00% 6.00% 4.00% 3.00% 2.00% 1.00% 0.00%
0
10,000,000
20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 70,000,000
Loss ($)
Figure 4-6 Distribution of Credit Loss
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and principal payments, or pay off on an option exercise or credit default swap [CDS] default event). With the advent of CDS trading, credit risk was sometimes bifurcated into credit spread risk, or the risk of a mark-tomarket loss resulting from an increase in a CDS spread caused by a perceived decline in credit quality, and credit default risk, or the realized loss resulting from the failure of an obligor to meet its financial obligations. The magnitude of the loss from a credit event, or loss given default (LGD), depends on the recovery rate, or the amount that the enterprise expected to recover in a bankruptcy. Typically, a recovery rate of 40 percent is assumed. Operational Risk. The risk of loss due to human failure. Operational risk can stem from inadequate technology and operational protocols, management failures, fraud, and more mundane errors such as data input errors. For example, it might range from simple accounting errors to more catastrophic failures such as the inability to control a rogue trader (as in the case of Nick Leeson and Barings Bank14) or failure to protect the enterprise from a cyber attack. Model risk, or the risk of poorly specifying a valuation or risk model such as VaR, is sometimes considered an operational risk. Liquidity Risk. There are two types of liquidity risk: funding liquidity risk and asset liquidity risk.15 Funding liquidity risk is the risk that an enterprise cannot fund its cash requirements for such purposes as posting margin or meeting collateral obligations. Asset liquidity risk is the risk that a decline in market activity causes bid/offer spreads to widen and the size of those bids and offers to decrease, increasing the cost of forced position liquidation. Other less quantifiable risks include legal risk (the risk of loss due to legal actions), political risk (the risk of loss due to political actions), and reputational risk (the risk of loss due to damage to the firm’s reputation). In addition, a more general type of business risk is strategic risk, in which the firm is at risk from less than optimal business decisions. SYSTEMATIC AND SPECIFIC RISK Today, most risk managers divide their market exposure into systematic risk and specific risk. In the financial community, systematic risk 16 refers to the sensitivity of an instrument or portfolio to a change in the general market level (usually relative to a broad stock market index such as the S&P 500). Conversely, specific risk or idiosyncratic risk refers to that portion of an asset’s volatility caused by factors specific to that asset (for example, for a stock, its line of business or the quality of its management).
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If the price of a given stock tracks a market index perfectly, then its correlation with that index is 100 percent, and it is exposed only to systematic risk. Conversely, if the price of the stock is totally independent of the market index, its correlation is zero, and it is exposed only to specific risk. As previously discussed, a well-known result of portfolio theory is that systematic risk cannot be eliminated through portfolio diversification, whereas specific risk can. Naturally, most assets are exposed to both types of risk. Asset managers routinely report statistics such as alpha (the premium above a benchmark index that a portfolio earns) and beta (a measure of the portfolio’s volatility relative to that benchmark) that assist investors in understanding their relative exposure to systematic and specific risks. ECONOMIC CAPITAL While VaR is used to manage routine trading, economic capital (EC) is used to manage capital adequacy and ensure the continued existence of the enterprise itself. Economic capital is the enterprise’s own internal estimate of its capital requirements and is different from regulatory capital, or capital requirements enforced by financial regulators. Economic capital is generally calculated at very high confidence levels (e.g., 0.01 percent), which reflect the probability that the enterprise will cease to exist. It is meant to estimate the damage to the enterprise under the worst set of events that is reasonably plausible. Since such events may be like or unlike any that the enterprise has previously experienced, economic capital is often estimated using scenario analysis and stress tests. Both economic capital and VaR can be used to create a metric of risk-adjusted return on capital (RAROC), first popularized by Bankers Trust in the 1970s. RAROC can be expressed as either Expected Return/EC or Expected Return/VaR. SCENARIO ANALYSIS AND STRESS TESTS In scenario analysis, a set of possible future outcomes (scenarios) is selected, and their impact on a portfolio is estimated. Scenario analysis can be used to identify simple sensitivity to a risk factor or to quantify the most extreme outcomes. For example, Figure 4-7 shows the effect (on return, in this case) of a number of shifts in interest rates [plus or minus 100, 200, and 300 basis points (bp)] on a generic bond portfolio. In a scenario analysis, these need not be catastrophic outcomes; such analysis is a standard tool that is useful in “what-if” analysis on the trading desk. Unlike VaR, scenario
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0
Return (%)
10
–10 –300 bp
–200 bp
–100 bp
Flat
+100 bp
+200 bp
+300 bp
Scenario
Figure 4-7 Scenario Analysis on a Generic Bond Portfolio Source: Bloomberg, L.P.
Scenarios
P&L
%Ret(P)
11) Black Monday
–3.719
–35.25
12) Russian Ruble Devalues
–1.635
–15.50
13) Flight to Quality
–1.499
–14.20
14) Small Cap Worries
–1.042
–9.88
15) Sep 11
–1.011
–9.58
16) Corporate Scandal
–954
–9.04
17) G7 Summit
–751
–7.12
18) Economic Recovery Falters
–742
–7.03
19) Market Bounce
–515
–4.88
Figure 4-8 Stress Tests for Sample Portfolio Source: Bloomberg, L.P.
analysis need not have a specific time horizon—it may assume an instantaneous change, or it may instead allow a historical scenario to play out to its conclusion over time. A stress test is a special form of scenario analysis, in that its purpose is to stress the system to its breaking point. The scenarios used may be either historical or theoretical. For example, in Figure 4-8, the effects on a test portfolio of actual scenarios such as Black Monday and theoretical scenarios such as flight to quality are shown. Figure 4-9 shows a more detailed description of these two scenarios. Figure 4-10 shows the distribution of returns for the same bond portfolio and its benchmark, along with the best-fit normal distribution. The stress test estimates that it is 1 percent likely that the loss will exceed an 8.4 percent return (far less than the loss of 35.25 percent under the Black Monday scenario). Of course, the results of any stress test depend on the scenarios used: they should be appropriate for the type of portfolio. For example, a shortonly portfolio would profit under a Black Monday scenario, so bullish scenarios would need to be included. Similarly, a portfolio that included short positions in long-dated, far-out-of-the-money options might be more
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Black Monday 340
SPX Index
320 300 280 260 240
Flight to Quality— 1 Week
220
Representative of fear of global systemic failure resulting in equities down 10%, all credit spreads rising 100 bp, all AAA Sovereign rates 100 bp lower, all nonsovereign rates 100 bp higher, and exchange rates unchanged across all geographic regions.
200 Sep 87 Oct 87 Nov 87 Dec 87 Many have noted that no major news or events occurred prior to the Monday of the crash B
A
Figure 4-9 Black Monday and Flight to Quality Scenario Descriptions Source: Bloomberg, L.P.
25%
10%
90%
Portfolio 1%
5%
10%
95%
15%
99%
Probability
20%
Normal
5%
0%
.6 .2 .8 .4 .0 .6 .2 .8 .4 .0 .4 .8 .2 .6 .0 .4 .8 .2 .6 .0 12 –11 - –9 - –8 - –7 - –5 - –4 - –2 - –1 - 0 - 1 - 2 - 4 - 5 - 7 - 8 - 9 - 11 - 12 - 14 – - - 2 8 4 0 6 2 8 .4 .0 .4 .8 .2 .6 .0 .4 8 2 6 .0 2.6 11. –9. –8. –7. –5. –4. –2. –1 0 1 2 4 5 7 8 9. 11. 12. 4 –1 –1 – Return (%) Buckets
Figure 4-10 Return Distribution for Sample Portfolio Source: Bloomberg, L.P.
exposed to an increase in implied volatility than it is to a change in the underlying price. The set of scenarios must therefore be comprehensive, specific, and realistic. If it is not comprehensive, the enterprise is at risk from an
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unanticipated shock from which it cannot recover. If it is not specific, then important risk factors might be ignored. If it is not realistic, the enterprise may take on too little risk, thus reducing its earnings and its competitive status. A systematic approach to generating such scenarios is ideal. Together, stress tests and economic capital calculations assist an enterprise in identifying its optimal location on the efficient frontier. Note that, of the four standard VaR models, two are actually scenariobased. Historical VaR implicitly assumes that each past date is one scenario, and Monte Carlo simulation creates thousands of theoretical scenarios. While the calculation of economic capital from stress tests is not concerned with the relative probabilities of each plausible extreme scenario, these two VaR calculations convert these de facto stress tests to probability distributions by assuming that each scenario is equally likely. EVERYDAY RISK VERSUS EXTREME RISK VaR and economic capital are calculated differently and reflect different time horizons and probability levels. More important, they’re used for different purposes. There’s an implicit assumption in each metric that the enterprise can do nothing to mitigate the loss—raise new capital during a crisis in the case of economic capital, or liquidate all positions in less than one day in the case of VaR. To summarize, everyday trading risk is generally estimated using stochastic models, quantified as VaR, and controlled by position limits expressed in terms of VaR. Extreme event risk is generally estimated using stress tests, quantified as economic capital and expected shortfall, and controlled by capital adequacy and strategic business decisions such as imposing concentration limits by business activity. SELECTING A MODEL Financial institutions such as Goldman Sachs, Morgan Stanley, and JPMorgan Chase use highly sophisticated (and expensive) risk models. These models may be entirely proprietary and built in-house, or they may use commercial off-the-shelf software that is customized for the firm’s use or is informed using internal protocols. Such models are capable of dealing with every asset class, every type of derivative security, and every exposure. The technology that supports the effort often provides real-time risk reporting, from the individual-trader level to senior management.
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However, not every enterprise needs or can afford such an allencompassing solution. For a hedge fund that, say, engages only in longshort trading in equities, such an implementation would be overkill. Nevertheless, there are certain best-practice standards for risk management irrespective of the size or style of the enterprise. What is always required is a deep understanding of the benefits and flaws of each type of risk model and their dependence on fundamental assumptions regarding market behavior. VaR should never be a “black box” statistic, even when it is communicated to the highest levels of management. ENTERPRISE RISK One of the hotly debated topics in risk management today concerns the estimation of enterprise risk, that is, quantitative measures of integrated risk with respect to all types of risk (market risk, credit risk, operational risk, and all the rest). All these different sources of risk combine to form enterprise risk. Because these risks are not independent, they cannot be added, and in fact may have very complex interdependencies. An integrated view of, say, market and operational risk requires information about the causal relationships between the two; for example, larger market moves may increase the consequences of a certain operational failure, if not its probability. If a back-office operational failure produces an erroneous position report, the magnitude of the loss depends on market prices at the time the position is corrected. Similarly, a failure to collect margin on an OTC transaction exposes the enterprise to both market and credit risk. Even legal and reputational risk may affect funding ability, with broad ramifications across the enterprise. For example, before Drexel Burnham’s bankruptcy, rumors about its legal and financial status abounded, causing lenders to pull credit lines virtually overnight and forcing the firm to cease trading activities in highly leveraged securities. Likewise, market risk and liquidity risk are highly related. A sharp change in market prices often leads to a loss of liquidity, as shell-shocked investors shy away from new transactions or require the payment of a substantial risk premium to take on new risk. Because of such interdependences, a comprehensive framework for enterprise risk management (ERM) is the holy grail of risk managers. This is so not only because the C-suite needs to know the magnitude of combined risk from all sources, but also because such a framework facilitates quantitative decision making, in which choices critical to the health and well-being of the enterprise are done as scientifically and objectively as possible.
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INTERNATIONAL STANDARDS: THE BASEL II ACCORD The Basel Committee on Banking Supervision has been a key driver of risk management best practice. In 1988, the committee first17 recommended quantitative methods for determining minimum capital requirements for banks. Basel I dealt only with traditional bank sources of credit risk, and it specified a simple protocol for the calculation of risk-weighted assets (RWA). In this protocol, each type of credit risk was put into one of five buckets. (The least risky bucket included home-country sovereign debt, and the most risky bucket included corporate lending.) Then, each bucket was weighted (with weights ranging from 0 to 100 percent) in proportion to the perceived risk in order to generate RWA. International banks were required to have capital of at least 8 percent of RWA. Basel I did not speak to market risk, operational risk, or any other types of risk to which banks were exposed. By 1994, the Basel Committee had extended the scope of its recommendations to include all major sources of risk to which both individual institutions and the banking system as a whole were exposed. The Basel II accord, published in 2004, attempted to ensure that regulatory capital requirements better corresponded to actual risk. It also provided incentives for banks to create better internal estimates of risk and to integrate risk management into their corporate culture. This far more sophisticated set of recommendations was expressed in terms of the three pillars: • Pillar I. Recommended minimum capital requirements as a function of market risk, credit risk, and operational risk. (Some other types of risk were either included as operational risk or considered too intangible or difficult to quantify.) • Pillar II. Provided regulators with better tools for oversight, including the ability to review each bank’s risk management models used for estimation of risk. • Pillar III. Recommended disclosure requirements and promoted best practice with respect to market discipline. Basel II explicitly bifurcates interest rate and equity risk into systematic risk and specific risk. All three pillars are necessary; for example, merely measuring risk—even with the most sophisticated models—is not sufficient to meet Basel standards. An enterprise must demonstrate that it is using its knowledge of risk to better manage its business. Within Pillar I, Basel II now permitted an institution to select one of several approaches for calculating regulatory capital. For credit risk, and depending on its size and sophistication, a bank could choose to use (1) the
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Standardized Approach, in which capital was computed in a manner similar to that of Basel I, although with redefined buckets and weights, (2) the Foundation Internal Ratings-Based (IRB) Approach, in which a bank that creates internal credit ratings might use these to provide a more refined estimate of credit risk, or (3) the Advanced IRB Approach, in which a bank with sophisticated risk measurement models might provide its own estimates for RWA using such credit risk metrics as probability of default (PD), exposure at default (EAD), and loss given default (LGD). As in Basel I, the bank’s minimum capital requirement was calculated as a fixed percentage of RWA. Basel II recommended that market risk be measured in terms of VaR.18 It also provided three different ways to calculate reserves for operational risk, including the simplest (1) Basic Indicator Approach (BIA) based on net revenue, (2) the Standardized Approach (TSA), based on net revenue in each of eight lines of business (e.g., corporate finance, trading and sales, and retail brokerage), and (c) the Advanced Measurement Approach (AMA), in which, as in the Advanced IRB Approach for credit risk, a bank is allowed to base its capital requirements on its own operational risk models. As intended, Basel II rewarded banks (in the form of lower capital requirements) for implementing sophisticated risk management systems and integrating them into the corporate culture. By providing for a “risk audit,” the second pillar was intended to ensure that any risk management system used to generate capital requirements is conceptually and mathematically sound and is operated objectively and without bias. The Basel Committee periodically updates its quantitative and technical standards.19 It most recently added additional requirements for the calculation of market risk: that VaR be calculated daily at a 1 percentile, one-tailed confidence interval, and that the instantaneous shock reflect movement over a holding period of 10 days. Similarly, the committee requires that the data set used include at least one year of empirical data, and that it be updated at least monthly. (There are a number of more specific criteria that further set standards, for example, how the risk of options is calculated.) It’s a moving target; future standards for Pillar I will newly include requirements for credit migration risk (i.e., the risk that the credit rating of a counterparty or obligor degrades) and estimation of a new metric of risk called stressed VaR (discussed later in this chapter). Although Basel II was intended for banks, some of its best-practice recommendations became the standard for other financial institutions as well; good risk management practice became an integral part of an increasing number of financial and nonfinancial enterprises, and the role of chief risk officer gained in importance. And, as this book is being
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written, there is even legislation pending in the United States that would require every publicly traded company to have a chief risk officer (CRO). Basel II has precipitated the use of RARORAC as a metric of riskadjusted return on risk-adjusted capital, where risk-adjusted capital is based upon Basel II standards of capital adequacy. BEST PRACTICE IN RISK MANAGEMENT Best practice in risk management is more than a set of quantitative models; risk measurement is not risk management. Although risk metrics such as value at risk or economic capital inform decision-making processes, a corporate culture that integrates risk-based thinking and expertise at every level of the enterprise is the best protection against catastrophic risk. Although the mathematical models and protocols used to measure risk may vary from firm to firm, best practice in risk management is a constant. It is intended to optimize both strategic and tactical decisions at every level of the enterprise. Toward this end, each enterprise ideally has a designated chief risk officer and a senior risk committee that has the final say on the firm’s risk management protocols and procedures. Just as they would for any other business activity, the members of this management team must continuously review the enterprise’s practices—especially as market conditions change or the firm enters new lines of business. Tactically, position limits based on VaR control known risks via militarylike command-and-control (C2) protocols: that is, the exercise of authority by a properly designated commanding officer (or CRO) for purposes of a specific mission. But senior management must also focus on unknown risks, including the risk that the internal risk management models or protocols are flawed or that they require revision in light of new market conditions. Strategically, business decisions based on enterprise risk and economic capital control unknown risks and optimize the enterprise’s riskreward profile. Such decisions—for example, the allocation of specific VaR-based limits to certain lines of business—are informed not only by aggregate metrics, but also by drilling down into the specific sources and magnitude of risk. Minimum management reporting standards are detailed here. Risk Limit/Usage Reports Figure 4-11 shows a typical Basel-compliant risk limit report. (A similar report might be used to show actual risk and compare it to the limits.) Note that risk limits and ancillary information are broken down by line of business
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Effective Date
1-Dec-09
Illustrative Black Diamond
Expiry Date
1-Dec-09
Limit Report
Risk Type
Risk Measure Foreign Exchange Risk Total FX Risk FX Outright Risk FX Vega Risk Interest Rate Risk Total Interest Rate Risk Interest Rate Outright Risk Interest Rate Vega Risk Swap Spread Risk Floating Rate Basis Risk Cross Currency Basis Risk Equity Risk Total Equity Risk Equity Price Risk Equity Market/Outright Specific Risk Equity Vega Risk
Profit Center A
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Profit Center E
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2,000 2,000 1,750
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Commodity Risk Total Commodity Risk Precious Metals Crude Oil & Petroleum Natural Gas Base Metals
Figure 4-11 Risk Limits Report Source: Black Diamond Risk Enterprises
or profit center (e.g., Debt Capital Markets or U.S. Equities) and by source of risk (e.g., Interest-Rate Risk or Commodity Risk). Note, too, that additional detail on those sources of risk can be either mathematically expressed (e.g., FX Vega Risk, where vega is the sensitivity of a portfolio to implied volatility), separated by drivers (e.g., Systematic and Specific Risk, as required by Basel II) or broken down by asset (e.g., Precious Metals versus Natural Gas). Performance Attribution Reports Performance attribution reports (often called P&L Explain reports) attempt to decompose the sources of profit and loss at the trader, profit center, or enterprise level. Using position information together with observed market activity, the algorithms used attempt to explain P&L in terms of certain risk factors appropriate to the portfolio. For example, for a fixed-income portfolio, those risk factors might be changes in the general level of risk-free interest rates (e.g., U.S. Treasuries), in the shape of the yield curve, in credit risk premiums, in basis relationships, and in implied volatility.
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Each portfolio manager and risk manager spends a good part of his day analyzing these reports for anomalous behavior. Such a report provides information about the types of exposure to which the enterprise is at risk, but it may also provide early warning of a control or measurement problem. For example, if VaR is calculated only once a day, traders may be gaming the system by taking large positions intraday and liquidating them by the end of the day. But such gaming might be revealed in patterns of daily P&L. Forensic Risk Review Reports Changing patterns of risk over time are also a powerful source of warnings, and such patterns can be identified via forensic risk reports, such as a report that compares theoretical VaR to actual performance over time. Any estimate of risk is nothing but a forecast, and implicit in the use of stochastic methods is the assumption that future market behavior will be similar to that of the past. So, just as in any other forecasting activity, the quality of the forecasts must be evaluated forensically. In risk management, this is done via a backtest report that compares estimates of VaR to actual performance. If an enterprise calculates daily VaR at the standard 1 percent probability level, this means that it can expect actual losses to exceed VaR about three times per year (1 percent of 260 trading days).20 Consider the typical backtest report of Figure 4-12, which compares daily income for trading units to VaR in 2008. There are a large number of outliers, far more than the three expected—especially in the last few months of the year, during the height of the financial crisis. Furthermore, the magnitude of some of these outliers (both losses and profits) substantially exceeds the theoretical on several days. Although VaR is estimated from the left side of the distribution (losses), even anomalously large profits are a warning signal. As with the P&L Explain report, such large deviations (by count or by magnitude) from VaR need to be explained. ADDITIONAL RISK CONTROL MECHANISMS AND BEST PRACTICE Although risk metrics are exceedingly useful in limiting enterprise risk and enhancing decision-making ability, even the best models will fail at times, and so management should make provisions for unknown unknowns. When this is done, an enterprise is not unknowingly dependent on the forecasting ability of its risk models, no matter how sophisticated they may be.
Income of Trading Units and Value at Risk in 2008 in € m. 600 500 400 300
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Figure 4-12 Daily Backtest Report, 2008 Source: Black Diamond Risk Enterprises
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Risk measurement failures may sometimes be specific to certain activities, asset classes, industry groups, or counterparties. Therefore, best practice includes imposing concentration limits on such bins. Such limits essentially acknowledge that increased diversification will tend to mitigate the most extreme losses when risk measures fail. Best practice also includes explicitly estimating model risk where possible. Although it is difficult to quantify the risk that a basic model poorly represents the future, it is possible to construct some estimates of parameter error, that is, the likelihood the protocols used to generate the parameters that inform the model are flawed. There are specific statistical techniques for doing so. (These are addressed in Chapter 8.) THE EVOLUTION OF MODELS AND BEST PRACTICE The field of financial engineering and risk modeling is highly robust. New models and methods are created and implemented at blinding speed, because any small advantage can result in substantial profits. These are impossible to detail or even to fully track, given that many models are protected as though they were state secrets. Nevertheless, there have been two important developments in next-generation best practice in recent years. Both of these developments recognize the dynamic nature of market evolution over time and the effect of human actions and changing risk preferences as a driver of change. Static versus Dynamic VaR Since about 2006, risk managers who compared theoretical risk to actual performance have found increasing discrepancies. Some came to the conclusion that static VaR, in which portfolio composition remains constant over the horizon, was an increasingly poor estimate of reality. And this was especially true when a horizon longer than one day was used. In real life, when a position starts to go bad, a trader might take mitigating actions, such as liquidating all or part of the position or adding a hedge. One can expect such actions to be successful more times than not. Humans are still the best pattern recognition engines, and if a trader weren’t good at this, she wouldn’t have a job for very long. Similarly, traders might take less voluntary actions when conditions changed. Even if a trader believed in his strategy, an increase in his portfolio’s VaR might force him to liquidate some of it. Consider the case of a trader with a $10 million VaR limit who is using $7 million, or 70 percent
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of it. Generally, such a percentage gives the trader some margin for error as VaR varies from day to day. However, if there’s a market shock and volatility doubles, even though the trader has not changed his portfolio, his VaR is now $14 million, and he must bring down the position size to remain under the limit. In practice, he would anticipate such a forced liquidation, mitigating his loss by starting to liquidate when, say, VaR hits 95 percent of the limit. Although a mathematical model cannot anticipate new positions that a trader might take, it can model some of the dynamics of market prices. For example, a large shock is almost certain to have the following predicable consequences, each of which greatly influences performance: • • • • • •
Implied and historical volatility increase. The bid/offer spread widens. Liquidity is reduced. Credit risk increases. Operational risk has higher consequences. The ability to fund positions is diminished.
These changes may not all occur simultaneously; instead, they may evolve over time via a causal cascade. One method of simulating a dynamic outcome is the use of agent-based approaches, in which rules are defined that simulate the dynamics of market prices and the actions of agents with cognitive and decision-making abilities. Use of dynamic VaR is consistent with the Basel Committee’s updated requirement that a bank must justify its time scaling of risk parameters. Previously, many stochastic models assumed that, consistent with statistical theory for Gaussian distributions, the standard deviation of a 10day period is equal to the square root of 10 times the standard deviation of a 1-day period (implicitly and unrealistically assuming that volatility remains constant over the entire period). The committee explicitly states, “A bank using this approach must periodically justify the reasonableness of its approach to the satisfaction of its supervisor.” Stressed VaR The Basel Committee will also add to Pillar I the requirement that banks using the Advanced Measurement Approach calculate stressed VaR weekly. Stressed VaR combines the features of a VaR calculation and a stress test, in that the VaR of the current portfolio is calculated using parameters taken from a historical period of extreme financial stress. The committee specifies,
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“As an example, for many portfolios, a 12-month period relating to significant losses in 2007/2008 would adequately reflect a period of such stress; although other periods relevant to the current portfolio must be considered by the bank.” Each bank must meet a daily capital requirement that is now a function of both daily VaR and the latest available stressed VaR. EXTREME SCENARIO GENERATION Best practice in stress testing is not yet well defined. The existence of an enterprise depends on the quality of the extreme scenarios used to ensure capital adequacy. However, analysis of recent events has demonstrated that the scenarios used by many enterprises were often inadequate. As described in a recent Basel Committee publication on stress testing, Most bank stress tests were not designed to capture the extreme market events that were experienced. Most firms discovered that one or several aspects of their stress tests did not even broadly match actual developments. In particular, scenarios tended to reflect mild shocks, assume shorter durations and underestimate the correlations between different positions, risk types and markets due to system-wide interactions and feedback effects. Prior to the crisis, “severe” stress scenarios typically resulted in estimates of losses that were no more than a quarter’s worth of earnings (and typically much less).21
The publication went on to describe a number of common failures, such as dependence on historical scenarios, use of theoretical scenarios that were insufficiently extreme, and use of scenarios that did not integrate all important market changes (e.g., that included directional risk but not basis risk or liquidity risk), did not properly account for the dependence between market risk and credit risk, and did not properly account for new instruments (e.g., CDS) that did not exist at the time of some historical scenarios. In part, this was due to the inability to justify certain extreme scenarios. As the publication continued, “At many banks, it was difficult for risk managers to obtain senior management buy-in for more severe scenarios. Scenarios that were considered extreme or innovative were often regarded as implausible by the board and senior management.” Since the crisis, best practice emphasizes constantly reviewing previous scenarios and looking for new ones. However, this is often done on an ad hoc basis. Advanced methods for generating and justifying plausible extreme scenarios via a “scenario engine” are next-generation state of the art in risk management.
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IN DEFENSE OF VAR In the aftermath of the credit crisis, there was a great deal of criticism of risk management practice in general and VaR in particular. Some critics objected to the use of VaR on empirical grounds: its predictive ability was poor because it failed to provide warnings of the impending financial crisis. Others objected to the use of VaR on theoretical grounds: its fundamental assumptions included Gaussian distributions that were not consistent with the fat-tailed distributions seen in real life. However, much of this criticism was based on confusion between VaR the metric and the original variance-covariance model used to estimate VaR, which was based on modern portfolio theory of the 1950s. But these criticisms (and their proposed solutions) are inconsistent with current best practice and modeling. First, VaR is a predictor of risk: the term measurement is a misnomer. Therefore, actual P&L is expected to exceed VaR some percentage of the time. Second, neither proprietary nor commercial off-the-shelf VaR models generally assume Gaussian distributions; for many years, even variance-covariance models have been adapted to correct for heteroskedasticity and for dynamic volatility. And even institutions that don’t use VaR-based measures (e.g., futures and options exchanges) have explicitly used fat-tailed distributions to ensure capital adequacy with respect to performance margin. Third, capital adequacy is defined not so much by estimates of VaR as by the results of stress tests based on extreme scenarios and calculated to a much higher level of confidence (e.g., 0.01 percent rather than 1 percent). Some critics also recommended that risk-based capital adequacy requirements (such as those in the Basel II Advanced Measurement Approach) be replaced by fixed rules, such as those in Basel I or the Standardized Approach in Basel II. However, even a set of rules more complicated than the tax code would not make capital requirements correspond to actual risk better than internally generated risk forecasts. Such a rules-based system would be a de facto predictive model, but one that would be far less sophisticated than current best practice, and one that would be unresponsive to current market conditions. Furthermore, such fixed external rules can always be gamed; there are often many ways to make the same bet, some of which require less capital than others. A more valid criticism is that the scenarios used for stress tests were insufficiently extreme or were based only on historical events rather than on plausible future events.
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As the Basel Committee pointed out, stress tests are far less quantitatively determined than VaR is, and they often failed to model secondary market effects that affected performance (such as loss of liquidity) or to adequately simulate a cascade of interconnected events that played out over time. Finally, it’s important to understand that VaR is nothing but a metric, like length: if a broken ruler is used to measure the length of an object, that doesn’t mean that the concept of length is flawed. And as a metric, VaR has the same usefulness in managing risk that it always did—that is, providing an objective, quantitative measure of risk that can be easily communicated and on which position controls can be based. SUMMARY In this chapter, we discussed the basic types of financial risk, the classic models used to estimate risk, and the assumptions about market behavior on which these models depend. We discussed risk as a forecast, the difference between risk measurement and risk management, and current best practice and reporting requirements. We also discussed two key developments on the horizon of risk management: dynamic VaR, stressed VaR, and improved specification of extreme yet plausible scenarios. WHAT’S NEXT The next chapter will discuss systems behavior and describe how, consistent with dynamic and stressed VaR, the evolution of a system over time can be revealed and modeled.
CHAPTER 5
Systemic Risk and Systems Thinking
ROGUE WAVES, DETERMINISM, AND CHANCE Oceanographers have accepted the existence of “rogue waves” (also called “extreme waves”): anomalously large and spontaneous waves that occur in the deep ocean and on the Great Lakes. Rogue waves are not the largest waves ever observed, but they present a risk to even the largest vessels1 because they can occur in perfectly clear weather conditions and at odds to the prevailing wind directions and currents. Oceanographers have a number of theories about how such waves are generated. Some consider them to be merely an instance, albeit rare (e.g., a 100-year event), of the normal spectrum of waves, created by the same forces that create lesser waves. Others consider the initial conditions and the physics that may produce them. The geometry of the coastline or the seabed may focus smaller waves that are in phase, causing massive constructive interference. Alternatively, they may be generated by nonlinear effects in which a wave sucks energy from surrounding waves and becomes freakishly large. All these theories depend on physics, not chance. Even the rare-butnormal theory is deterministic: mechanical processes drive wave formation. Nevertheless, sometimes a statistical representation of wave heights is useful, particularly when the interaction among wave, shore, and wind is too complex to model physically. Of course, there might be tremendous value in knowing which of these theories is correct. If rogue waves are just a rare event that can’t be directly linked to the starting conditions, statistical representations of ocean systems are relatively unhelpful. However, if scientists are able to identify the congruence of initial conditions that causes rogue waves in the proximity of a vessel, risk modeling and warning systems based on such models might aid in risk mitigation.
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SURVIVING WITHIN A SYSTEM In much the same way, it is helpful to understand the systems in which we operate, and the systemic risk to which we’re exposed. In Chapter 1, we discussed two alternative worldviews: the world of the plausible and the world of the probable. One of our objectives in examining any system is to understand how well we understand both known unknowns and unknown unknowns. In finance, this will help us determine when a statistical representation is sufficient for identifying extreme scenarios and when only a causal model will do. The answer affects optimal decision making, whether the decision involves putting ships to sea, dealing with a new virus, or trading stocks. If catastrophic events are unpredictable, an enterprise that is concerned about its continuing survival must reduce its level of exposure at the expense of its profit. If, instead, such events can be anticipated, the enterprise can use more creative and specific solutions that constrain extreme risk while allowing business as usual. Whether the extreme event we wish to evaluate is a rogue wave, a collapse in the collateralized debt obligation (CDO) markets, or even military action by North Korea, it’s instructive to characterize systems that generate such outcomes in a more abstract manner. All threats, no matter what their source, can be considered in light of the vulnerability of the system that might generate them, the chain of events that might produce highly adverse consequences, and the likelihood and magnitude of resultant outlier events. It’s important to account for interdependence between systems as well. Systems can interact with other systems; the global markets can interact with, say, geopolitical systems. Either can drive or be driven by the other, and a clash or interaction between the systems might result in price controls on oil, an embargo on Cuba, or a deliberate attempt by a state actor to embed itself in the U.S. critical infrastructure. SYSTEMIC RISK, CONNECTIVITY, AND CONTAGION Economists sometimes explain the source of systemic risk in terms of two types of shocks to the system: macro or “common” shocks and micro or “chain reaction” shocks. The terms macro and micro do not refer to the magnitude of the shock, but rather to the influence of its drivers. A macro shock is a shock that affects all economies and markets directly, whereas a micro shock is one that permeates though the entire system via a process of contagion.
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Depending on the contagion process, the speed of a micro shock may be slower than that of a macro shock. The chain reaction may take time, whereas a macro shock—say, in the financial system—affects all asset classes everywhere at the same time. An example of a macro shock might be the events of 9/11, which caused a nearly instantaneous drop of over $2 trillion in global market capitalization. An example of a micro shock might be the credit crisis of 2007–2008, in which the effect of trading losses in mortgage-backed securities on banks and other financial institutions rippled though the global capital markets, leaving virtually no country or asset class untouched. What both of these definitions have in common is an explicit recognition of the connectivity of the global economies and capital markets and acknowledgment that it may be impossible to isolate financial, economic, and geopolitical risk. Change is risk, and determining the sensitivity of a system to micro or macro shocks requires systems thinking. SYSTEMS AND SYSTEMS THINKING A system is defined as a set of elements that have one or more relationships between them, and systems thinking is the process by which one seeks to understand those elements and relationships so as to be able to understand the behavior of the system as a whole. Systems are usually visualized graphically as a set of nodes with links or connections between them. A system is more than the sum of its parts, particularly if it’s large or complex. It may exhibit unique behavior that cannot necessarily be inferred from the behavior of its individual elements or any subset of them. In systems theory, it’s important to have perspective, as a very small observer of a single element may be oblivious to larger interactions that might be clear to a giant observer of the entire system. The relationships between system elements can be strictly deterministic (i.e., controlled by physical or other laws), completely stochastic (subject to chance), or more complex. Where human decision making is involved, some of the interactions can include behavioral effects as well. Modeling a system can involve both art and science when the modeler seeks to decide what is to be included in a system abstraction and what is to be excluded. The boundaries of an individual system depend on the nature of the relationships that link the nodes and drive change. The relationships between elements inside the system are different from the relationships those elements have with elements outside the system. For example, our solar system interacts with every celestial body in our
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galactic system via gravity, but it is the strongly linked nature of our own solar system relative to its other relationships that defines it as a system. If understanding a particular system requires that its interactions with other systems be understood as well, a modeler might create a kind of meta-system in which the elements of the system may be systems themselves. One of the most fundamental attributes we wish to understand about a system is its predictability (also called its banality): the degree to which we are able to forecast the system’s next state or states. This change in state might be an inevitable response to endogenous vulnerabilities that are already present in the system (e.g., too many high-risk mortgages), or it might be an unanticipated response to an exogenous shock (e.g., military action in the Mideast that raises the price of oil to $300 per barrel). A model without predictive ability has little value in managing extreme risk and can provide few insights that add value to the decisionmaking process. Conversely, a model with predictive ability may provide forecasts of possible future scenarios that are substantially different from those generated using other analytic methods and greatly aid in risk measurement and mitigation. DRIVERS OF SYSTEM BEHAVIOR: REGIME CHANGE AND BLACK SWAN EVENTS Micro and macro drivers may have different effects on a system. As they cascade though the pathways that connect the nodes, all those multiple relationships may interact in a way that forces equilibrium. Alternatively, they may create chaotic, oscillating, or extreme behavior. Events that occur within the system may be separated by distance or time, but, depending on the complexity of the system and the nature of its relationships, they may drive change in the system as a whole in unexpected ways. The reaction of the system to an exogenous or endogenous driver may even cause it to jump to a new and different version of itself that is unlikely to react to micro and macro drivers the same way it did before. Like political change in a sovereign state, economists call such a shift regime change. Sometimes such regime change is patently obvious, particularly if it occurred in response to a macro driver. However, sometimes the transition is less obvious. Although the new regime will no longer respond to old or new drivers in the same manner as the previous regime, traditional metrics such as historical volatility may not provide clear indicators that something very important has changed.
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The mechanism for change over time varies with the nature of the system. A system may evolve via a process of self-organization aided by positive (destabilizing) or negative (stabilizing) feedback. Systems can evolve in relatively smooth steps (e.g., in linear systems in which small changes create small effects) or can suddenly jump from one state to a radically different one (e.g., in nonlinear systems in which the same small changes create large effects). In the extreme, a system might be expected to exist for the indefinite future or might already include the seeds of its own inevitable destruction. Even a small and temporary perturbation may affect a system in various ways. If its influence dies out as the system assimilates the perturbation (i.e., returns to the same state of equilibrium), the system is called asymptotically stable. Alternatively, depending on the nature of the interconnections, the same perturbation may instead take the system over a tipping point and lead to black swan events such as the precipitous decline in housing prices in the late 2000s. Systems may or may not exhibit hysteresis (from the Greek for “lagging behind”), that is, retain memory even when the external input is removed. A system that does so is said to exhibit path dependence. Even natural systems can exhibit hysteresis. For example, the invention of the computer hard drive depends on it in that a piece of metal retains a small magnetic charge even when the external magnetic field is removed. Systems may also include a temporal component (e.g., effects take time to be fully realized) or may be represented independently of time (e.g., drug trials and results). Financial and economic systems often exhibit hysteresis. Because a market is nothing more than an aggregate of human participants, memory is, of course, explicitly present—both in the human mind, but also in the historical data used to inform investment strategies. COMPLEX SYSTEMS AND EMERGENT BEHAVIOR A system is considered complex if it has many elements and many relationships between those elements. A complex system’s collective behavior cannot be inferred from the behavior of the individual elements because of the high degree of interconnectivity. Conceptually, such collective behavior is similar to portfolio risk, in which the behavior of a portfolio cannot be inferred from the behavior of the individual securities that constitute it (unless there is no correlation between any of those securities, a special case that is analogous to blocked communication between the elements of the system).
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The mathematician Warren Weaver drew a distinction between “organized complexity” and “disorganized complexity” in a system. In disorganized complexity, the behavior of a very large number (say, millions) of moving parts can’t be distinguished from random behavior, even though the physics of the process is deterministic at a sufficiently microscopic level. In Weaver’s view, a system that exhibits disorganized complexity becomes something else: a new entity that’s different from the sum of its parts emerges from the chaos. In disorganized complexity, statistical models and methods might be used to characterize this emergent system rather than dealing with the computationally intractable problem of modeling the behavior of its component elements. Physical or statistical measures can then substitute for a deeper understanding of the causal relationships between the elements of the system. The classic example of disorganized complexity is that of gas in a container. Although Newton’s equations of motion control the interactions of each molecule of gas, metrics such as temperature and pressure can be used to characterize the system fully. Barring an exogenous change to the container of gas, it contains a stable system within its walls; we don’t expect pressure or temperature to change spontaneously except in response to an outside influence. Conversely, a system of organized complexity might be a city such as Paris, including both its physical infrastructure and its citizens. Paris’s layout was shaped by Napoleon III in a manner that was meant to stymie revolutionaries.2 The behavior of a complex system must be understood in terms of both its drivers and its current environment at any point in time. One critical feature of a complex system is its sensitivity to initial or changing conditions. These conditions determine whether the air movement caused by a minor weather condition will be lost in atmospheric noise or trigger a major hurricane. Decision makers must be especially cognizant of the fact that the same action taken a second time may not have the same effect if the environment has changed. For example, a speculator may attempt to squeeze cotton futures by buying 10,000 contracts of the nearby delivery month. However, that transaction will have wildly different outcomes, profitwise, if the open interest in that contract is 100 contracts or 100,000 contracts. Drivers of change need not be large themselves; a series of microscopic changes (many of them simultaneous) can lead to macroscopic change that is discernible by manual or automated means. For example, a number of small trades, unrelated but executed simultaneously, may
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trigger larger price movements because their net effect is consistent with that of news or insider trading by sophisticated traders, and thus triggers automated alerts. In the following sections, we will discuss various types of systems to better determine which of these best characterize economic and financial systems. Appropriate identification leads to alternative approaches for identifying system behavior and for identifying the elements and interactions that are most likely to lead to extreme outcomes. Dynamic Systems A system can be characterized as dynamic; that is, it changes with time. Such a characterization implicitly assumes that the system is at least partially deterministic; change in one of its elements inevitably breeds change in other elements. A dynamic system is not to be confused with a dynamical system, which is characterized by a set of differential equations that describe its behavior with respect to time, albeit for only a short period. We have no reason to believe that a financial or economic system can be expressed in so convenient a form. In the physical world, a dynamical system stops moving when an outside force is removed; it has no memory. Conversely, financial and economic systems can reasonably be expected to exhibit hysteresis and continue to react after the force is removed because human decision makers are capable of retained memory, both accurate and biased. Furthermore, we have no evidence, either intuitive or empirical, that the driving mechanisms or the equations that might be used to describe them are continuous with respect to time. The presence of so-called tipping points and black swan events provides evidence of noncontinuous behavior, as do the logical and continuing consequences of various discrete drivers (e.g., regulatory or policy changes). We do know, however, that the global financial system is dynamic; it interacts with other systems that are time-dependent (e.g., economic or geopolitical systems) and therefore changes with time. Even without specific outside stimuli, the passage of time alone may be sufficient to change the financial system as a result of behavioral effects. Stable foreign exchange or interest rates may change decisionmaking protocols or create the perception of a lower-risk environment that spurs investment or risk taking. For example, if market prices have been stable for some time, an investor may be enticed to swap out of lower-risk assets such as Treasuries and into higher-risk assets such as equities or commodities.
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There may be behavioral effects as well. For example, traders who maintain short positions in options receive positive reinforcement by reaping steady rewards in quiet markets.3 They may suffer from perception bias, which induces them to become overconfident and repeat the strategy even when it is inappropriate. Chaotic Systems A system can also exhibit chaos (more properly, deterministic chaos). A dynamical system may exhibit behavior that appears to be random, but only because of its complexity. A Tilt-a-Whirl carnival ride, which unexpectedly rotates or jerks from side to side, is an example of a chaotic system. Contrary to the colloquial use of the term, a chaotic system is fully deterministic at a sufficiently granular level. Even the result of a toss of a die is deterministic based on the physics of the throw, the characteristics of the table on which it’s tossed, and other relevant conditions. At the most granular level, we might consider the global capital markets as a deterministic system no different from a container of gas. Changing as it does with time, a chaotic system is highly sensitive to initial conditions and may exhibit the famous “butterfly effect,” in which a small perturbation early in the process multiplies exponentially and generates extreme outcomes such as hurricanes. As such, its changing state is entirely determined by the initial conditions; there is no random element involved. Complex Adaptive Systems We now consider the mechanisms by which a system changes. A complex adaptive system is a complex system that is able to adapt to its environment by changing in response to either exogenous shocks or changes in current conditions. For example, in a biological system, bacteria evolve in response to the use of antibiotics. The system has some or all of the following characteristics: • It is highly dependent on its initial state. • It has memory. • The number of elements that it contains and/or the number of relationships between elements is nontrivial, either in scope (e.g., there are many different drivers) or in form (e.g., they are nonlinear or discontinuous). • It is capable of feedback4 into the system. • It can interact with its environment (i.e., other systems).
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Such adaptation may result in a self-correcting process that attempts to maintain the current state. Alternatively, the adaptation might require the system to jump to an entirely new state—one that is considered catastrophic by some observers. This ability of an adaptive system can present a real danger to those who interact with it or use metrics to analyze it. Action and reaction may change, but this new dynamic may be invisible to the observer. Having taken one evolutionary path, the system is irrevocably changed, if only by new patterns of behavior influenced by memory. EVOLUTIONARY FORCES AND THE SELF-ORGANIZING SYSTEM An evolutionary system is one that changes over time in response to external drivers in a manner dictated by the nature of the internal interactions. Self-organization is the spontaneous generation of order in a complex adaptive system. A self-organizing system achieves such order via multiple interactions between its elements until some optimal system state is realized. In a self-organizing system, complex behavior can arise as the net result of myriad simple interactions between interconnected parts of the system and wholly within its boundaries. The system may evolve to a new form when positive and negative reactions occur at a highly granular level, which in turn can cause the system to increase in complexity without direction by an outside force. A market economy is one example of a self-organizing system, whereas its opposite, a command economy, is considered far less efficient in distributing assets. In practice, most economies are mixed economies, in which government provides some level of direction intended to orient the system toward a goal. In a system that is controlled by human interactions, a self-organizing system can be thought of as attempting to reach Nash equilibrium (named after the great mathematician and game theorist John Nash), in which equilibrium might be reached via a set of strategic interactions in which the participants attempt to maximize their own self-interests. However, such equilibrium often tends to gravitate toward minimum expected outcomes. For example, if the participants formed a cartel that fixed prices, they might increase their expected payoffs—both individually and as a group. However, it’s not always the case that equilibrium can be reached in such a system. Some systems are inherently unstable because stability is achieved only when each game player has no incentive to change her
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strategy. Furthermore, some economists believe that the conditions required to reach equilibrium are dauntingly unrealistic. Equilibrium may be temporary and transient, like the process by which humans walk on two legs. Self-organized systems often—but not necessarily—display emergent properties. Emergent properties are properties that cannot be inferred from an understanding of the granular interactions, but instead are something entirely new, created from the sum of many such interactions. In the physical and biological sciences, researchers characterize many phenomena as manifestations of self-organizing systems. If one searches the literature, one can find academic papers on applications as diverse as “Dynamical Model of the Baseball-Bat Collision” (physics), “The Emergence of Scale-Invariant Architecture in Rimmed-Pool Mineral Deposits in Yellowstone Hot Springs and Illinois Caves” (geology), “Multi-Resolution Modeling of Protein-DNA Systems” (biophysics), and “Division of Labor and the Behavioral Design of Social Insect Colonies” (entomology). However, there are relatively few studies on the application of complexity theory to the global capital markets. The reason for this dearth is unclear. Perhaps the degree of difficulty is the primary issue in light of the scale and complexity of the global financial system or the behavioral aspects of the interactions that rule most market evolution. Perhaps it’s the fact that a more computationally tractable alternative—that is, the use of stochastic methods—came to be viewed as best practice. Or perhaps it’s because when financial best practice was being defined, systems theory was less developed than it is now. This is no less true of the human ecosystem and its evolution, and considering market evolution as a complex, evolutionary system might well be productive in better understanding both systemic and specific risk. Such a view of the global economy is buttressed by the economist Leo Tilman, who discusses the forces of dynamic finance and characterizes the current state as one in which evolutionary processes and “financial Darwinism” involve an “ongoing tectonic financial shift.”5 EVOLUTIONARY MECHANISMS Generally, the only way to understand the emergent behavior of a complex system is by the use of experimental mathematics. In this field, the properties of an object are explored using numerical methods. For example, the integral of a complex function might be calculated numerically (when it has no closed form) by using a software tool such as Mathematica.
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Experimental mathematics is often used in pattern recognition problems and can be used to gain insight when a theory about the source of the pattern is lacking. The Bak-Sneppen Evolution Model In practice, a modeler will create some abstraction of the system of interest in the form of a network representation. Only after such a network is defined and populated can analysis proceed. Although it deals with a problem in biology, the classic Bak-Sneppen model of evolution provides many insights about how systems of any type evolve and how experimental mathematics can be used to identify emergent behavior. In the early 1990s, Per Bak and Kim Sneppen proposed a model that was intended to explain the very uneven history of evolution as evidenced by fossil records. These records provide evidence that biological evolution occurs in rare, random bursts (a phenomenon known as punctuated equilibrium) and is accompanied by a sudden and rapid decrease in the variety of species (known as extinction events). Bak and Sneppen hypothesized that these spikes in the rates of origination and extinction might be a feature of a self-organizing ecosystem whose model dynamics reproduces a process of natural selection. When this biological system is simulated by using only a simple assumption of codependence between nearby species, behavior consistent with observed historical patterns emerges. As time is stepped forward, the dynamics of the model repeatedly eliminates the least fit species, forces its neighbors to adapt to their missing presence, and causes the system to converge to a new state that allows an optimal response to new drivers. In a sense, preservation of the species is replaced by preservation of the system, albeit in a mutated form. As shown in Figure 5-1, in the Bak-Sneppen model, the system is represented by nodes in a d-dimensional lattice structure6 that serves as a representation of species interaction. Each node represents a different species, and random “fitness” (for survival) values are initially assigned to each node in the lattice. Then the simulation can proceed. As time moves forward in discrete steps, the least fit species (the nodes with the smallest fitness value) are identified, and only the 2d nodes surrounding them are assigned random new fitness values. Such a rule is intended to force the most rapid evolution on the least fit species, which in turn will most affect their immediate neighbors.
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Figure 5-1 Lattice Structure for Ecosystem Evolutionary Model
As the process continues, “coevolution” can be observed, in which proximate species exhibit synchronous change for better or worse. Such behavior helps account for the emergent properties of the system, in which patterns emerge in the system as a whole that are not apparent from the individual elements of the system. As the simulation progresses, the system exhibits the phenomenon of clustering, in which a set of nearby neighbors have extreme fitness values (either high or low), each of which was preceded by a neighbor with a similar extreme value. As this evolutionary cascade (referred to as an “avalanche”) proceeds over time, the system tends toward a limit in which no species has a fitness level below a certain threshold (i.e., the weak have been eliminated), and the fitness levels of the surviving species are uniformly distributed. The Distribution of Outcomes The Bak-Sneppen model allows estimation of the probability of cluster size S (where the size of a cluster is the time it took to reach the critical state), which can be shown to converge to a power law. A power law f(x) = xa has the property that the relative change f(kx) a f(x) = k is independent of x. That is, the probability of a given cluster size is of the form St, where t is a function of the particular system. Power laws lack scale and are often characteristic of fractals (geometric shapes or
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functions that exhibit self-similarity at any scale) in that each subset of a fractal shape has essentially the same shape as the whole. It must be noted that for systems that are specified differently from that of the simple Bak-Sneppen model, the clusters may be better represented by a function different from a power law. Although a power law may best fit the simulation results (in the case of the Bak-Sneppen model, cluster size as a function of time), it is only an empirical result and not a theoretical result. Other distributions might fit nearly as well, and slight tweaks to the artificial rules that control system evolution might result in a different coefficient for the power law, an entirely different function, or even a reduction of clustering with time if the model includes some mechanism (e.g., negative feedback) that prevents clustering. For example, other studies have used an approach similar to that of Bak and Sneppen to simulate a forest and its vulnerability to sparks and fire. If trees are initially clustered rather than being spaced equilaterally on a grid, a forest fire can self-propagate, and cluster size is better represented by a Poisson (exponential) distribution than by a power law. The results of an experimental simulation might then provide evidence that the network is not size-invariant, and it cannot be assumed to be represented by fractals. SELF-ORGANIZED CRITICALITY AND NETWORK-CENTRIC OPERATIONS In a self-organizing system that represents a conflict between parties, the clustering of strength on one side leads to casualties on the other side. Whether those parties are competing organisms or state actors, when a self-organized critical point7 is achieved, the system has the maximum flexibility to respond to a new driver. These nodes might similarly represent a network-centric view of military operations, where the nodes are assets of various types.8 As Professor James Moffat (an expert in complexity and warfare theory) points out, “One of the requirements of military command is to arrange things so that the forces collaborate locally and thus self-organize into this optimal state.” This characterization is key to the concept of net-centric operations (NCO, previously known as net-centric warfare), in which the military takes advantage of self-organizing features via increased information awareness and communication at the local level. In large part, the computers, headsets, and other technology available to the modern military facilitate this approach, and the NCO approach is given credit by some for success on the ground in Iraq.
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Such an evolutionary model also has implications for those who would control systemic risk, whether on the battlefield or in the global economy. A bottom-up approach, in which self-organization is recognized as an evolutionary inevitability, might be optimal. The focus might be placed on facilitating beneficial interactions between proximate elements that lead to the desired state rather than on top-down intervention. CREATING SYSTEM MODELS The Bak-Sneppen evolutionary model is only one example of a structural representation of a systems network. In their ecosystem model, Bak and Sneppen forced communication within the system, both temporally (by selecting the least fit at each time step) and spatially (by changing the fitness values only for near neighbors). Of course, the spatial dimension need not be strictly geographic; it is a metaphor for any nontemporal links between elements.9 Thus, with relatively homogeneous elements (differing only in the random fitness values initially assigned to them) and with influence determined by their geospatial proximity, Bak and Sneppen’s choice of a lattice structure in two dimensions was appropriate and efficient. However, other configurations of a network might be more appropriate for a different system; an alternative configuration of nodes and links might better describe the elements and relationships of the network. The network modeler is free to determine the most reasonable configuration in terms of fairly representing elements and relationships and in terms of creating computational efficiency. For example, a hub-and-spoke or tree structure might be more appropriate than a lattice structure, depending on how information flows between nodes. We might think of the evolutionary process as one that is facilitated by communication between elements: any network abstraction of the system is really an information grid rather than a physical grid. The network structure can also be as complex as required. For example, the elements of the system may be connected in any dimension and in more than one dimension. Both correlation and coincidence might be assumed to occur across any dimension of the system. We can imagine a d-dimensional space that accounts for different correlation and coincident events. The network representation might even explicitly include a time dimension: the interactions across this dimension might serve as proxies for correlated events, and the interactions within the dimension might do the same thing for coincident events. As the system adapts and evolves, as long as any element of the system still survives, information is transmitted throughout the system.
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Creating an abstraction of a real-life system is useful in another way. As an external stimulus triggers various responses within the system, we may be able to infer information about that stimulus even if we can’t directly observe it. We do so by measuring the response function in the observable parts of the system. For example, intercepting terrorist communications and observing the responses to them (say, physical movement by members of a terrorist cell) might lead an intelligence analyst to other information about the system. Similarly, observing the change in the price of a home builder’s stock synchronous with a large increase in interest rates might lead to inferences about the firm’s exposure to interest rates and its hedging strategy or lack thereof. SIMULATION AND TOY MODELS Clearly, the rules applied in the Bak-Sneppen model are simplistic and have a more random relationship between proximate nodes than might, say, a financial or military system. Such a simplistic system is sometimes called a toy system because it necessarily lacks certain features of the real world. Although instructive, its results will be only as good as the modelers’ choices with respect to network design and rules of interaction. Nevertheless, such toy systems allow study of the emergent behavior of any system as well as its sensitivities to variations in those rules. Simulations using toy models demonstrate how certain characteristics of systems of interest emerge and suggest strategies for influencing a highly complex self-organizing system and prodding it toward a desirable goal. This is especially true in the case of the financial markets, since only self-organization is feasible in the global capital markets. Although outside forces such as those present in a command economy can influence the system, there is no outside entity that is capable of imposing order on the entire system; in fact, this is one of the reasons why grand gestures such as trade embargos often fail to achieve the desired economic results. As mathematical psychologist Dr. Paul Lehner of MITRE Corp. said, “Simulations always generate surprising results. We code a few rules into the simulation, have certain expectations about what will evolve (based on our internal mental simulation), and then are surprised when things don’t evolve as expected. We learn a lot about what we don’t know about the implications of what we do know. So I may not trust the simulation results, but I have learned not to trust my intuition.” One of the most important potential uses of a systems model is to manage systemic risk. Testing various strategies in a toy model rather than the real world might allow decision makers to maximize positive impact, achieve the desired goal, and avoid unintended and adverse consequences.
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One of those adverse consequences might be relatively invisible except via simulation, that is, forcing the system to a state that is more fragile and sensitive to unanticipated shocks. ALTERNATIVE THEORIES: SELF-ORGANIZED CRITICALITY VERSUS HIGHLY OPTIMIZED TOLERANCE In the late 1990s, the mathematician John Doyle and the physicist Jean Carlson proposed an alternative to self-organized criticality (SOC) that they named highly optimized tolerance (HOT). They noted that some systems, such as energy delivery systems that include electrical grids and power generators, are optimized in such a way (often for economic reasons) that they have a split personality: they are both robust and fragile. Without some room for error, they are more likely to exceed their operating limits and cause blackouts. While power grids are created by humans, the same robust and fragile behavior might be true of systems that evolved naturally via selforganization. Like SOC systems, HOT systems can display a distribution of high-consequence events in the form of a power law. However, it is beyond the point of criticality with which HOT is concerned; that is, it can be used to estimate consequences when the upper limit is breached. HOT may therefore be especially applicable to cybersecurity models, in which the consequences of an attack on critical infrastructure are extreme. PATTERN CREATION IN A COMPLEX DYNAMIC SYSTEM We may be able to infer some of a system’s dynamics by observing the patterns that the system creates. In physics, there is a concept known as symmetry breaking. In a physical system, microscopic fluctuations that might cross some critical threshold can determine which of two very different states the system will take. The term breaking comes from the fact that this jump can take the system from a disorderly state (in which those fluctuations are just so much noise) to a more ordered (and less probable) state. This is the physical equivalent of a tipping point. Whether in a physical system or some other system, such a phenomenon can be a driver of pattern formation. Such patterns can also be an artifact of human behavior. For example, assume that, as described in the previous discussion of dynamic VaR, a trader loses money today on a long position in interest-rate futures because rates increased dramatically (when rates go up, prices go down).
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Further assume that the trader has utilized his entire risk limit as measured in terms of VaR. At the end of the day, the risk measurement models used by most firms will assimilate that new piece of data, and recalculation of the trader’s VaR at a new and higher estimate of variance will show an increase in risk. Thus, because the large move increased VaR, the trader starts the next day over limit in terms of risk and must therefore liquidate or otherwise hedge part of his position. This trader and others in a similar situation may set off a causal chain of selling that further exacerbates the subsequent increases in rates. This scenario is an example of a symmetry break in that if the price move had not been quite so large, the traders would have been allowed to keep their positions intact, and forced selling would not have been triggered. THE GLOBAL CAPITAL MARKETS AS SELF-ORGANIZING SYSTEMS If the system we are studying is a financial system, we might imagine the dimensions of the lattice as having some physical meaning other than spatial. Instead of modeling the evolution of biological species, we might instead use asset classes, institutions, sovereign states, or industries as the elements of the system that we wish to simulate. Alternatively, we might use more granular elements that represent individual securities, trading desks, or risk factors. Associations might be abstracted in a manner appropriate to the system under consideration. For example, in a financial network, a trader in Singapore who hedges interest-rate exposure with Eurodollar futures on the Chicago Mercantile Exchange might be considered a near neighbor of another trader who is doing the same thing with an interest rate swaps position in London. Or, they might be indirectly connected by a third trader who arbitrages Eurodollar futures in Chicago against Euribor futures in London. Systems modeling can assist in simulating the effect of structural changes as well. For example, the effect of new rules with an increased command structure on the ability of the financial system to self-organize might be determined to be critically important, futile, or disastrously harmful. In the financial markets, we can imagine an external driver such as a news release or an asset reallocation by a large fund manager triggering communication throughout the financial system. If, say, PIMCO decides to move a substantial portion of its portfolios out of equities and into bonds, this information will race through the financial network at lightning pace: initially in the transactions space, while PIMCO is able to keep its intent secret, and later via social networks as its strategy is revealed or surmised.
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Such communication can be seen to move across system dimensions as well. For example, one might characterize the dimensions of a global capital markets model as asset classes or types of instruments. Specific intelligence regarding the stocks that PIMCO is selling and the bonds that it is buying might leap from an equity dimension and a bond dimension to a volatility-dependent derivatives dimension orthogonal to the other two. On a darker note, more extreme events, such as the failures of Lehman Brothers and Bear Stearns, might trigger a less orderly reorganization and precipitate a new state that is very different from the previous one. It might take a correspondingly long time to achieve self-organized criticality, especially since interventions taken by regulators and policy makers will interfere (for good or ill) with the natural evolution of the system. We have some empirical evidence of self-organizing behavior in the form of patterns in price behavior. For example, if we use a mathematical simulation to model interactions between the prices of various securities (or even a single security perturbed by external forces and internal dependencies), it should be intuitively obvious that clustering behavior may manifest itself in the form of serial correlation.10 Such correlation, if it continues over time, will reveal itself in classic chart formations such as trends and trading ranges. It can also lead to volatility clusters observed in nearly all price series, in which anomalous periods of high volatility tend to occur at random intervals. For example, consider the six-month price history of spot gold ending November 25, 2009, as shown in Figure 5-2. Note that prices rose
+15.98% (+546.22%ann.) 1192.40 Last Price High on 11/26/09 1192.40 995.59 Average Low on 07/08/09 909.50
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Figure 5-2 Daily Prices of Spot Gold, May 25, 2009, to November 25, 2009 Source: Bloomberg, L.P.
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15.98 percent during the last four weeks of this period, more than doubling the gains of the previous five months. Although the price of gold in U.S. dollars had been slowly rising because of dollar weakness and fears of systemic failure, the purchase by the Reserve Bank of India of 200 tons of gold from the International Monetary Fund on November 2, 2009, triggered substantial new buying. (At the end date of the chart, rumors abounded that India would purchase another 200 tons.) This significant event touched off a pattern in which successive price movements were highly correlated and a strongly monotonic pattern of price movement was created. During those last 20 trading days, prices fell on only 20 percent of the 20 trading days, and there were no two successive down days. THE GLOBAL CAPITAL MARKETS: STABLE OR CHAOTIC? In practice, it’s difficult to determine conclusively whether a system on the scale of the global capital markets is random or deterministic, stable or chaotic. The traditional method for differentiating random and deterministic systems is to identify similar states that occurred over time and establish whether they evolved in an essentially similar manner. For example, in the simple physical system of a pendulum, the movement over time starting with the peak of the swing always progresses in a predictable manner. However, there will always be some uncertainty in the analysis because few real-life problems consist of pure signal. Instead, they usually include random noise that complicates the identification problem. Characterization of the system perhaps best flows from examination of the physics of the system, that is, whether the system has the characteristics that permit self-organization, to discovering to what extent the system is deterministic and the level of complexity of those interactions. In a forward-looking systems design, intuition and expert knowledge may be a better guide than historical behavior in specifying the nature and vulnerability of a system. For example, Nouriel Roubini proved prescient in his analysis of how the dominoes might fall. As related by the New York Times on August 15, 2008, On Sept. 7, 2006, Nouriel Roubini, an economics professor at New York University, stood before an audience of economists at the International Monetary Fund and announced that a crisis was brewing. In the coming months and years, he warned, the United States was likely to face a once-ina-lifetime housing bust, an oil shock, sharply declining consumer confidence and, ultimately, a deep recession. He laid out a bleak sequence of
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events: homeowners defaulting on mortgages, trillions of dollars of mortgage-backed securities unraveling worldwide and the global financial system shuddering to a halt. These developments, he went on, could cripple or destroy hedge funds, investment banks and other major financial institutions like Fannie Mae and Freddie Mac.11
Three years later, Joseph Stiglitz, who won the Nobel Prize in Economics in 2001 for his analyses of markets with asymmetric information, warned, “Structurally, things are worse [now than they were last year],” in discussing the treatment of “too big to fail” institutions. This statement, made at the end of September 2009, was in direct contradiction to market behavior and sentiment, both of which seemingly indicated a return to normality. Whether or not a system is stable can best be determined using expert knowledge regarding its drivers, rather than from any stochastic metrics (although the later can provide contrary evidence). SUMMARY In this chapter, we discussed the need for a systems approach to modeling the behavior of large-scale systems such as the global capital markets. We defined various types of systems, such as complex, chaotic, and dynamic, and the process by which complex systems might evolve over time in response to endogenous or exogenous shocks. We illustrated the usefulness of using mathematical simulations to identify emergent behavior of the system that is unknowable from an analysis of its component elements and interconnections. We further posited that the global financial system is a form of a complex adaptive system called a self-organizing system, with all the attendant implications for risk and risk management. WHAT’S NEXT This chapter presages a discussion of agent-based approaches, in which the necessarily uncomplicated rules of the Bak-Sneppen model are replaced by rules that simulate the behavior of agents with more advanced cognitive and decision-making abilities. In the next chapter, we will discuss systemic risk in the global capital markets more specifically.
CHAPTER 6
Belief Systems and the Inadvertent Conspiracy: The Global Capital Markets as System
BELIEF SYSTEMS AND WORLDVIEWS For all the advanced mathematics and technology used by the global financial community, there is still a large subjective element and belief system underlying this quantitative world. A worldview is a set of beliefs that influences how an individual interprets the world and interacts with it. However, as in a Bayesian framework, prior beliefs become posterior beliefs as the individuals who make up the world markets are informed by new events or advances in theory. A scientific belief system is based on observation and reason, but in this age of specialization, a market participant may participate in an inadvertent conspiracy by making decisions based on an incomplete worldview. If such a worldview is widely held, it may artificially promote stability (at least temporarily) through a self-fulfilling prophecy. For example, common belief in the concept of “too big to fail” may have induced financial institutions to take too much credit risk, while common use of stochastic models might have disguised the true risk and encouraged risk-taking behavior. However, if faith in this belief is broken, the consequences can be dire. Systemic risk is as much affected by our worldview as it is by more fundamental forces. So, better awareness of the drivers of systemic risk can enhance decision making and assist in reducing this greatest source of risk. A SYSTEMS VIEWPOINT OF SYSTEMIC RISK The financial crisis of 2007–2008 made the term systemic risk nearly a household term. In finance, systemic risk (not to be confused with systematic risk) is the risk of failure of the entire banking or market system. As 81
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defined by Tom Daula, the chief risk officer of Morgan Stanley, systemic risk is “financial system instability, potentially catastrophic, caused or exacerbated by idiosyncratic events or conditions in financial intermediaries. It is the risk that the financial system fails. It is not the risk that a financial institution fails provided that failure does not result in system instability.”1 In the context of the previous chapter, we might alternatively define systemic risk as the risk that a complex, adaptive, self-organizing system rapidly and unexpectedly evolves to an undesirable state. Depending on the path such a reorganization takes, this new state might be an inferior version of the current state, or it might instead be something entirely new and different. Thus, the choice of an appropriate risk management framework is critical. Economic and financial systems are so complex that a systems approach is required to properly assist decision makers in preventing or mitigating the most adverse outcomes. THE GLOBAL CAPITAL MARKETS AS SYSTEM The first step in creating a conceptual model of any system is defining its boundaries. Although the global economic, financial, and geopolitical systems interact in a number of important ways, they can be differentiated based on the nature of their internal relationships. For example, the relationships between interest rates in different sovereign states in a market system are very different from the laws of supply and demand in a macroeconomic system. Figure 6-1 shows one worldview in which the world economy is portrayed as a complex system consisting of dynamically interacting subsystems, such as national economies, markets, industries, and companies. Even related subsystems may be differentiated on the basis of how freely information can be transmitted across the subsystem (thus facilitating self-organization). For example, one major fund manager recently described the pipeline between the market system and the economic system as clogged because of a dearth of lending. Therefore, drawing a boundary around the markets as a distinct system is reasonable, because the market transactions whose effects flow from one end of the globe to the other in near real time are fundamentally different from the forces of supply and demand that drive economies or the geopolitical forces that drive nations. THE ROLE OF HUMAN DECISION MAKING Any market system is nothing more that the aggregate of all its participants, acting according to their knowledge, biases, preferences, and resources.
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etc NATIONAL ECONOMIES Macroeconomic Data>
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Figure 6-1 Systems Representation of World Economy Source: Quantum 4D, Inc.
The price of a security moves only when a human being (acting either directly or via automated agents) bids for or offers a security. With an economic microscope, we might be able to identify the market drivers for each price as a combination of rational and irrational drivers. At their most granular level, market prices are deterministic; they are completely determined by human actors, acting under external or internal influences. Some of these external influences are incentive-created and imposed by regulators (e.g., to minimize capital usage), while others are internal and a product of rational or irrational bias. If we knew everything there is to know about the fundamental drivers of every security, the rules under which every automated trading system operated, the identity of all market participants, and their exact positions, their capital, their risk limits, their preferences, and even the state of their psyches, we might be able to estimate the new price of every security in response to an external event.
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CHARACTERIZING THE MARKET SYSTEM In the previous chapter, we described various attributes that might characterize a large-scale system such as that of the global markets (e.g., dynamic, complex, or adaptive) and discussed the difficulty of identifying them conclusively. Nevertheless, such an attempt is useful, because it has implications with respect to our ability to predict an imminent shock, prevent it, or mitigate its damage after it has occurred. As Bak and Sneppen demonstrated, it is possible that even very simple interactions in a complex system may lead to emergent behavior and high-consequence events. In the following sections, we will define the criteria for a complex, adaptive, self-organizing system, and provide evidence that the global market system meets these criteria. The Global Markets as a Complex, Adaptive, Self-Organizing System We might consider the global financial markets to be one distinct system, distinguishable from the broader economic system. (These financial markets specifically include equity, fixed-income, interest rate, commodity, energy, and foreign exchange markets in any form or venue.) Depending on how we characterize this market system, the implications with respect to systemic risk might be profound. In brief, the system appears to meet four principal criteria for a complex, adaptive, selforganizing system: • It lacks external control. There is no central command for the global financial markets. Although individual state actors or groups acting in concert attempt to exert control to various degrees via legal and regulatory authority or more heavy-handed means, they have limited ability to force a desirable outcome. • It possesses mechanisms for self-organization. Global financial markets can be well represented by a complex network of elements and links, both literal and abstract. Exchange and over-the-counter trading venues provide mechanisms by which pricing, news, and transactional information are transmitted both locally and globally. Each firm is linked to every other firm through trading relationships, either directly or via exchanges. • It involves complex dynamics. Many of the securities traded have complex structures, as well as nonlinear relationships with related securities. And behavioral effects such as changing appetites for risk contribute additional complex dynamics, initiated as they are by the humans that ultimately make up the system.
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• Its evolutionary path is uncertain. The critical state to which the market system is evolving is difficult to anticipate, and this may lead to surprising and high-consequence events. We can observe this empirically in the form of a number of unanticipated market shocks in recent years, theoretically in the degree of difficulty involved in making accurate market predictions, and statistically in the presence of market features such as fat-tailed distributions and jump-diffusion processes for prices and market volatility. Self-Organization in Markets The global markets are a self-organizing system, that is, a dynamic system that, even in the absence of a designing intelligence, is capable of evolving from chaos (say, after an exogenous market shock) and forming a new structure with a higher level of organization. However, this is not to say that this new structure will necessarily please market participants, nor does it imply that such reorganization will not leave casualties. Examples of self-organization are abundant in every discipline. For example, a bee colony is a biological example of a self-organizing system. Similarly, so-called language death, in which a minor language is assimilated into that of a nearby neighbor, is a sociological example. In both cases, small interactions at a highly granular level eventually cause the system to attain a new and superior state (e.g., the bee colony survives; more people are able to communicate). In The Wealth of Nations, Adam Smith described this self-organizing property as the “invisible hand” that regulates economic systems. He posited that the forces of supply and demand, facilitated by competition and motivated by self-interest, would find their own equilibrium if they were unconstrained by government interference or other intervening constraints. However, Standard Oil—the horizontal monopoly created by John D. Rockefeller in the late nineteenth century—provides anecdotal evidence that, at least for a time, such equilibrium might be most unpleasant. In the language of systems analysis, Smith’s statement is an early characterization of a self-organized system in which millions of small transactions (e.g., choices of one product over another by individual consumers) promote price efficiency throughout the economy. However, the idea of an invisible hand is somewhat of a misnomer, in that it implies that some larger, controlling force is managing system evolution. Instead, such evolution is driven by small interactions at a local level that roll up into systemic change.
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At a microscopic level, we might consider the global capital markets to be a deterministic system. If we were able to specify the cascade of consequences of each market driver (including behavioral considerations, such as biases and preferences) down to the level of each individual decision maker, we might be able to create a massively complex model of market behavior. Although this is nearly as impossible as modeling the movements of molecules in a container of gas, market behavior is nevertheless sufficiently deterministic to enable us to assume that markets are capable of adaptive behavior that is somewhat predictable. CONNECTIVITY, COMMUNICATION, AND CONTAGION Today, the global market system possesses one of the most critical characteristics of a self-organizing system; that is, it allows information to flow freely between distinct elements. Such connectivity transforms the behavior of diverse, isolated actors into the fundamentally different behavior of a system, with all its attendant uncertainty. Connectivity has increased dramatically in recent years. Years ago, Russia and China were minor players in the global capital markets. Today, a trader can monitor Turkish derivatives or view his Bloomberg screen in Russian. Traders can trade anything, anywhere, any time. The formerly isolated are now enthusiastic participants and agents for interconnectivity. And even the most isolated state actors, such as North Korea, are economically vulnerable to local and global supply chains, and financially and politically vulnerable to the price of commodities, such as the uranium required for the development of nuclear capabilities. The primary mechanism for connectivity in the global financial system is the transaction. Although traders have social networks and common information services in abundance, transactions are the message packets between elements of the system. Even if each transaction is executed locally, arbitrageurs assist in transmitting such information across products, asset classes, and geospatial dimensions in real time, thus facilitating global synchronization and calibration. And these messages are credible; actions speak louder than words. Specific activities such as real-time algorithmic trading, location arbitrage,2 and the use of common information services result in the nearly instantaneous transmission of information across the globe and force synchronization and calibration within the system’s boundaries. For example, if an over-the-counter derivatives trade is executed in Shenzhen, its interest-rate sensitivity may be hedged on the Chicago Board of Trade
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(CBOT) in note futures or their options. And, since the CBOT’s prices are completely transparent (both on trading screens and via automated execution systems), any resultant shift in rates or implied volatility is apparent worldwide. Consistent with both the efficient market hypothesis (EMH), which postulates that the market price of any security reflects all information known about that security at a particular point in time, and the principles of behavioral finance, each transaction reveals information about both expectations and preferences. For example, each options trade contains the trader’s expectations about how far and how fast a price might move by the expiration date of the option, as well as his degree of uncertainty and discomfort about the outcome. Although EMH has fallen into some disrepute recently, it is nevertheless true that a new transaction reflects a new opinion about the value of a security. Reverse-engineering a change in consensus opinion as reflected in market price often provides more credible information than all the research reports in the world. The same structure that allows efficiency also creates vulnerability. Such high-speed communication across the system can either promote stability or provoke turmoil. When it serves to increase global liquidity, this is called efficiency. When it forces a cascade of adverse reactions, this is called contagion. Recall that macro shocks affect all markets and economies directly, whereas micro shocks permeate throughout the entire system via a process of contagion. While an unconnected system is vulnerable to macro shocks, a highly connected system is also vulnerable to micro shocks, thus increasing systemic risk. There are few obstructed paths throughout the global markets, and as long as information can find a path, it will affect the system’s evolution. COMPLEX MARKET DYNAMICS We can infer that market dynamics are complex, not only from direct knowledge of the codependence of various market elements, but also from empirical observation of patterns in market price movements. There are abundant examples of complex rules of interaction between asset classes and securities based on economic or financial fundamentals. Such rules may be nonlinear, may apply only within a certain range, or may depend on several variables. Consider an economic example: the interaction between corn prices and energy prices. Corn and energy may have a direct relationship
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only at prices at which one can compete with the other—that is, only when natural gas prices are sufficiently high (or corn prices sufficiently low) that ethanol can be produced at a cost competitive with that of natural gas. Thus, corn prices can have a complex direct relationship with the price of energy. And these direct relationships can, in turn, create indirect relationships between the causal parents of corn (e.g., weather) and the causal children of energy (e.g., airlines). Consider also a financial example: the interaction between margining rules and trading activity. Rules designed to limit risk may sometimes exacerbate it instead. Sophisticated risk management protocols can, paradoxically, precipitate a chain reaction of buying or selling that increases potential loss, when risk measures used to define traders’ position limits are a function of market behavior. Besides such fundamental economic and financial evidence, we can also observe empirical evidence of complexity. If we examine the probability distribution of historical returns in almost any security or commodity, we can observe evidence of leptokurtosis (i.e., a distribution with a more acute peak at its mean and fatter tails). Such a distribution provides some evidence of nonrandom, complex behavior, because one might infer that there are mechanisms that generate both positive and negative feedback, leading to higher probabilities of insignificant moves as well as extreme moves. Furthermore, if we examine time series of historical volatility, we can observe volatility clustering, in which periods of high volatility are interspersed with periods of normal volatility. Such patterns are again consistent with nonnormal drivers and complex behavior. Markets and Memory Recall that some of the intellectual foundations of current mathematical finance depend on the assumption that the price-generation process is a memoryless one (i.e., it follows a Markov process). If this assumption is not correct, then the stochastic methods that are so widely used may be based on an invalid worldview. It is reasonable to believe that market and economic systems will exhibit hysteresis (i.e., memory), if only because any market or economic system is nothing more than the sum of its participants, with all their fear and greed, with their history of failures and successes, and with their risk preferences and cognitive biases. Thus, to the extent that human biases and preferences are a driver of market prices, the markets possess memory. For example, traders’ compensation structures are an oft-cited contributor to excessive risk taking.
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Proprietary traders at investment banks are paid an annual bonus based on their performance, and this bonus is generally the lion’s share of their income. Hedge fund managers are paid based on performance as well, generally according to the “two and twenty” rule—that is, a 2 percent annual management fee and 20 percent of earnings, subject to high-watermark rules.3 So, a trader’s personal utility function at any point in time is driven by both his performance and the calendar: if the trader has generated a substantial profit year-to-date and it is now November, he is risking his own money with every trade—a far different value proposition from that in January. Although behavioral effects are often thought of as being suboptimal at best and irrational at worst, such mechanisms may drive exceedingly rational decision making that is not immediately obvious. Memory is present in a more subtle way as well, even for algorithmic traders who design completely emotionless and automated trading strategies. Because their quantitative models are informed by historical data (for example, in calculating market volatility or in setting trading limits), the models, too, have a memory. The Role of Self-Fulfilling Prophesies The inadvertent conspiracy rests on two common beliefs: 1. There are “best practice” models for the valuation of complex derivative instruments that rely on calibration to current market prices to obtain input parameters (e.g., volatility surfaces). 2. If a technique has been making money consistently in the past, it must be based on a model that correctly reflects reality. To some extent, such common beliefs lead to self-fulfilling prophecies that increase causal capacity (the ability to make choices that change the system) and the corresponding magnitude of potential change, while simultaneously decreasing the perception of systemic risk. As a case in point, economist Burton Malkiel recently described some of the conditions that let to the credit crisis: During the 20th century, banks made mortgage loans to individual homeowners and then kept these loans as assets on their balance sheets until they were repaid. This system was known as the originate-and-hold model. That system changed, however, during the 2000s to an originate-and-distribute model. Banks continued to originate mortgage loans (as well as other kinds of loans) but held them only briefly until they could be sold to an investment banking institution, which packaged the mortgages into mortgagebacked securities.4
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Malkiel went on to describe the successive repackaging of different elements of risk (e.g., slicing mortgage-backed securities into tranches with various claims on principal and interest, and credit default swaps that bifurcated credit risk from interest-rate risk). “Through this system, by a kind of alchemy, investment banks produced very highly rated securities on the senior tranches, even though the underlying mortgages might be of relatively low quality or subprime.” Malkiel noted how such a system led to a deterioration in lending standards and the subsequent chain of consequences. But there’s another lesson in this story, as well: this narration also shows a huge increase in systemic risk facilitated by the common use of best-practice valuation models and this inadvertent conspiracy. No investment bank would have commenced the origination and repackaging process unless it was confident of how the marketplace would price the newly created derivative securities days or weeks hence. Yet More Complexity: Human Preferences and Biases Complexity is further exacerbated by behavioral effects, since any market is, ultimately, composed of humans, with their biases, preferences, and sometimes flawed decision-making abilities. The shifting balance between fear and greed causes human biases to be a major driver of change, as evidenced by the existence of sentiment indexes. The market system can be driven by both macro and micro shocks. We have evidence from the field of behavioral finance that risk preferences can sometimes be irrational and complex. Recall that the efficient market hypothesis implies that charting can provide no insights. However, virtually every trader in the world relies on the use of charts. Chart formations may be an indicator of a change in sentiment, with all its market consequences. For example, a support level might indicate the lowest price at which new positions were initiated, and the psychological effect of crossing the boundary from winner to loser (if only by pennies) might affect human behavior. Such emotional dynamics can shift suddenly, as well; there is reason to believe that overconfidence or faith in models, strategies, and government may allow a system to exist in equilibrium for too long (negative feedback), while a corresponding loss of faith and resultant panic may cause the system to jump to a new state (positive feedback). In 1936, John Maynard Keynes used the term animal spirits to refer to human emotions such as confidence that are sufficiently important to be able to generate boom-and-bust cycles rather than just a series of small corrections to a stable system. Far more recently, Yale Professor
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Robert Shiller has coined the terms virtuous cycle and vicious cycle to describe different types of feedback mechanisms. The question may not be, “What causes market shocks?” so much as, “Why is the market stable for prolonged periods of time?”
ROBUSTNESS AND FRAGILITY IN COMPLEX SYSTEMS It’s difficult to predict the evolution of any system under the best of conditions, but the most dangerous system is one that is both opaque and resilient. An outside observer who is unaware of the system’s internal dynamics might be led to a false sense of security regarding the system’s stability. As in the case of a sleeping volcano, it’s difficult to infer from historical metrics alone that a system is stable. Extreme risk comes from not knowing what the system is doing and not knowing how it is changing. The system may have complex interdependencies that cannot be reverse-engineered from outcomes. They may not even be synchronized in time; for example, the elements of a feedback loop might be displaced in time and amplified by the intervening dynamics. And the more complex the dynamics, the more difficult it is to predict outcomes. For example, we might posit that a market system exhibits highly optimized tolerance (HOT) rather than mere self-organized criticality (SOC) because its behavior is expected to be both robust and fragile. The bimodal behavior of some markets—that is, either quiet or volatile— is evidence of both robustness and fragility. (Two examples of such behavior are electricity prices as shown in Figure 4-4 and credit spreads as shown in Figure 3-2.) Paradoxically, the ability of the system to evolve to a significantly different state via a chain of causal consequences might increase while apparent systemic risk appears to decrease. For example, this might occur when open interest in OTC credit default swaps increases, but only because the arbitrage activities of new market participants are reducing market spreads and instrument volatility as they compete for return and push the efficient frontier to less advantageous levels. If it is valid, the HOT hypothesis has far-reaching implications. Traditional indicators of systemic risk, such as volatility and interest rates, may provide little warning of a jump from a normal to a high-risk regime. The hypothesis has policy implications, as well. Perhaps the most effective action that a systemic risk regulator might take should be to ensure that there is sufficient slack in the system to reduce its fragility.
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Traditionally, such slack is imposed at the enterprise level (i.e., by imposing higher regulatory capital requirements). However, like portfolio risk, system tolerance is not the sum of the tolerances of its component elements but depends on their interactions. So, next-generation regulatory requirements might impose new or different constraints, particularly those, such as liquidity requirements, that are related to interdependencies with other enterprises. THE ILLUSION OF CONTROL The magnitude of systemic risk depends on the elements and interconnections of the specific system. Just as in the Bak-Sneppen evolutionary model, the failure of even a single entity may infect a cluster of entities to which it’s linked, triggering a cascade of adverse consequences. Thus, any entity that is either “too big to fail” or “too connected to fail” puts the entire system at substantial risk. A fundamental question remains: how can a self-aware node of a complex system save itself from such systemic risk? With the benefit of systems thinking, an individual enterprise might be able to reduce its exposure in a number of ways. Once some causal cascade has commenced, it might be better able to determine the effectiveness of certain risk mitigation actions along the path. It might dynamically change its risk profile even during an apparently stable period, depending on its estimate of the system’s causal capacity. And it might identify indications and warnings of a structural break and a potential shift to a new risk regime in time to benefit relative to its competitors. However, even the most sophisticated financial institution will not be privy to all the information that might be required in order to properly estimate systemic risk and to protect itself fully—at least while remaining competitive during stable periods. The most accurate and most robust models may require a much higher level of transparency (e.g., details of counterparty and other credit exposure) that might be available only to a regulator. Instead, such an institution might engage with policy makers on improved methods for measuring and managing systemic risk, and specifically include in the discussion interaction with other systems (e.g., geopolitical). Ideally, such methods will acknowledge the selforganizing nature of global markets and reject a command-and-control philosophy.
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SUMMARY The global capital markets make up a distinct system, separate from global economic systems or geopolitical systems. A market system has many of the characteristics required for a complex, adaptive system: interrelations between its elements are instant, nonlinear, and at least somewhat deterministic and predictable. The market system lacks a command-and-control structure, possesses mechanisms for self-organization, involves complex dynamics, and has an uncertain evolutionary path. Because humans are involved, the interrelations are especially complex in that they include both behavioral effects and changing risk preferences. The market system is both robust and fragile, but it is exceedingly difficult to identify the potential for structural breaks or to measure systemic risk from observational metrics alone. WHAT’S NEXT In the next chapter, we discuss the topic of analytic tradecraft and its application to the broader topic of the design of objective models that are less vulnerable to cognitive bias, groupthink, or a flawed worldview.
CHAPTER 7
Analytic Tradecraft and Model Risk
INTRODUCTION The most insidious type of risk to which any complex enterprise is exposed is model risk, or the risk that a model used to inform critical decision making is incorrectly specified or erroneously applied.1 This is so because the decision makers who are consumers of risk analyses are often unaware of the degree of uncertainty surrounding any assessment and of the sensitivity of the optimal decision to model risk. Model risk is a meta-risk that affects the measurement and mitigation of every type of risk. In both the intelligence and financial communities, the consequences of failure to acknowledge and deal with model risk can be catastrophic. If an analytic model fails to represent reality adequately, plausible future scenarios with highly adverse outcomes may not be identified. Failure to identify a risk means failure to mitigate it. Both qualitative analysis and quantitative analysis are subject to model risk, although the sources of such risk may be different. For example, in the financial community, with its highly mathematical models, the source of model risk may be the uncertainty associated with model parameters such as mean and standard deviation or with dependence on key assumptions about price behavior over time, such as a mean-reversion process. Conversely, in the intelligence community, with its greater dependence on qualitative models, the source of model risk may be human failings. Such failings may include the analysts’ own cognitive biases or even secondhand biases such as a field collector’s misinterpretation of information. Thus, creating a model of reality, no matter how quantitatively that model is expressed, involves both art and science. Art is present in the choices made by the analyst in constructing her view of reality for the problem at hand, and science is present in the manner in which the model is quantified. The financial analyst and the intelligence analyst must each be aware of the process of model building, using a structured 94
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approach that serves to minimize model risk while ensuring that the model will serve the purpose for which it’s intended.
ANALYTIC TRADECRAFT In the intelligence community (IC), the best analysts are intensely aware of their vulnerability to model risk and apply structured approaches to analysis to minimize model risk. The community is starting to place a high premium on the value of critical thinking skills toward this end and includes them as an element of tradecraft. Tradecraft is the term applied to the collective skills required in the field of intelligence. Analytic tradecraft is used to refer to the set of skills required for intelligence analysis as opposed to intelligence gathering. Such a structured approach is necessary for making sense of information from diverse sources. Such sources range from the highly qualitative and untrustworthy to the highly quantitative and trustworthy. For example, human intelligence (HUMINT), or intelligence gathered from human sources, is an example of the former, whereas signals intelligence (SIGINT) and image intelligence (IMINT), both of which are types of intelligence gathered via mechanical means such as satellites, are examples of the latter. An intelligence analyst’s model of reality may therefore range from completely subjective and informed only by the creativity, imagination, and expert knowledge of the analyst to completely objective and informed by highly reliable and quantitative data. In either case, the analyst’s task is often hampered by missing data; he is used to information gaps, including “known unknowns” and even “unknown unknowns.” Thus, the community places great emphasis on the use of all available data sources—including both confidential information and open-source intelligence (OSINT)— because one source or another may either fill in those gaps or confirm information that is of uncertain reliability. The use of such “all-source intelligence” serves to minimize model risk. When information is gathered from diverse and orthogonal sources, the fusion of that information may validate or invalidate hypotheses or conclusions and allow a higher degree of confidence in conclusions. Nevertheless, good information alone doesn’t guarantee good models. Models created by intelligence analysts—whether they are used to forecast possible future states or to provide a theory that explains certain observations—are still vulnerable to the quality of the analytic process itself. Although there are statistical methods for measuring the uncertainty
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associated with hard data, the intelligence community must depend on control of the analytic process itself to minimize model risk. CRITICAL THINKING IN THE INTELLIGENCE COMMUNITY Control is achieved via the use of techniques for performing structured analysis. The principles of these techniques mirror the scientific method used by researchers in other disciplines and are taught to analysts joining the intelligence community. For example, “Analysis 101” is a course that provides new analysts with intensive training in such methods. This training was initially sponsored by the Directorate of National Intelligence (DNI) to provide new analysts with the skills necessary to meet the IC Analytic Standards as defined by the DNI’s Office of Analytic Integrity and Standards (see Table 7-1). As any financial analyst will immediately observe, these standards are oriented toward far less quantitative assessments than those that are typical in the financial space. Intelligence analysts operate under far greater uncertainty than do financial analysts. They are often required to T A B L E 7-1
IC Analytic Standards and Standards of Analytic Tradecraft
IC Analytical Standards 1. 2. 3. 4. 5.
Objectivity Independent of political considerations Timeliness Based on all available sources of intelligence Exhibits proper standards of analytic tradecraft Standards of Analytic Tradecraft
1. Properly describes quality and reliability of sources 2. Properly caveats and expresses uncertainties or confidence in analytical judgments 3. Incorporates alternative analysis where appropriate 4. Relevance to U.S. national security 5. Logical argumentation 6. Consistency, or highlights change 7. Accurate judgments, assessments* * Assessment is the preferred term within the intelligence community for the results of an analysis.
Source: For more information, see www.dni.gov/content/AT/Analytic_Standards.pdf
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make a forecast or provide an assessment based on only spotty information of unreliable origin. Unlike a financial analyst, they cannot rely on history for an estimate of the likelihood of extreme events, but must instead identify the most plausible scenarios and likely outcomes based on a fusion of facts, heuristics, and their own expert judgment. Although such analysts may use a variety of tools and technology to enhance their cognitive abilities, the quality of their results often depends on as much on their ability to enforce analytic rigor, proceed with their analysis in a structured manner, and avoid certain cognitive pitfalls as it does on data and subject matter expertise. As cognitive and computer science advance, the intelligence analysis process can and will be become more quantitative. The increasing use of mathematically rigorous models that can explicitly capture and correct for human biases and preferences will improve the ability to make probabilistic predictions. MODELS AND METHODS The models, methods, and tools used by the intelligence community are those that facilitate critical thinking and a structured approach toward analysis. For example, analysts make great use of visualization and link analysis tools to assist them in their sensemaking efforts. Such tools, which create a graphic representation of how the nodes in a network are related, are also heavily used by the law enforcement community to identify patterns best recognized by humans. Similarly, some intelligence analysts use a cognitive portal known as A-Space2 (Analytic Space), which creates a collaborative environment that facilitates information sharing and elicitation of diverse viewpoints. Nevertheless, analysts must be especially careful to avoid certain analytical pitfalls to which all humans are subject and must always think critically about the process of analysis instead of just the task at hand. THE ROLE OF CRITICAL THINKING In the intelligence community, critical thinking can be viewed as a type of quality control for analysts’ cognitive processes as they solve problems and reason to a conclusion. Because the ultimate purpose of analysis is to inform decision makers, both the quality of their decisions and their confidence in those decisions are driven by the quality of the analytical process and its ability to mirror reality accurately. Critical thinking ultimately requires the analyst to adhere to high standards of logic in which she conforms to universally accepted principles
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that allow reasoning beyond facts (i.e., making sound inferences). In the intelligence community, the criteria for critical thinking include clarity, accuracy, and logic. One key element of critical thinking is cohesiveness, which requires that the analysis include those and only those factors that are relevant to the problem at hand. The analyst’s representation of reality should include all relevant information, be sufficiently specific to support the reasoning process (whether human or machine-generated), and acknowledge any missing information that would benefit the analysis. These criteria are especially important in minimizing model risk, as they exclude irrelevant sources of uncertainty and specifically recognize incompleteness where it exists. MINDSETS AND BIASES All analysis that includes subjective elements is vulnerable to mindsets and cognitive biases. A mindset is a mental framework of rules, heuristics, beliefs, and experiences used by an individual to filter, organize, value, and interpret data that might be used to assess a risk or come to a conclusion. Mindsets are essentially mental shortcuts that often speed understanding. However, they may fail the analyst when experience is not a reliable guide or when aspects of the analysis are outside the analyst’s area of expertise. Mindsets can often be subconscious and therefore difficult to challenge or even recognize. They can also be a characteristic of an individual or of a governmental or private-sector institution and its internal culture, resulting in groupthink. Similarly, analysts and institutions may possess biases, that is, preferences for one thing over another. There are value-based biases, in which an analyst might filter data based on an illogical perception of value, and cognitive biases, in which an analyst might form faulty conclusions from available data based on how he processes information. Because so many modeling choices depend on cognitive skills and prior knowledge, they are vulnerable to both value-based and cognitive biases, against which every analyst must guard. For example, a financial analyst may exhibit a value-based bias by considering only statistical models, or an intelligence analyst working in relative isolation may exhibit cognitive bias by failing to identify risk factors that are outside of her experience. Historical experience alone may be of little use here, as enemies and competitors continue to change and refine their tactics, and the quality of results often depends on the creativity of subject matter experts.
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There are a number of different cognitive biases that can jeopardize the quality of the analytical process and decision makers’ confidence in its results. For example, humans often suffer from confirmation bias, or the tendency to value information that confirms their existing beliefs over information that contradicts those beliefs. Such a bias influences the type of data that is collected and narrows the range of competing hypotheses that might be considered. Similarly, a human might also suffer from random bias (also known as conspiracy bias), in which he sees patterns where none exist. In fact, a common phenomenon among new analysts in watch centers (that is, centers tasked with monitoring a particular threat) is the tendency to generate far too many false positives from the massive amount of information freshly available to them. The amount of cognitive bias may also be affected by the agency or corporate culture. Sometimes the reward system for analysts—particularly for financial analysts, whose models may be costly to implement—tends to discourage critical reexamination and instead rewards incremental improvements to existing models. Table 7-2 contains a partial list of cognitive biases that are common to both the intelligence and financial communities. There are a number of additional biases that are more specific to the intelligence community, such as a bias in favor of confidential information and information gathered using covert methods over open-source information or information that is publicly available. T A B L E 7-2
Common Cognitive Biases
Bias
Description
Impact on Analysis
Mitigation Method
Confirmation bias
The tendency to value information that confirms existing beliefs over information that contradicts those beliefs.
This bias may cause the analyst to ignore relevant data or narrow the range of possible hypotheses considered.
Continuously reexamine competing hypotheses, seeking to disprove even those hypotheses that have been previously accepted, and freshly reranking competing hypotheses. (Continued )
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T A B L E 7-2
(Continued)
Bias
Description
Impact on Analysis
Mitigation Method
Anchoring bias
The tendency to value initial information over subsequent information.
The order in which information is assimilated into a conceptual model affects its development.
Reorganize the data set as new information is acquired, and reconsider the problem.
Random bias
The tendency to believe that coincident events must be related rather than accepting the possibility that such a pattern may be random.
This bias may generate false assumptions about causation or overestimate the likelihood of certain events.
Consider chance as a possible explanation, and apply mathematical rigor to prove or disprove a relationship between the events. Explicitly model causality where appropriate rather than depending on correlation.
Availability bias
The tendency to value information that is more readily available, either in human memory or from readily accessible sources of quantitative data.
This bias overweights the impact of readily available data or data that are within the analyst’s area of subject matter expertise and underweights the impact of potentially important but difficult to obtain data.
Objectively determine the data required for the analysis rather than working forward from the available data. Specifically acknowledge the importance of unknowns.
Framing bias
The tendency to present information in a format designed to elicit a specific response or decision.
This bias causes an analyst to skew the results to produce a particular decision.
Maintain objectivity and neutrality, and create a culture within the enterprise that rewards self-criticism.
Statistical bias
The tendency to use statistics blindly and overweight their reliability.
This bias creates overconfidence in results and may cause decision makers to make nonoptimal choices.
Question the basic assumptions on which statistical parameters are based as well as those of the methods used to generate them.
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STRUCTURED ANALYSIS AND THE CONCEPTUAL MODEL An analyst can help ensure the creation of a complete and cohesive model through the use of structured analysis,3 a systematic method for building a conceptual model of reality. A conceptual model is a collection of knowledge and interdependencies used to represent the dynamics of a real-life situation. Such a model can be used forward or backward; that is, it can be used to identify plausible future scenarios or to explain observed events in terms of their root causes. Depending on the question to be answered, an analyst can employ one of two different approaches. Most often, the intelligence community uses hypothesis testing to answer limited questions or explain isolated incidents (e.g., a nuclear test by North Korea). Conversely, conceptual model creation is used to answer more complex questions or to assist with continuing efforts in which the inputs to the model may vary, but the question remains the same. Conceptual model creation is the more encompassing solution, as it involves building a highly structured and well-specified model of the relevant reality. However, constraints such as time and resources don’t always permit such an approach, especially when actionable intelligence is required. Therefore, hypothesis testing takes advantage of cognitive shortcuts and utilizes the creativity and intuition of the analyst to filter and rank competing hypotheses in a timely fashion. In both hypothesis testing and conceptual model development, the intelligence community promotes a structured approach that minimizes model risk caused by cognitive biases or other impediments to objectivity and completeness. At the start of the analytic process, the analyst should select the appropriate approach: hypothesis testing or conceptual model building. If the problem is sufficiently simple and straightforward, the analyst may choose to generate and test competing hypotheses. For example, if an analyst is asked a very specific question, such as, “How many nuclear weapons does North Korea have today?” such an approach might be used. If that analyst were instead asked to create a threat metric or warning system for the use of nuclear weapons by North Korea, then he might instead choose to build a conceptual model. In real life, an analyst may take advantage of both approaches. A need for critical but unavailable data is often a fact of life for an intelligence analyst. In building a conceptual model, the analyst may need to populate the model with a mixture of opinion and fact, substituting expert knowledge and informed guesses for hard data or deterministic relationships.
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STRUCTURING INFORMATION AND HYPOTHESIS GENERATION Before an analyst can generate competing hypotheses, she must structure the information in a manner that enhances cognition. Such structuring enables the use of link analysis and visualization tools, which facilitate the pattern recognition at which humans excel. It is meant to be thoughtprovoking in a way that unleashes the analyst’s creativity and expert knowledge. Some of the visualization techniques used by the intelligence community include the creation of timelines of chronological data, mapping of geospatial data, construction of link charts of associations based on any of a number of characteristics and attributes (e.g., network diagrams or concept maps), and diagramming a decision or process flow. Structuring Information The three steps in structuring information that precede hypothesis generation and testing are as follows: 1. Organizing information into useful sets. Generally, such sets have a hierarchical structure. In threat assessment, the categories might have an inheritance structure in which lowerlevel sets have the attributes of their parents. For example, when analyzing means of transportation, a Hummer inherits the qualities of its parent Motor Vehicles and its parent Transportation Vehicles, but it also has attributes and characteristics of its own. 2. Visualizing the information sets in order to obtain insights. The forms of such visualization may include displaying the information in temporal order, creating link-analysis graphs in which relationships between elements based on common attributes are displayed, and mapping the data into another form (e.g., geospatial). 3. Analyzing the nature of the relationships. The analyst may be able to detect relationships when data are properly organized and visualized or transformed into patterns, trends, and statistics. He may be able to distinguish causality from mere correlation and determine boundary conditions outside of which observed relationships may fail. The best analysts take advantage of several of these methods in order to search exhaustively for nonobvious relationships and eliminate spurious correlations. There are a number of commercial off-the-shelf tools that are used by the intelligence and financial communities for such purposes. Figure 7-1
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Figure 7-1 Sample Link Analysis of Corporate-Human Relationships Source: Quantum 4D, Inc., and Edgar
illustrates the use of one such visualization tool. In it, links between corporations on the basis of humans (e.g., common members of the board of directors) are shown. In counterterrorism efforts, such links might be based on personal relationships, phone communications, or monetary flows.4 One application of such link analysis is Non-Obvious Relationship Awareness (NORA),5 in which, for example, data are mined to identify persons who should be excluded from Las Vegas casinos based on their relationships. Generating Competing Hypotheses A hypothesis is a conjecture that is used either as an explanation of known facts or to predict an outcome based on those facts. Thus, hypothesis generation can be used as either a forensic tool or a forecasting tool. In the intelligence space, the analytic process is often one of identifying competing hypotheses and, by a logical process of elimination and evaluation, identifying the most likely one. In the financial space, the task may be far broader and require the analyst to identify a conceptual model of the global capital markets and their most important drivers and interactions. Unless analytic rigor controls this process, hypothesis generation can lead to model error. If left to their own devices, humans may generate the set of competing hypotheses in a nonsystematic fashion based on their
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own experiences. They may, therefore, be vulnerable to the limitations of their own knowledge, mindsets, and cognitive biases. They may miss scenarios that are outside their experience or that have never before occurred. For example, analysts might have missed the September 11 scenario in which terrorists hijacked planes and used them as weapons because the purpose of nearly all previous hijackings was to obtain leverage in hostage negotiations. TESTING AND REFINING HYPOTHESES To be truly useful in identifying sources of extreme risk in either the intelligence space or the financial space, an analyst should ideally create every plausible scenario of interest, using manual or automated means. Then each scenario can be evaluated for its likelihood and consequences, and solutions that might block or mitigate the worst outcomes can be identified. The process of refining a hypothesis involves specifying the necessary and sufficient conditions for the hypothesis to be valid and the necessary implications if it is. A necessary condition is something that must occur or be true. For example, if the trial hypothesis is that Iran has a nuclear weapon, a necessary condition for this hypothesis is that Iran possesses weapons-grade fissionable material. A sufficient condition is something that must occur or be true if the condition is valid. For the same hypothesis, if Iran can be shown to be successfully enriching U-238, that information is sufficient to assume that it possesses that weapons-grade fissionable material. A necessary implication is something that must occur if the hypothesis is valid. For example, if Iran has a nuclear weapon, it must be storing and securing the weapon—at least if it is operating in accordance with Western standards. The logical rigor and completeness required to test hypotheses can be achieved by the use of a decision tree (also known as a hypothesis tree). A decision tree is a decision support tool that is most commonly used to identify the decisions that are most likely to result in a desired outcome or as a method for estimating conditional probabilities for all possible outcomes. The nodes and branches of the decision tree are populated via a process of tightly controlled questions regarding conditions and implications. The two most basic questions that guide such an inquiry are, “For this hypothesis to be valid, what must be true?” and “If this hypothesis is valid, what do I then expect to be true?”
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Status of Missing Person
Dead Murder
Suicide
Accident
Alive Natural
Kidnap
Runaway
Lost
Figure 7-2 Decision Tree for Status of Missing Person
Each level of each branch of the decision tree must be mutually exclusive, and the levels must be collectively exhaustive. The branches generally start with the broadest attributes that differentiate the hypotheses and branch into more specific attributes that help refine the hypotheses. Figure 7-2 displays a simple decision tree in which every logical branch of a search for a missing person is included. Although this decision tree attaches no probabilities to each branch and contains no outcomes that depend on chance, the tree could certainly be formulated to do both, for example, on the basis of historical experience that is based on the characteristics of the missing person.6 Financial engineers will be familiar with one version of a decision tree: the binomial tree used to price American-style options, which can be exercised at any time. At each step in the tree, the binomial model simulates rational action by the owner of the option—that is, continue to hold the option or exercise it, whichever maximizes expected profit. The quality of the decision tree depends in large part on the expertise of the analyst. For example, if one had created all possible combinations of terrorist objectives, targets, and means of attack in the United States along with prior conditions that must be true for each (e.g., get operatives into the United States, give them flight lessons, obtain a plane, fly the plane), the September 11 event might have been generated as one plausible attack scenario, and observations of some of the necessary preconditions might have generated warnings of precisely that scenario. However, if the analyst did not consider planes as a method of attack, no structured approach would have led to the actual scenario and thereby created actionable intelligence. CREATING AND IMPLEMENTING CONCEPTUAL MODELS Hypothesis testing, although exceedingly useful, may be insufficient for some problems. Instead, if the model of reality required for the problem space is sufficiently complex, if the model will continue to be used in an
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ongoing effort, and if time and resources permit, the creation of a conceptual model—especially one that can be automated—is well worth the effort. For any but the simplest models, such a model can lead to nonobvious outcomes and superior decisions. Steps in Conceptual Model Design The following steps provide a framework for the design of a conceptual model. When critical thinking and a structured approach are applied in each step in the stated order, model risk is minimized. The analyst must first define the problem; she must ensure that the analytic effort is geared toward answering the most appropriate question. The purpose of most models is to inform decision makers by allowing them to better understand complex situations and interactions, and the analyst can achieve this goal by defining the problem in a manner that identifies and quantifies all the important outcomes in the model of reality (even one that is nonlinear and dynamic). Sometimes, a slight restatement of the question to be answered can speed progress in model design. Such a tweak might cast the problem in a revealing new light and speed conceptual model development. The next step is to seek answers by generating and refining hypotheses. If the purpose of the model is to assist a decision maker in selecting from among a number of options, the model must generate every plausible outcome (using decision trees or some other formal approach that enforces completeness) with which the decision maker would be most concerned. If the purpose of the model is to better understand a complex situation, the scenarios should include illustrative cases extracted from the available history. After having identified the purpose of the model and the comprehensive set of plausible scenarios, the analyst must next define output parameters that can be used to inform the decision maker. The output might be the optimal decision, the answer to a true-false question, or even a metric. For example, the decision maker might require a threat-level metric that can be monitored as conditions change. Similarly, he might want to know the sensitivity of the metric to an input parameter or a decision. The next step is to acquire information. The analyst identifies input parameters in order to avoid availability bias and then obtains the requisite data. In this step, any critical information gaps are identified. There are three main categories of inputs: (1) observables (i.e., facts or data that can be directly observed), (2) fundamental assumptions (i.e., knowledge that can’t be directly observed or inferred), and (3) decisions.
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One of the methods that is often used to identify required inputs is to work backward from the desired output and ask the question, “What influences or determines that output?” In this step, it’s also necessary to identify any data that are critical to or would enhance the analysis but are not readily available. Either an effort must be made to obtain these data, or the increase in model error caused by some type of workaround (e.g., substituting expert opinion for knowledge) should be explicitly acknowledged. Such a substitution does not necessarily degrade the model. Sometimes a model that includes an expert analyst’s best guesses (i.e., an expert system) can produce better forecasts than a model that was compromised by including only available data or historical data that are considered unrepresentative of the future. The next step is to structure information. After the analyst specifies all outputs and inputs, she can specify the relationships between them. These relationships, which connect inputs and outputs, can take the form of heuristics, rules, generalizations, equations, or logical operations. They can be completely deterministic, be related by a conditional probability (i.e.,8Y|X9 = P),7 or even be linked by a statistical function such as correlation. Each output can be a function of more than one input, and time can be explicitly included as a variable if the system is dynamic. A conceptual model can include more complex relationships between variables, such as feedback loops (in which an output affects its own input) and competing forces (in which there are multiple pathways between an input and an output that have opposite effects). Such relationships may dampen or amplify the outcome or even demonstrate that the system will tend toward some equilibrium or is inherently unstable. The next step is making assessments. This step answers the question, “Why do I believe that my model represents reality?” In general, this step might consist of backtesting the model against observed data (and in the process calibrating it to history where appropriate) or subjecting it to expert review (i.e., by evaluating whether various outputs are consistent with test inputs). In this stage, experts might test selected hypotheses in the manner previously described in order to spot-check the model. After making assessments, the analyst uses the model to generate the requisite results. For some purposes (e.g., a military operation), the model might be used to reverse-engineer optimum input parameters. For example, depending on the risk of an amphibious assault on Taiwan by the People’s Republic of China, it might identify the ideal location of the U.S. Seventh Fleet and describe the sensitivity of the outcome if the fleet is out of place. Similarly, it might be used to identify optimum decisions (e.g., move the Seventh Fleet) based on the decision maker’s utility function.
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The final step is to communicate the assessment. The results of a model—irrespective of its quality—must be effectively communicated to the decision maker to elicit the optimum decision. The analyst should endeavor to achieve full transparency when informing the consumer of the assessment. He should explicitly detail any uncertainty about input quality and model error so that less mathematical consumers of the results do not confuse mathematical precision with accuracy. The great utility of a conceptual model—particularly for a complex problem—is that the information and relationships with which the analyst informs it can produce surprising results, ones that might not have been anticipated using a less structured process. This is akin to the emergent behavior described in Chapter 5 in a complex, self-organizing system. Similarly, a properly structured model may identify out-of-the-box solutions. Thus, the process of creating a conceptual model reduces model error by attempting to ensure that all plausible outcomes—and only plausible outcomes—are generated by avoiding logical fallacies and cognitive biases. CASE STUDY: AN INTEGRATED CONCEPTUAL MODEL OF DUBAI Figure 7-3 illustrates one version of a conceptual model inspired by the market-shaking events triggered by Dubai World in November 2009. Although it is only a toy model created for illustrative purposes and is very much oversimplified, it touches on the interdependency between the Dubai real estate activities, regional politics, and systemic risk in the global economy and markets. The events are as follows. On November 25, 2009, Dubai World (a holding company owned by the government of Dubai8) issued $5 billion of new debt for the benefit of the Dubai Financial Support Fund, intended to shore up its real estate and financial industries. The principal buyers were two Abu Dhabi government-controlled banks. However, shortly after the announcement of the sale, Dubai World and its property development unit Nakheel PJSC (the developer of palmtree-shaped islands off the coast of Dubai) asked their creditors for a “standstill agreement” in which the maturities of debt that was imminently due would be extended until at least May 30, 2010. At the same time, Dubai’s Supreme Fiscal Committee hired Deloitte LLP to assist it with restructuring Dubai World and its $59 billion in liabilities. Previous to those events, there had been continuing concern by global investors about Dubai’s creditworthiness. Housing prices had
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Level of New Construction in Dubai
Price of Real Estate Assets in Dubai
State of Global
Willingness of Foreign Banks to Make Loans
Economy
Relations with Abu Dhabi and Other Emirates
Regional Economic Instability
Dubai Creditworthiness Uncontrollable Input Willingness of Abu Dhabi to Prevent Default
Controllable Input Intermediate Step Model Output Direct Relationship Inverse Relationship Input Value (Direction)
Figure 7-3 Dubai World Conceptual Model: Regional Economic Instability
declined about 50 percent from their 2008 highs. As shown in Figure 7-4, credit default swaps (CDS) on Dubai’s sovereign debt had traded as high as 977 basis points (bp) on February 17, 2009. At that time, Emir Mohammed bin Rashid Al Maktoum, the ruler of Dubai (and also the prime minister and vice president of the United Arab Emirates), turned to the country’s richer neighbor, Abu Dhabi (just 90 miles away), for a $10 billion bailout. Abu Dhabi’s central bank complied, purchasing the entire 4 percent five-year note offering on February 23, 2009. On that day, Dubai’s CDS spread dropped to 720 bp, off 178 bp from the previous day and 257 bp from its high just four trading days before.9 The markets widely considered Nakheel’s ability to pay on a $3.52 billion Islamic bond maturing on December 14 to be a litmus test of Dubai’s ability to pay, so the timing of Dubai’s standstill announcement was a shock. It was probably not an accident, either. Although all eyes were on December 14, the announcement instead occurred just before the U.S.
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Figure 7-4 Global Credit Default Swap History: Two Years Ending November 27,
2009 Source: Bloomberg, L.P.
Thanksgiving holiday on November 26 and the Islamic Eid al-Adha holiday on November 26 and 29, when markets were closed or had diminished trading activity.10 As shown in Figures 7-4 and 7-5, by end of day November 27, Dubai’s CDS were trading at 647 bp, or 329 bp higher than just three days earlier.11 Such an increase in yield implies a huge markdown in price for the $10 billion in notes just purchased in Abu Dhabi. The Dubai event rattled world markets as well; the cost of protecting both emerging-market and G-10 debt against default increased, and stock markets everywhere fell when trading resumed. The U.S. dollar strengthened against all but one of its 16 most-traded counterparts (Japan) in an oldstyle “flight to quality.” After touching an all-time high, gold dropped about $60 per ounce and oil dropped nearly $6 per barrel on November 27, although both recovered most of their losses later in the day. Although countries and companies with direct links to Dubai were the most affected, even those without such links were damaged as perceptions of systemic risk increased. Vietnam’s dong, the world’s worstperforming currency, fell 3.3 percent against the dollar. Even South
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Dubai
Abu Dhabi
Qatar
Saudi Arabia
Japan
United States
F T W T M
11/27 11/26 11/25 11/24 11/23
647 541 440 318 313
176 160 136 100 100
120 114 104 94 94
111 108 90 75 75
80 72 71 72 71
34 33 32 32 32
F T
11/20 11/19
313 304
100 100
93 94
74 78
71 68
32 32
305 304 304
100 100 100
94 99 90
76 75 74
66 65 66
31 30 31
W 11/18 T 11/17 M 11/18
Figure 7-5 Daily Closing CDS Spreads for Select Sovereign Debt Source: Bloomberg, L.P.
Africa’s rand fell 1.1 percent as a result of the secondhand influence of the fall in the price of gold. The astute reader may wonder why the change in spread was not instantaneous; markets are usually far quicker in reacting to bad news. As shown in Figure 7-5, the CDS spread had moved only 122 bp by the end of the day on November 25 (the day of the announcement). In fact, concurrent news stories reported muted reactions; a Bloomberg news story reported that Dubai CDS were trading at 319.5 bp after the announcement, or just 6.5 bp higher than the previous day.12 This delayed reaction may have been due in large part to Abu Dhabi’s complicated relationship with Dubai. Investors have long considered this much wealthier emirate to be a de facto guarantor of Dubai’s debt, although there is no such formal relationship in place. But Abu Dhabi was hurt as well. Its CDS swap rate surged from 100 bp to 176 bp over the same four-day period. But as time passed, analysts and investors became less certain of Abu Dhabi’s response, particularly in light of the less-than-stellar manner in which Abu Dhabi had been treated. On November 25, Rami Sidani, a portfolio manager at Schroeders Investment Management Ltd. in Dubai, said, “Abu Dhabi will help Dubai because Abu Dhabi simply cannot afford the repercussions of Dubai going under.”13 On November 27, Bank of America analysts Benoit Ann and Daniel Tenengauzer wrote, “Dubai’s debt woes may worsen to become a ‘major sovereign default’ that roils developing nations and cuts off capital flows to emerging markets. . . . One cannot rule out—as a tail risk—a case where this would escalate into a major sovereign default problem, which
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would then resonate across global emerging markets in the same way that Argentina did in the early 2000s or Russia in the late 1990s.”14 By November 28, Reuters was reporting that “Abu Dhabi, Dubai’s oil rich neighbor, will ‘pick and choose’ which of Dubai’s assets to underwrite, Reuters reported, citing an unidentified Abu Dhabi official. Abu Dhabi won’t fund all of Dubai’s debt, the official said.”15 Markets—which are notoriously poor at dealing with uncertainty—reacted in a manner consistent with such increasing perceptions of risk. Irrespective of the short- or long-term consequences of the Dubai World event, the observed market reactions and the expert commentary and analysis provide a foundation for the construction of a conceptual model for regional instability in the Mideast. In the conceptual model of Figure 7-3, the modeler transformed a qualitative analysis into this conceptual model. The objective of the model is to measure the level of instability in the Mideast as a function of a number of key variables (both economic and political), such as “Level of New Construction in Dubai” and “Relations with Abu Dhabi and Other Emirates.” This model does not attach a likelihood or other metric to each driver, but it does describe the direction of the sensitivity (i.e., direct or inverse relationship) to each variable. Note that the modeler found it convenient to create a number of intermediate variables, such as Dubai Creditworthiness. Note too that the model includes feedback loops, for example, one in which Abu Dhabi’s political will affects Dubai’s creditworthiness. In addition, note that some variables (e.g., Dubai Creditworthiness and State of Global Economy) can be directly observed and therefore might be used to infer values for some of the other unobservable variables. SOURCES OF MODEL RISK IN FINANCIAL MODELING The financial community is rich in models that represent reality, although the source of model risk is somewhat different from what it is in other disciplines. Just as in any other discipline, errors in financial models result when a securities valuation or risk measurement model is incorrectly specified or erroneously applied. Consumers of risk forecasts, whether they are C-suite executives or regulators, are sometimes unaware of the magnitude of the model risk inherent in the results that inform their most important decisions, ranging from the allocation of risk capital to standards for capital adequacy.
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Because such models are used almost exclusively for forecasting outcomes rather than for explaining observed events, they are particularly dependent on a number of assumptions that cannot be validated with facts. Because such forecasts are usually the results of stochastic models rather than causal models, the implicit or explicit assumptions on which they depend can be subtle. The advanced mathematics on which most models depend may leave consumers with a false sense of security about a model’s validity. Risk forecasts already indicate substantial uncertainty about outcomes (even if parameters such as mean and variance are known with certainty); they are generally expressed in terms of a metric, such as VaR, that is a function of the distribution of possible outcomes (i.e., a continuous representation of possible future states). Therefore, it may not be immediately apparent to the consumer that all sources of uncertainty are not included. Just like decision makers in the intelligence space, financial decision makers need to be aware of the important assumptions that are made by the modeler and upon which the results depend. Such disclosure is especially necessary when more complex mathematics is involved because of the lack of transparency that a black-box model engenders. One example of an erroneously applied model may be the exclusive use of stochastic models to represent reality in the global capital markets. The most fundamental assumption implicit in the use of any stochastic model (financial or econometric) is that past behavior is representative of future behavior, that is, that the system represented by the model is reasonably stable. But changing fundamentals such as public and regulatory policy, credit availability, geopolitical considerations, and even behavioral preferences may precipitate a shift to a new risk regime. In such an event, backward-looking models are likely to over- or underestimate risk. Even if the system is assumed to be stable, another fundamental assumption implicit in many financial models is that price patterns reveal everything, that is, that risk can be modeled using only time series of asset prices and economic indicators. However, the price of a security reflects the net effect of myriad drivers and events. Thus, the assumption that energy prices are stable may implicitly imply that events such as pipeline disruptions are randomly distributed and that their frequency and magnitude are stable as well, even if known facts and common sense indicate otherwise. Erroneously applied models are a major source of model risk in the financial space, but so too are incorrectly specified models. Protocols for generating the parameters that inform such models vary greatly from firm to firm, and no two will generate identical measures of risk for a specific
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portfolio. For example, most risk analysts use a standard term (e.g., the most recent three years) to estimate risk parameters such as standard deviation.16 However, when there is a change in risk regime, such as the one that occurred in late 2008, such protocols may be unjustifiable, and no amount of statistical tweaking is likely to enable them to provide an adequate forecast of risk. Critical Thinking and Financial Modeling Fortunately, the same standards of analytic tradecraft that mitigate model risk in the intelligence community can be applied in the financial community. If we apply critical thinking to every assumption that must be true if we are to rely on a risk measurement model, we can (1) select a model that best represents reality, (2) inform it with the best possible data and knowledge, whether in the form of statistical parameters or expert opinion, (3) be aware of the degree of confidence we can justifiably have in that model, and (4) have some insights into the conditions under which the model might fail. To do so, financial engineers must guard themselves against the same cognitive biases to which intelligence analysts are vulnerable. As noted in Chapter 2, behavioral economists have particularly noted innumeracy, confirmation bias, and illusory correlations (i.e., statistical bias) as biases to which humans making market choices might fall prey. Financial engineers may also be particularly vulnerable to confirmation bias and availability bias because they have a personal stake in the models that they’ve specified and because their firms often have very large investments in the proprietary technology used to support those models. Structured Approaches and Conceptual Model Building in Finance A structured approach in which some hierarchical representation of reality is created also has analogs in the financial space. Such an approach may provide an ideal framework for the separation of systemic and specific risks and categorization of various types and sources of specific risk. The creation of a conceptual model with all its ordered steps applies in the financial space. For example, rather than answering a question such as, “What is the value of VaR?” a more appropriate question might be, “What are the drivers of the most extreme scenarios?” or “What might indicate a shift from the current risk regime?” Similarly, analysis of inputs, outputs, and the relationships that connect them might identify critical data. For example, a regulator might determine that it requires more granular data, such as detail on all
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over-the-counter (OTC) transactions (including the identity of counterparties) from those who engage in credit default swaps, in order to estimate and monitor systemic credit risk. Even hypothesis testing has its place in financial modeling. Logical elimination or validation of competing hypotheses might well improve the analyst’s model of reality and its drivers and assist in defining the best possible model for the question. CRITICAL QUESTIONS IN FINANCIAL MODELING The following list of questions includes many that a risk analyst might ask when specifying a model and estimating model risk. • What is the system or subsystem that I am modeling? • What do I need to assume about that system? Can I assume that the system is stable? • Are there critical events (e.g., legal, regulatory, or policy changes) that will significantly affect human behavior and preferences and therefore market behavior? • What evidence might I observe that would indicate that a regime change in risk has occurred or is about to occur? • What are the boundary conditions within which my model is expected to be valid? What market or structural events might invalidate my model? • What is the magnitude of model error inherent in the way in which I estimate parameters for the model? • Are consumers of the model aware of the sources and the magnitude of model risk? • What other sources of data (or creative new use of existing data) might I use to supplement the model (i.e., use all-source intelligence, including nonquantitative data)? • How can I enhance cognitive abilities and collaboration with associates? • Would visualization and link-analysis tools benefit my analysis? SUMMARY Model risk is a subtle yet important source of risk that can lead to flawed decisions. It is often the result of cognitive biases or a failure to properly represent reality and all its plausible permutations and is equivalent to a
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loss of quality control during the modeling process. There are a number of methods that the intelligence community uses to minimize model risk, whether the model is intended to explain observed events or to make forecasts. The magnitude of model risk for financial applications can be minimized by routinely applying the same critical thinking and structured approach to representing reality and a problem space used by the intelligence community. WHAT’S NEXT In the next chapter, we will discuss sources of model risk specific to financial modeling. We will introduce concepts from Bayesian analysis, such as prior and posterior distributions, and discuss the effect of the explicit inclusion of model risk on valuation and risk models.
CHAPTER 8
The Future as Forecast: Probability, Likelihood, and Uncertainty
PARAMETER RISK: ACKNOWLEDGING UNCERTAINTY The concept of risk measurement is something of a misnomer. Any representation of risk is nothing but a forecast, though of a range of possible outcomes rather than just the most likely outcome. Like any other forecast, it is subject to error—error whose source is a flawed predictive model, faulty estimation of the parameters used to inform that model, or simple chance. The error here is not the uncertainty about which number will come up on the spin of a roulette wheel, but instead the uncertainty about whether the wheel is skewed in some way. In the previous chapter we discussed some sources of model risk, particularly in the context of cognitive biases present when intelligence analysts produce qualitative forecasts. But model risk is present in a variety of ways in even the most mathematically sophisticated risk measurement models. And worse, the sources and magnitude of model risk may be invisible to senior decision makers, veiled as it may be by scientific respectability. But even the best financial engineer is subject to cognitive biases, which may subtly manifest in his worldview of how, say, prices change over time. And beyond any flaws in models he builds are flaws in the parameters used to inform them; these too are forecasts and therefore an additional source of model error. The larger topic is the appropriate meaning of the term “uncertainty,” the related term “probability,” and uncertainty about one’s uncertainty— commonly referred to by Bayesians as higher order uncertainty. Some probabilities are objective (e.g., the probability that a coin will land heads up), while others are matters of opinion (e.g., the probability that there is life in other galaxies). There is a rich literature in such topics, and higher order uncertainty is sometimes characterized as a “spread of opinions” in which objective truth does not exist. Bayesians promote the use of 117
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Bayesian statistics to deduce the probability that a true value is within a credible interval, analogous to a confidence interval in classical statistics, but without the assumption of objective truth. A deep understanding of uncertainty in all its aspects is critical to quantitative analysts because the value of so many of today’s derivative securities depends in large part on quantifying that uncertainty. For example, because the theoretical value of a simple noncallable bond is the present value of all future cash flows discounted at the appropriate reinvestment rates, that value depends only on expected forward reinvestment rates. Conversely, the value of an option or any financial instrument that contains implicit optionality depends instead on all the possible outcomes by the option’s expiration. This is a very high bar. Not only must an analyst predict the expected future, but ideally he must also predict all the possible futures that may or may not occur. Clearly, then, astute analysts explicitly acknowledge the risk that their risk predictions themselves are flawed and make an attempt to quantify that risk. Best practice in risk management now includes some estimate of model risk from all its sources. In previous chapters, we discussed methods for characterizing a dynamic system and defining the relationships that drive change. In this chapter, we will focus on one source of model error: parameter error, that is, the risk that an otherwise valid model is informed by less than perfect estimates of the parameters on which it depends. FOUNDATIONS OF A STATISTICAL APPROACH TO FORECASTING If we are to rely on a statistical representation of a system, past and future must be one. The analyst must believe that the data that she sampled from the past are an adequate representation of (and not fundamentally different from) data that might be sampled from the future. Thus, the use of statistical methods may be no more scientific and objective than other methods for estimating likelihood. FREQUENTIST VERSUS BAYESIAN APPROACHES IN FINANCE Experts in statistics come in two flavors: frequentists and Bayesians. The difference lies in their attitude toward the concept of probability for the topics we examine here. To a frequentist, the probability of an event is the frequency of its occurrence over the long run. That is, as the period over which its frequency was sampled goes to infinity, the frequency observed converges to
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some theoretical probability that is an intrinsic characteristic of the system observed. Conversely, to a Bayesian, there is no such thing as probability. At best, probability is a measure of the state of knowledge about the system and reflects the degree of belief in a particular representation of behavior. Although a Bayesian may use probability calculus (which requires assumptions about the relative frequency of events), he doesn’t implicitly assume that those values accurately reflect the real world. In a sense, a Bayesian acknowledges the possibility of model error more explicitly than a frequentist does.While a frequentist depends on some sort of controlled or natural experiment to estimate probabilities, a Bayesian can instead use any means to estimate degree of belief—even an educated guess. The difference between the two camps is most obvious in their attitude toward new information. In their concept of prior and posterior distributions, Bayesians explicitly acknowledge the fact that absolute truth is unobtainable, no matter how many millennia of historical data is examined. A frequentist uses new data to further refine the probabilities previously observed, whereas a Bayesian uses the new data to check whether his prior model needs revision. The frequentist implicitly assumes system stability, but a Bayesian is not so constrained. In practice, most quantitative analysts in finance are frequentists with a twist. As previously described, the frequentist approach was a natural choice within the financial community for both philosophical and practical reasons. The valuation and risk models that were created generally contain an assumption that changes in price follow some variation of random Brownian motion (usually that daily returns are normally distributed) and that the parameters that describe those distributions, such as mean and standard deviation, are estimated from observed market prices. However, the “with a twist” comes from the fact that they have made some practical concessions (for example, assuming a future mean of zero irrespective of the observed mean) when estimating parameters, or allowing the inclusion of market features such as volatility clustering. In contrast, most risk modelers in disciplines such as threat assessment, epidemiology, and operational risk are Bayesians, at least in attitude. In such problems, probability need not be derived from historical experience; instead, an analyst can use expert opinion based on prior evidence to inform a risk model. Although a lack of historical experience hampers a frequentist approach in some of these fields, a larger consideration is the fact that recent history cannot be assumed to even approximately represent the
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5.0% 0.4
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future adequately. This is especially true in assessing a catastrophic risk such as nuclear proliferation, an attack by a state actor, or a new pandemic. In the case of operational risk, understanding a source of human error may lead to a repair of the fault, reducing the likelihood of the same error. Uncertainty is another topic about which the two camps disagree. For example, consider the normal distribution in Figure 8-1. It is completely specified by two parameters: the mean m (with a value of 0) and the standard deviation s (with a value of 1 percent). Assume that these two parameters were estimated from the returns of historical stock prices. To a frequentist, uncertainty is captured in the distribution of possible prices implied by a probability distribution taken from historical market prices, and the primary source of uncertainty is the outcome. For example, if the initial stock price is 100, the probability of a change in price greater than 1.645 percent (to a price greater than 101.645) is 5 percent. Conversely, to a Bayesian, these probabilities represent a degree of belief in the statistical model. In Bayesian eyes, a frequentist has inordinate
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faith that the statistical parameters estimated from history will converge to a true characteristic of the system as the time series becomes infinitely long. A Bayesian considers that there are at least two sources of uncertainty with respect to this model of random stock price behavior. In addition to the uncertainty of outcome for a random process specified by a mean and standard deviation, an additional source of uncertainty is the values of those two parameters themselves. (Other sources of uncertainty might be the shape of the distribution and even the validity of representing changes in stock prices with a statistical model.) To a Bayesian, the process of forming best estimates and calculating the degree of uncertainty in those estimates is a moving target. As additional knowledge is gained (via the revealing passage of time or other intelligencegathering methods), a Bayesian revises her opinion about a prior probability distribution and forms a new posterior probability distribution. The Bayesian continuously rejects her previous opinion about the reliability of the model and revises it to one that she believes to be more accurate. Consider the manner in which a frequentist estimates historical volatility. No matter how changes in price are distributed, it’s possible to calculate a mean and standard deviation for a set of sample data. For example, one can estimate those parameters even for a fat-tailed, bimodal, or other oddly shaped distribution that is not well represented by a Gaussian distribution. Although there are statistics that measure the goodness of fit, they provide a static opinion. Obviously, one way in which to examine the assumption of normality is to plot a histogram for the historical data and examine it (either visually or via distribution-fitting methods). In essence, one is trying to form an opinion of the likelihood that the data used were in fact taken from a normal distribution. However, a more quantitative way of evaluating this prior assumption and forming a posterior assumption about the distribution is the use of Bayesian methods of calculating likelihood. BAYESIAN INFERENCE AND HYPOTHESIS TESTING It’s been said that classical statistics plus common sense get one close to Bayesian statistics. Bayesian methods provide a mathematical approach to the process of hypothesis testing discussed in Chapter 7. A Bayesian’s attitude toward hypothesis testing is expressed in the famous formula given here, which indicates that the degree of belief that hypothesis H is valid, given new evidence e, is the product of P8e|H9 (the likelihood that e will occur if H is valid) and P(H) (our previous belief in H).
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The conditional probability P8H|e9 (the likelihood that H is valid when e occurs) is the result when the product is divided by P(e) (the likelihood of e). P8H|e9 =
P8e|H9P(H) P(e)
To those who are familiar with the mathematics of conditional probabilities, this formula may seem like a trivial restatement of a basic Bayesian formula. However, to a Bayesian, it is a meaningful expression about how to revise one’s opinions about a hypothesis. As so eloquently observed by Judea Pearl, “The Bayesian subjectivist regards [this equation] as a normative rule for updating beliefs in response to evidence. In other words, although conditional probabilities can be viewed as purely mathematical constructs, the Bayes adherent views them as primitives of the language and as faithful translations of the English expression, ‘. . . Given that I know A.’”l Bayesian mathematics therefore gives us the ability to quantitatively answer a question such as, “What is my degree of belief that my sample data were taken from a normal distribution with the given parameters?” With enough data and continuous examination and reexamination of each of the successive prior distributions, one theoretically converges on more likely representations of reality. However, this may not be so, depending on the nature of the system. Although it might be true in a problem such as analyzing the spins of a roulette wheel, this may not be a fair assumption in a system as complex as the global capital markets. Although the former is deterministic (and, indeed, we can calculate relative distributions theoretically rather than empirically for certain physical problems), there is no guarantee that the mechanics of market price movement haven’t altered over time in some profound manner as a result of exogenous factors. THE FUSION OF BAYESIAN AND FREQUENTIST APPROACHES In real life, the financial community makes a number of concessions to Bayesian thought in estimating statistical parameters and applying them to practical problems such as the valuation of derivative instruments or measurement of risk. First, frequentists are well aware of the limitations of estimating probabilities from a finite data set or a data set that is inappropriate for sampling. To a strict frequentist, the more data the better, since the averages of observed probabilities converge to the real probability only as the number of observations approaches infinity.
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Nevertheless, instead of using as many historical data as are available, the financial community implicitly concedes that the system is unstable and that older data are a far poorer predictor of future behavior than are the most recent data. Instead, most analysts compromise between a statistically significant period of time and the most recent period by using the most recent n days of data (for estimating equity volatilities, as little as 90 trading days; for estimating risk, generally two or three years). By doing so, such analysts implicitly account for important changes in market conditions that might drive behavior. For example, increased participation by new players (e.g., algorithmic traders or sovereign wealth funds), new instruments [e.g., the growth of credit default swaps (CDS)], and structural and legislative change [e.g., the Troubled Asset Relief Program (TARP)] might all serve to make past behavior misleading. As long as these drivers affect markets gradually, using the most recent n days might be reasonably accurate. However, if any such drivers generate sudden shocks to the system, this will no longer be the case. One additional flaw of using such a moving estimator is the fact that the days dropped off are as important to the results as the new days added. Some modelers give more weight to recent events—say, by using exponentially weighted averages of past returns—in an effort to make the estimate more representative of the present. It can be shown that such a method provides a good estimate of current implied volatility (that is, consensus market opinion) for stock options using past price behavior. Second, frequentists almost universally override estimates of the mean calculated from historical data, instead assuming a mean of zero or one implied by risk-free interest rates. Such an override might be justified on the basis of belief in an assumption of market efficiency, that is, the current market price already reflects all information known to market participants, and there is no reason to believe that an upward or downward trend will continue. Gold Volatility and Chart Patterns Such a fusion of frequentist methods and concessions to prior knowledge leads to somewhat inconsistent protocols for parameter estimation and requires analysts to take care with their use. As an illustrative example, consider the estimation of option parameters. In finance, the standard deviation of returns is generally calculated relative to their mean, that is, around a trendline. Examine once again the gold price history shown in Figure 5-2. Recall that the price of spot gold advanced a heady 15.98 percent in the four weeks ending November 25, 2009. One might characterize this
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four-week period as extraordinarily volatile in the colloquial sense of the word, especially when compared with the relatively modest 7.23 percent advance of the prior five months. However, daily returns during the more recent period were so regular that they exhibited little deviation relative to their mean of 0.7 percent per day (as compared to only 0.06 percent for the earlier period). This period’s historical volatility (i.e., annualized standard deviation2) was only 14.2 percent, counterintuitively less than the 15 percent of the previous five months. In fact, if the graph of the four-week period were laid on its side so that the mean return was zero and the trendline was horizontal, volatility would be the same. As a reductio ad absurdum, consider a case in which the price of gold increases a constant 1 percent every day for 20 trading days. At the end of this period, gold would be 22 percent higher, but historical volatility would be zero! Using historical estimates for mean, volatility, or both would clearly result in nonsensical estimates for options value and risk. Traders are smarter than that and make their own forward-looking estimates of possible price distributions; whether movement comes from future trends or future volatility, price change is price change. Consider the graph in Figure 8-2, which compares 60-day historical volatility to three-month implied volatility for at-the-money options on gold futures. Implied volatility (the volatility implied by option prices) was almost always substantially higher than historical volatility during the same six-month period. CASE STUDY: THE ANALYSIS OF A FINITE SAMPLE DRAWN FROM A NORMAL DISTRIBUTION In Bayesian analysis, likelihood is a quantitative measure of the degree of belief in a statistical model and can be estimated when statistical sampling is employed to estimate model parameters. It explicitly measures the uncertainty inherent in estimating parameter values from a finite data set. Because normal distributions are the mainstay of many valuation and risk models, analyzing sample data drawn from a normal distribution is a useful exercise. In this case study, a random-number generator was used to produce 100 observations drawn from a normal (Gaussian) distribution with a mean m of 0 and a standard deviation s of 1. Because there are only 100 observations, the estimated3 mean and standard deviation of the sample are slightly different from the targets: mN = 0.0110 sN = 1.0151
Period Daily: 6M AnnFactor 260 Ccy LCL Statistics Range 05/25/09 11/25/09 Type Level Lag Security Type Level Lag Security GCG0 Comdty HVol 60 CLA 0D GCG0 Comdty HVol 60 CLA 0D GCG0 Comdty % Money 100.0% 3M 0D GCG0 Comdty % Money 100.0% 3M 0D Spread(Absolute) Spread(Absolute) Legend
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Figure 8-2 Historical versus Implied Volatility in Gold Futures, May 25, 2009, to November 25, 2009 Source: Bloomberg, L.P.
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Figure 8-3 Histogram of 100 Random Observations [Target Mean ⫽ 0,
Standard Deviation (STD) ⫽ 1]
Of course, given only the data and not the process that generated them, we are uncertain that these are the real parameters of the system. (In fact, they are not exactly the same as our target parameters.) Just as in a reallife sample, bad luck might have caused us to under- or overestimate the parameters. Furthermore, with only 100 trading days, rare events—say, ones that occur only once per year or even once per decade—may not have been captured. Nevertheless, as shown in Figure 8-3, a histogram of the random numbers generated seems to be well represented by a normal distribution. Let’s further assume that these data represent some market process, such as daily returns for 100 trading days of a particular stock. If we give that stock an initial price of 100, the random data produce a simulated time series such as that shown in Figure 8-4. Note that although the returns are normally distributed and their mean is close to zero, the price of the stock can deviate quite far from its initial value, even though it ends nearly unchanged. We can contrast the approaches that a frequentist and a Bayesian might take when building a financial model informed by these data.
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Figure 8-4 Simulated Price and Returns History for Sample Data
A frequentist might say, “The data support my opinion that returns are normally distributed. I can build valuation and risk models based on this assumption, using the estimated values for mean and standard deviation as input parameters to my models.” A Bayesian might say, “Like my frequentist colleague, I am also of the opinion that returns are normally distributed. However, I’d like to use these data to help me decide whether this is a rational assumption. And even if it is, although the estimated values for mean and standard deviation from
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the sample may be the most likely values, there are other pairs of values that are also reasonably likely. I’d like to measure their relative likelihood and understand the sensitivity of my valuation and risk models to this additional source of uncertainty.” Both the frequentist and the Bayesian started with a prior distribution; that is, each assumed that returns are normally distributed. But whereas the frequentist used the historical data to identify the parameters for his prior distribution, the Bayesian also used those data to refine her opinion in light of this new information (the observed returns) and shape a posterior distribution. Each has identified the maximum likelihood mean and standard deviation, but only the Bayesian has explicitly accounted for the uncertainty in specifying those variables. Although the estimated mean and standard deviation represent the maximum likelihood estimators (MLEs) for those parameters, we also need to estimate the likelihood of additional plausible (albeit less likely) pairs of values for the mean and standard deviation. For example, it’s far from implausible that the next 100 days will have a mean of ⫺0.02 and a standard deviation of 1.03. Unfortunately, the qualifier “maximum likelihood” is often dropped by quantitative analysts, and those who are not expert in statistics may be unaware that other values are likely, too—even in a stable system. It can be shown that for the special case of a prior distribution that is normally distributed, the likelihood function L as a function of mean m and standard deviation s is a function of the time series xt, where n is the number of observations.4 L(m, s|x) = (2ps2)-n/2 expe -
1 2s2
[n(m - mN )2 + (n - 1)sN 2] f
where n
2 a (xi - mN )
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xi mN = a i=1 n
and
sN 2 =
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If we calculate the likelihood L for a number of (m, s) pairs using the simulation data, we get a three-dimensional surface, as shown in Figure 8-5.5 The peak of the surface is at the maximum likelihood estimates for the mean (0.0110) and standard deviation (1.0151). The shading represents 10 percent increments in likelihood. This surface has a fairly wide spread; the likelihood of values for mean and standard deviation that differ from the maximum likelihood estimates are far from insignificant.
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n = 100
Figure 8-5 Likelihood Surface as a Function of Mean and Standard Deviation
Such uncertainty about parameter choices has profound implications for pricing and risk management. For example, the value of an option depends heavily on both the mean and the standard deviation. However, using the maximum likelihood estimates gives one value, whereas using some less likely pair of estimates gives another. Even though the distribution is symmetrical, a likelihood-weighted option value can increase only if some other pair of variables results in a higher value for the option. This is so because option rules are asymmetrical; ex-fees, the option value cannot go below zero. Similarly, the probability of extreme events may be far greater than that estimated at the maximum likelihood values. Even if we assume randomly distributed noise in a stable system, there are two sources of uncertainty: uncertainty that is due to random movement, and uncertainty that is due to the scale (s) and location (m) parameters of that random movement. It’s important to note that observational data might sometimes be misleading because of such uncertainty. Fat or thin tails of empirical distributions may be an artifact of parameter error, that is, a difference between the MLE and the theoretical parameters. DEPENDENCE ON THE NUMBER OF OBSERVATIONS In a frequentist view, more data produce more confidence in the model and its parameters, at least for a stable time series. (A Bayesian might say that such confidence is unjustified.) As shown in Figure 8-6, the likelihood
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Figure 8-6 Likelihood Surface as a Function of Sample Size
surface expands with fewer observations and contracts with more observations. The fact that we used only 100 observations accounts for the fairly dispersed spread of Figure 8-5. DEPENDENCE BETWEEN MEAN AND STANDARD DEVIATION As may be intuitively obvious, mean and standard deviation are codependent for a given value of likelihood. Figure 8-7 shows a cross section of the likelihood surface of Figure 8-5 in 10 percent increments. (On this chart,
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Figure 8-7 Contour Chart of Likelihood: Difference from MLE
the axes are shown in terms of the difference from the mean likelihood estimator). The perimeter of each cross section reflects pairs of mean and standard deviation that are equally likely. From the previous equations, it can be shown that for a given value for likelihood, we can calculate all pairs of values for standard deviation and mean6 for a given constant Likelihood LC:
m =
-2s2 ln(LC(2ps2)n/2) - (n - 1)sN 2 + mN n B
All points on the closed curve labeled “90% likely” have a value for L of 10 percent (normalized); this curve represents the outer boundary of the region that contains all pairs that sum to a 90 percent likelihood.
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For example, each of the following pairs of parameters on the 10 percent perimeter is equally likely: Pair 1: m ⫽ 0% and s ⫽ 1.0432% Pair 2: m ⫽ 0.0356%7 and s ⫽ 1.0151% This dependency between mean and standard deviation makes intuitive sense, as either parameter can cause the price of a security to deviate from its starting level. These two scenarios are equally likely: price movement is trendless but volatile, or it exhibits a significant trend but is less volatile. Note that, based on our test data, the area within the 10 percent likelihood perimeter (i.e., near the maximum likelihood estimates) is quite small. This implies that the degree of uncertainty in the value of an instrument such as an option that is highly dependent on these two parameters is large. Although these contours are symmetrical with respect to standard deviation (horizontally), they are not symmetrical with respect to mean (vertically). This can be better shown with two vertical cross sections of the surface. In Figure 8-8, standard deviation is held constant at its maximum likelihood of 1.0151. In Figure 8-9, mean is instead held constant at its maximum likelihood of 0.0110. These two cross sections of the likelihood surface demonstrate a number of interesting features. When the standard deviation is held constant at its maximum likelihood value, the mean is symmetrical and exhibits the shape of a normal distribution. The point of maximum likelihood (the peak of the distribution) is equal to the mean of the sample data. Conversely, when the mean is held constant at its maximum likelihood value (a cut across the surface perpendicular to that of Figure 8-8), the values for the standard deviation on the likelihood surface are asymmetrical and exhibit a right tail that is more pronounced than the left.8 In fact, the standard deviation is lognormally distributed, and the point of maximum likelihood is equal to the standard deviation of the sample data. Experienced options traders may get a more intuitive sense of the magnitude of such uncertainty if we convert to conventional market units. Because we assumed that our test series would reflect daily returns for stock prices, we can convert the dimensionless standard deviation of 1.0151 percent (in daily return) to the generic market metric of volatility, which is the annualized standard deviation of returns.
Figure 8-8 Cross Section of Likelihood Surface with Constant Standard
Deviation
Figure 8-9 Cross Section of Likelihood Surface with Constant Mean 133
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The maximum likelihood standard deviation of 1.0151 therefore converts to a volatility of 16.37 percent. And as shown in Figure 8-9, it’s about 5 percent likely that the value for standard deviation will be less than 0.91 (14.66 percent) or greater than 1.15 (18.56 percent). This is a fairly substantial range and—particularly for far-out-of-the-money options—can greatly increase theoretical value. We can calculate the likelihood-weighted value of an option that takes this asymmetry and its effect on theoretical price into account. If we assume that the option is European-style and that we can therefore use the Black-Scholes formula or the Black formula (for options on futures), the calculation is trivial. It’s worth noting that, as previously discussed, although most risk managers use historical data to estimate standard deviation, they routinely discard any nonzero mean and instead assume no directional bias in their estimates of future distributions.9 (If they failed to do so, mean might dominate estimates of value and risk.) When the actual mean is overridden, the cross section of standard deviation will intersect the likelihood curve at a point other than its maximum. THE VOLATILITY OF VOLATILITY The previous discussion of likelihood from a Bayesian perspective demonstrated that historical values for volatility are uncertain even if the statistical sampling process is valid. The market itself gives the lie to the use of historical statistics as predictors of future volatility. As we saw in Figure 8-2, forward-looking implied volatility derived from market prices for options is often quite different from backward-looking historical volatility calculated from past prices. We can also observe traded volatility directly in financial instruments such as the CBOE’s Volatility Index (VIX), the premier benchmark for volatility that is often used as a surrogate for market instability. The VIX is calculated from the price quotations of the nearby and second option series for the S&P 500 Index (SPX) and is expressed in terms of volatility. Moreover, we can also observe the volatility of volatility of SPX, because options on the VIX are traded as well. Figure 8-10 shows intraday values for implied volatility on at-themoney calls on the VIX expiring three weeks hence on November 25, 2009. One can observe that even during the course of a single trading day, the implied volatility of both the underlying security and its option vary widely. The magnitude of VIX volatility is substantial as well, ranging
VIX Index Date 11/25/09 Time 09:30 – 16:30 Expiry 16 DEC 2009 Option Ticker VIX+LD Index Rate 0.2272
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from about 135 percent to 165 percent on that date. Even the volatility of volatility of volatility is volatile! The high volatility of the VIX options provides evidence that, at least in the opinion of traders, historical volatility is an uncertain predictor of future volatility and is unresponsive to new events, revised opinions, and shifting tolerance for risk. This opinion is further reinforced by the longer-term behavior of the VIX. Consider the 9 years of pricing history for the VIX shown in Figure 8-11. In addition to the values for VIX, two additional statistics were calculated: rolling volatility, in which the volatility of volatility for the previous three months was calculated, and the volatility of volatility as recalculated from the start of the time series. Theoretically, if stock prices are sampled only from a stable system, market volatility should be relatively constant as should the volatility of volatility. (If some level of volatility were a characteristic of a stable system, we would expect the latter statistic to converge to some fixed value.) Instead, we can observe a great deal of variance in both and can associate some of the extreme movements with specific events. For example, the peak value for the VIX on November 20, 2008, coincides with the height of systemic risk and bank failures on Wall Street.
Figure 8-11 VIX Index and Volatility: Weekly Data, June 11, 2000, to June 12, 2009
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Figure 8-12 3-D Plot of Historical VIX Volatility: 10-Year Period Ending June 12,
2009
HISTORICAL DISTRIBUTIONS OF VIX The amount of variance in any given three-month period (a typical term for an options contract) can be better visualized in the 3-D plot shown in Figure 8-12. The plot seems to indicate almost bimodal behavior, that is, there is a cluster of observations in the lower left of the plot, but a number of observations on the right side of the plot as well (i.e., extreme values for volatility alone and for both volatility and return). Return is an important measure even for a volatility index because it is possible to trade the VIX or options on it directly. The profit or loss on an option trade liquidated before expiration depends on the implied volatility at the time of liquidation, particularly for long-dated options.10 THEORETICAL EXPLANATIONS AND MODELS Clearly, then, historical volatility varies substantially over time. In addition, the market appears to tacitly accept some likelihood that future volatility will be higher than consensus expectations, as demonstrated by the fact that far-out-of-the-money options often trade at much higher implied volatility levels than at-the-money options (i.e., a volatility “smile” or “smirk” when volatility is plotted as a function of the strike price).
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Such behavior has not been lost on economists, who have created a number of stochastic models to account for such behavior, in which volatility is assumed to follow a random process governed by certain state variables (e.g., the variance of the volatility process). The argument might go as follows: “We clearly observe from history that volatility varies over time. Moreover, it tends to cluster: there are distinct periods of high volatility and low volatility. We posit that the evolution of volatility may be characterized as a jump-diffusion process in which random events occasionally shock the market before their effects dissipate.” However, clustering behavior implies that there is a deterministic component to volatility: one day’s volatility depends on the volatility of the day before. In addition, the diffusion process implies that there must be some mechanism that forces reversion to the mean. Clustering behavior and reversion to the mean are both consistent with behavioral effects. When a surprise event first occurs, investors may require some time to work out its implications and consequences and may require a higher risk premium while that process continues. One popular stochastic representation of dynamic volatility is the generalized autoregressive conditional heteroskedasticity (GARCH) model. In this model, the random component of variance depends on variance itself. As illustrated by the name, the term autoregressive refers to dependence on previous values in the time series, and the term heteroskedasticity refers to differing variance. In one common version of the GARCH model,11 the differential equation for volatility is dvt = u(v - vt)dt + jvt dBt where vt ⫽ variance at time t v ⫽ mean long-term volatility u ⫽ the rate at which long-term volatility reverts to its mean j ⫽ the volatility of the volatility process itself Bt ⫽ a Gaussian distribution with a zero mean and unit standard deviation There are a number of alternative stochastic volatility models as well as a number of variations of the GARCH model. Often, an analyst favors one over another because it better explains historical behavior or can be better calibrated to market prices. Nevertheless, most such models assume
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reversion to some long-term mean. By doing so, they implicitly assume system stability in the form of some constant value for the long-term mean. EMPIRICAL EVIDENCE OF REGIME CHANGE In a sense, a stochastic volatility model such as GARCH implies the existence of mini risk regimes. Risk levels may be anomalously high at times but can be expected to return to normal. But what if this assumption is not true? What if instead the system evolves to an enduring new state in which risk is substantially higher? If such a shift in risk regime occurs, it has profound implications for securities valuation and risk measurement. Such an evolutionary path might be driven by some fundamental change, such as policy change. Alternatively, it might be driven by a volatility spike of such magnitude (or one that occurs when the underlying conditions are just right) that it triggers some technical change, such as massive deleveraging by institutional investors. We might examine the history of VIX for empirical evidence of such regime changes.12 Consider the historical behavior of the VIX as shown in Figure 8-13. If we somewhat arbitrarily break its history into three regimes based only on visual inspection, the mean volatilities of the three periods vary substantially. Whereas the period 1999–2002 averaged 25.06 percent, the period 2003–2006 averaged only 15.77 percent, and the period commencing in 2007 averaged 28.84 percent. As Figure 8-13 shows, reversion to some theoretical mean can take a long time. For example, when the VIX dipped below its 1999–2002 average of 25.06 percent on April 11, 2003, it took more than four years for its value to recover to that level. Figure 8-13 also demonstrates that other factors may be more important drivers of the VIX. Investor risk aversion appears to be an important determining factor; in a bull market, volatility is low, whereas in a bear market, it is high. Recall that the VIX is often used as a surrogate for market instability and that it is often used to hedge broad market exposure. Investors—who are, on average, risk averse—tend to buy puts to limit their losses when prices drop (increasing volatility) and sell calls to increase their gains when prices rally (decreasing volatility). Based on such empirical evidence, we might consider risk to come routinely in two sizes: normal and extreme. To compare behavior, we might bifurcate that same time series into two different periods: the first nine years and the last year of the ten-year period ending on June 11, 2009.
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VIX Index - Last Price (R1) SPX Index - Last Price (L1)
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Figure 8-13 Historical S&P and VIX Indexes with VIX Regime Averages, 1999–2009
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Figure 8-14 Contour Plot of Historical VIX Volatility: 10-Year Period Ending
June 12, 2009
Figure 8-14 shows a contour plot of the entire period (including both hypothetical risk regimes); Figure 8-15 includes only the first nine years (the “normal” period), and Figure 8-16 includes only the last year (the “extreme” period). Figures 8-15 and 8-16 are very different; each shows a dramatically different distribution of values for return and volatility. The patterns are different, too; the extreme period is not just a more dispersed version of the normal period. Compared to the normal period, the extreme period looks almost like a time-lapse photo that reveals underwater rocks after the tide has gone out. Such very different patterns of volatility provide some empirical evidence that risk regimes can shift and that stochastic volatility models may be ineffectual at the point of transition. Furthermore, the correlation between volatility and economic fundamentals (using the S&P 500 as a surrogate for the state of the economy) hints that alternative models might provide warnings of such regime shifts. In a sense, this is another application of a Bayesian approach in which behavior different from that assumed in a prior model is used to create a new posterior model. And that posterior model might be informed by all-source intelligence; economic statistics, including expert knowledge; or other exogenous information.
Figure 8-15 Contour Plot of Historical VIX Volatility: 9-Year Period Ending
June 12, 2008
Figure 8-16 Contour Plot of Historical VIX Volatility: 1-Year Period Ending
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SUMMARY In this chapter, we discussed degrees of belief that a model or the parameters used to inform it represent the global market system. We discussed sources of model risk, including the choice of unrepresentative parameters and misspecification of the physical system from which statistical observations were drawn. We pointed out the difference between the frequentist and Bayesian approaches and the more appropriate assumptions of the latter, specifically, explicit acknowledgment that even in a randomwalk world, we cannot be confident that parameters chosen using a finite time series are characteristic of a stable market system. We demonstrated that the magnitude of such uncertainty is significant and also noted that for instrument types such as options whose value depends on uncertainty, an alternative valuation model that explicitly accounts for such uncertainty can produce very different estimates of both value and risk. Finally, we also discussed the assumptions implicit in standard stochastic volatility models and their potential failings if the market system is unstable and can evolve from one risk regime to another. WHAT’S NEXT In the next chapter, we discuss alternative methods for estimation of risk, that is, methods that do not depend on assumptions about the system, such as random motion, and do not require historical data to inform them.
CHAPTER 9
An Alternative Path to Actionable Intelligence
THE CREATION OF ACTIONABLE INTELLIGENCE One premier management consulting firm considers the financial domain to be the area of the private sector that is most like the national intelligence domain. Each performs surveillance, gathers intelligence, and analyzes massive amounts of real-time data using automated tools. In the end, each ultimately attempts to decipher the actions of humans, receives a high payoff for success, and suffers a high cost for failure. Members of both the financial and intelligence communities are given the task of anticipating adverse events and devising strategies to mitigate the consequences of those events. The ultimate goal of each is actionable intelligence—that is, intelligence that facilitates timely decision making under uncertainty. For an intelligence officer, finding actionable intelligence might mean obtaining information that thwarts a terrorist attack. For a risk manager, it might mean anticipating extreme scenarios and devising an appropriate hedging strategy. Traders are adept at running intelligence-gathering operations. Their sources include real-time news feeds, inquiries to company management, and phone calls to counterparties, research analysts, and others who can shed light in real time on potential sources of unusual trading activity. Some may even use more nefarious means and engage in insider trading based on information that they have illicitly obtained. Thus, many financial institutions also engage in counterintelligence operations: external connections on PCs are disabled, shades are always pulled down at meetings, and window vibrators that thwart listening devices are used. One firm supposedly has a clever protocol for interfering with cell phone transmissions from inside the building without violating the law. Both communities are aided in their efforts by massive amounts of real-time data, sophisticated information systems, and analytical engines, 144
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as well as visualization tools that aid human cognition. The National Security Agency (NSA) might be proud to handle the throughput on U.S. exchanges. For example, 1.83 million messages per second (where each message was an automated price indication or an order) were handled successfully at 12:17 on September 16, 2008, the day after the Lehman bankruptcy. (The average is about 200,000 messages per second.) WHEN VIEWPOINTS DIVERGE However, the two communities’ viewpoints diverge when it comes to analytical methods. Over the last 30 years or so, the financial community has focused on the development of methods to anticipate and measure known threats. With its abundance of historical pricing data, the financial community has focused on calculating the probability of possible future events, using history as its guide. These future events are expressed statistically, e.g., the probability of a 10 percent drop in the price of one security or of a loss of $1 million in one day for a securities portfolio. Such market events might have been directly caused by a news item such as a robust economic release, a poor earnings report, or news of an accounting fraud. Nevertheless, the stochastic techniques that are nearly universally used to address this task implicitly assume that such events will occur with the same frequency in the future as they have in the past. Causal relationships are not explicitly modeled, but rather inferred from statistical measures such as correlation. Conversely, the intelligence community has focused on anticipating and ranking unknown threats. For example, since there have been few instances of successful terrorist attacks on U.S. soil, historical data on such attacks are sparse, and the intelligence community instead measures the plausibility of possible future events such as a radiological or biological attack by Al Qaeda. Thus, the financial community, with its abundance of historical data, has generally taken a stochastic approach that does not require expert knowledge of fundamental drivers. Conversely, the intelligence community, with its sparse historical data amenable to statistical analysis, has taken a causal modeling approach that instead relies on expert opinion and interpretation of past experience. Essentially, the financial community considers the future to be well represented by the past, while the intelligence community does not. Today, the homeland security community has been moving toward more objective and quantitative measures of risk. In 2005, Michael Chertoff, the former secretary of the Department of Homeland Security
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(DHS), outlined an emerging strategy for assessing homeland security risks. According to the secretary, the department will use a combination of threat, vulnerability, and consequence analysis as a general model for assessing risk and deciding what protective measures, if any, should be taken. SCENARIO GENERATION Scenario Generation in the Financial Community Most risk managers in the financial community generate scenarios both quantitatively and qualitatively. For purposes of trading and estimation of everyday risk measures such as VaR, risk modelers employ statistical methods that explicitly specify all possible scenarios in the form of a continuous distribution. For purposes of capital adequacy and the estimation of extreme risk measures such as enterprise risk, risk managers generally identify actual historical scenarios and hypothetical extreme scenarios posited by experts. Scenario Generation in the Intelligence Community Conversely, analysts in the intelligence community don’t often have the option of creating statistical models of threats to national security. Whether they are analyzing threats to a particular facility (for example, a power plant) or a more diffused threat such as that from cyber attacks, history provides little quantitative guidance. This is so not only because historical experience is sparse, but because external threats, such as those from Al Qaeda or state actors, are the ultimate complex, adaptive system. Measures, countermeasures, and counter-countermeasures by all parties involved mean that the precise nature of any attack is unlikely to play out in the same manner as any previous one. Modeling of threat scenarios (where models might range from conceptual models to internal cognitive models) is therefore conducted in a more qualitative fashion, albeit using a disciplined approach. (In the context of this book, the term “model” includes both mathematical models and conceptual models). Experts often create case studies, in which a particular attack scenario is analyzed from every angle. To assist them in making this analysis as complete and realistic as possible, intelligence analysts elicit expert opinion in a number of different ways. For example, they often conduct so-called red-team exercises, in which experts with various skill sets are gathered together and asked to put
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themselves in the role of the adversary and create ingenious strategies and tactical maneuvers. Similarly, they might also conduct war games, in which experts are assigned to various adversarial teams (e.g., the U.S. team or that of a hostile nation) and play out some threat according to predefined rules. In the military, such war games might involve aircraft carriers and submarines, but in northern Virginia, they might be conducted in an office with the aid of computer models. One version is Command Post Exercises (CPX), in which forces are simulated including interplay between commanders and staff in the field and at headquarters. War games have the added benefit of introducing the effects of human behavior into the mix—sometimes leading to surprising results. THE HUMAN INABILITY TO MODEL COMPLEXITY Humans are not particularly skilled at identifying plausible future scenarios or determining their consequences. This is especially true when the most adverse outcomes are the result of a complex chain of causal events. Furthermore, without the aid of a sufficiently structured approach, humans are particularly vulnerable to confirmation bias, or the tendency to value information that confirms their existing beliefs over information that contradicts those beliefs. Confirmation bias intersects with greed, as well; risk managers have been fired for suggesting to senior management that risk (and consequently profits) should be dialed down. Causality in Action: AIG Financial Products For example, consider the multiple risk management failures of AIG. In retrospect, we know that AIG held massive, mostly unhedged short positions in swaps that insured collateralized debt obligations (CDOs).1 Such securities are illiquid and difficult to value—at least when held in AIG’s size. Although AIG was vulnerable to market risk, its greatest source of peril came from credit risk and liquidity risk. If the portfolio lost value on a mark-to-market basis or if AIG became less creditworthy, AIG might be forced to post huge amounts of collateral to its counterparties in these over-the-counter (OTC) transactions. Since AIG had been downgraded once before (in 2005), the counterparty agreements required AIG to post billions in additional margin if either the value of its portfolio fell or AIG’s credit quality declined. These rules set up a feedback loop: if the portfolio lost value, then AIG became
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less creditworthy and had to supply additional margin, which in turn made it even less creditworthy and triggered more margin calls. (And when AIG finally reached its tipping point, it infected the entire financial system through its direct and indirect links with other financial institutions.) Furthermore, AIG had little ability to modify its risk profile. Once the slide began, liquidating part of its position or otherwise mitigating its losses would have been prohibitively expensive. This was true not only because market prices had already moved against AIG, but because any major restructuring or hedging activities would have been instantly observed by the rest of the trading community, and it would have smelled blood. In a dynamic VaR model (in which both changes in market conditions and voluntary actions along the path are simulated), such a feedback loop would have been recognized, and the probability of an extreme outcome would have been estimated to be far greater than that predicted by a static VaR model. With the benefit of hindsight, it seems obvious that AIG was playing with fire. But exacerbating its risk was the fact that, by all accounts, AIG was a top-heavy (command-and-control) organization, in which risk decisions were made in a highly subjective fashion. Furthermore, the head of AIG Financial Products (AIGFP) was Joseph Cassano, who, although he was deemed an excellent operational manager, had no quantitative background. As one article relates, “As late as August 2007, Cassano had failed to recognize the danger. ‘It’s hard for us, without being flippant, to even see a scenario within any kind of realm of reason that would see us losing a dollar in any of those transactions,’ he told AIG investors that month on a conference call.”2 Cassano made this statement in spite of direct evidence that credit quality was already slipping. As shown in Figure 9-1, all grades of credit spreads (as represented by the Dow Jones CDX indexes3 for the United States) had already started to spike by July 2007. The die was probably already cast at the time of Cassano’s statement. AIG was subsequently downgraded several times in 2008, Cassano resigned just seven months after his statement, and the U.S. government moved in to take control of AIG just six months after that. GENERATING PLAUSIBLE SCENARIOS At the heart of all risk measurement (and in fact all financial engineering) is the ability to generate every plausible future scenario and estimate its likelihood. But whether plausible and probable are close enough for risk
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2000 Investment Grade Crossover High Yield
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management depends on the nature of the system under consideration. If that system is more or less stable, then probable may be good enough. But if, instead, the system is vulnerable to endogenous or exogenous shocks that lead to extreme scenarios, then history is an inadequate guide and may even be a liar. QUANTITATIVE SCENARIO GENERATION In Chapter 7, we discussed structured analysis, that is, a systematic method for building a conceptual model of reality. Recall that a conceptual model is a collection of knowledge and interdependencies used to represent the dynamics of a real-life situation. Such structured analysis is a kind of quality control designed to enforce completeness. We can also impose a more rigorous framework to guide model building. One such framework is particularly relevant to the field of threat assessment (including physical threats). A Framework for Threat Assessment One framework proposed by Bryan Ware, CEO of Digital Sandbox (a threat risk management firm in McLean, Virginia), states that a company’s risks are determined by what the company is, what relationships it
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has, what it provides, and what it requires. The financial analog to this framework might be a hierarchical, object-oriented inheritance system (based on industry classification codes or the like) that integrates historical observations, fundamental market drivers, and expert opinions about the consequences of those drivers. In a true decision support framework, the risk metrics used by Ware to quantify an event are • Likelihood/probability • Susceptibility/vulnerability • Consequences/impact These are particularly appropriate where only actionable intelligence is of value. For example, the results of an analysis might be used to harden a target and reduce the consequences of an attack if there is no way to decrease the likelihood of the attack. To implement this approach, Ware creates Bayesian risk metrics that are fundamentally different from the stochastic methods that are generally used in finance. In this methodology, risk is considered to be a function of likelihood, susceptibility, and consequences. Bayesian networks4 can be used to explicitly generate every possible scenario that is consistent with model assumptions and estimate the likelihood and consequences of each. Unlike classical inferential models, Bayesian inference models allow the introduction of prior knowledge and expert opinion into the calculation.5 Such alternative methods are ideal for generating actionable intelligence. Causality makes risk actionable; removing the cause removes the effect. In addition, scenarios must be understandable if they are to be actionable, and the transparency of a causal model (in which it is possible to directly trace the path to a particular outcome) is head and shoulders over that of a statistical black box. (Such models will be explained in additional detail starting in Chapter 11.) COMPARISON OF RISK METHODOLOGIES Fortunately for the financial community, even though the past is not a perfect predictor of the future, historical patterns in prices provide a great deal of information that might be useful in informing both stochastic and causal models. Because prices reflect aggregate opinion, changes in prices tend to be driven by repetitive human emotions such as fear and greed. Causality, too, might be inferred from historical relationships. Although correlations between an asset and a fundamental risk factor might provide
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some indication of a causal relationship, there are more explicit methods used to infer causality in the fields of econometrics and decision science. Likewise, even though historical information may not be of much direct use in modeling a hypothetical threat, the intelligence community might benefit from information derived from open-source market prices converted to knowledge using quantitative sensemaking models. For example, the credit default swap (CDS) spread for the sovereign debt of a given state actor can be mathematically converted to a probability of default by a given horizon date, and this might be used as a metric of sovereign state instability. Analysts from both communities might benefit from a fusion of their best models and methodologies. The financial community might more
T A B L E 9-1
Comparison of Attitudes toward Risk between the Intelligence and Financial Communities
Characteristic
Intelligence Community
Financial Community
Purpose of risk management Attitude toward risk
Defend homeland
Profit
Always a negative; to be eliminated or mitigated
Makes markets work (risk transference); taken voluntarily and deliberately (within limits) to earn risk premia
Sources of risk Types of models Focus
External forces (e.g., state and nonstate actors) Conceptual/causal Catastrophic scenarios
Data View Transparency Methods for risk control
Expert opinion Forward-looking High Prevent attack; harden target
Solutions
Last line of defense
Provide information tools (e.g., data to knowledge) to analyst None
Style
Collaborative (theoretically)
Taken voluntarily and deliberately Stochastic Everyday and extreme scenarios Historical experience Backward-looking Low Risk-based position limits; reallocation of risk capital; hedging strategies More and better models
U.S. and world government intervention Competitive (theoretically)
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explicitly include cause and effect and expert opinion in its models, while the intelligence community might likewise include more mathematical models, automated sensemaking tools, and open-source market data. Table 9-1 compares their attitudes toward risk and general approaches toward solutions. SUMMARY In this chapter, we discussed the importance of creating actionable intelligence. We discussed the similarity of the financial and intelligence communities, but also compared the very different analytical methods that each uses for risk measurement and threat assessment. We posited that each might benefit from adapting some of the models and methods of the other when evaluating the likelihood and consequences of extreme events. WHAT’S NEXT In the next chapter, we discuss general approaches toward obtaining knowledge that might be used to make practical the construction of a connectivist model that links market drivers and market movements.
CHAPTER 10
Solutions: Moving toward a Connectivist Approach
CONNECTIVISM AND LEARNING As described by learning theorist George Siemens,1 “Connectivism is the integration of principles explored by chaos, network, and complexity and self-organization theories.” Learning might be described as the search for actionable knowledge, and connectivism can facilitate this search. A learning system is an analytical system that is adaptive and has a feedback mechanism. When information is viewed in a framework of a rich and interconnected network, inferential methods can be used to learn accurate, up-to-date knowledge. Mathematician Ian Stewart described chaos as “a cryptic form of order.” As he explained, “Chaos is not random: it is apparently random behavior resulting from precise rules.” T. K. Landauer and S. T. Dumais2 pointed the way toward making sense of such chaos when they noted, “The simple notion that some domains of knowledge contain vast numbers of weak interrelations that, if properly exploited, can greatly amplify learning by a process of inference.” In a sense, learning is the creation of patterns via connections and recognition of the meaning of those patterns. Naturally, such a network is dynamic. As Siemens also pointed out, “Connectivism is driven by the understanding that decisions are based on rapidly altering foundations.” In this information age, chaos is increased, but so too are the tools that can extract meaning from chaos. The data that might be used to inform an inferential model—both raw data and data tagged information that can be used to establish connections—make it possible to leverage recent advances in systems and network theory. Possibly the greatest advantage of a more formal approach toward converting data to knowledge is that it reduces uncertainty. These principles of 153
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learning give us the means to identify knowledge and use it to better predict expected and extreme outcomes and to affect a system’s evolution. THE KNOWLEDGE LANDSCAPE Optimal decisions—whether they are reached subjectively by humans or in an automated fashion by machines—are best informed not by data or information, but by knowledge. In the field of knowledge engineering (that is, the field of skills required to build knowledge systems such as databases, expert systems, and decision support systems), knowledge has different meanings. As data, it may represent a single fact. As information, it may represent many pieces of data organized so that they carry meaning. Knowledge, then, is information that must always be expressed in context, where issues such as importance and accuracy are critical to the use of that information. In this field, a knowledge model may be defined as a personalized representation of an individual’s knowledge. A book review is an example of a nonquantitative knowledge model. Similarly, a knowledge landscape is a map of all knowledge models.3 A list of the best reviews on a given subject is an example of a nonquantitative knowledge landscape. The term knowledge model has a similar meaning to software engineers: it is a formalized framework that is used to identify the knowledge needed for decision support. A key objective is the implementation of methods that allow sharing of the idiosyncratic knowledge of expert practitioners within an organization or among organizations. A knowledge model may be object-oriented, or it may have some other equally valid structure. The knowledge landscape, then, for a financial application might include statistical representations of history, deterministic relationships identified by subject matter experts, causal relationships inferred from historical patterns, and factual information such as regulatory requirements or margin and collateral rules. SENSEMAKING: TRANSFORMING DATA TO KNOWLEDGE Connectivism facilitates the transformation of data to information and information to knowledge via a sensemaking process. Given the disparate data with which it must deal, the U.S. intelligence community is acutely interested in identifying advanced techniques for converting data to knowledge.
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Knowledge Discovery in the Intelligence Community A case in point is the Intelligence Advanced Research Projects Activity (IARPA), a government entity that has been given the task of investing in innovative and out-of-the-box research. Reporting to the Director of National Intelligence’s Director of Science and Technology (ODNI/ DS&T), IARPA has no direct operational responsibility, but instead focuses on high-risk/high-payoff research that might potentially provide the U.S. intelligence community with future advantages. IARPA has three areas, two of which are the Office of Smart Collection and the Office of Incisive Analysis. Together, these two areas advance the process of knowledge creation. In IARPA’s own words,4 “Intelligence analysts are tasked with identifying relevant information within massive data and synthesizing these fragments into a coherent understanding of the entities, events, and relational networks that characterize a data space. This process of adaptively filtering and interpreting data has been termed ‘sensemaking’ in the literature.” The Role of All-Source Intelligence The intelligence community values all-source intelligence highly. Consistent with connectivist learning theory, the fusion of information from diverse disciplines has been proved to enhance knowledge discovery. Such fusion is a method for connecting the dots, for eliminating false positives, and for ranking the quality and reliability of hypotheses. This principle is one of the primary reasons for the creation of the Directorate of National Intelligence and the increased emphasis on information sharing since 9/11. The connection of specialized information from diverse sources, or the connection of knowledge to create better knowledge, can increase our confidence in the accuracy of that knowledge. And increasingly, the intelligence community is using open-source intelligence toward that end. With the tremendous growth in the quantity and quality of information gleaned from completely public sources, this community can leverage the information-gathering and information-structuring activities of other disciplines. However, sensemaking is critical. For members of the intelligence community, too much data is often more of a problem than too little. The decision-making process of an intelligence analyst may be informed by HUMINT (human intelligence), by SIGINT (signals intelligence), or by one of several other “INTs.” Therefore, decision support tools in this community take the form of fused intelligence in a form and format that allows
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quick action. Such tools include intelligent information filtering tools, customized visualization and drill-down tools, and useful risk metrics. SENSEMAKING IN COMMAND AND CONTROL The command and control (C2) of military forces involves perhaps the most advanced use of sensemaking anywhere. Clearly, it is impossible for military commanders to micromanage the complex system that is modern warfare, especially given the required response time for new decisions. This is so because they are dealing with a complex adaptive (i.e., self-organizing) system that evolves quickly as a result of changes in the system or in its environment. Thus, the modern military utilizes sensemaking in all its forms. Sensemaking involves the creation of situational awareness, the transformation of information to knowledge, and enhanced decision making—all in an atmosphere of uncertainty and rapidly changing dynamics. Such concepts have moved well beyond theory; they have been implemented in the form of network-centric operations (NCO). NETWORK-CENTRIC OPERATIONS AND MODERN WARFARE Network-centric operations—even for very large-scale and complex networks—have a proven track record of success. In previous chapters, we discussed the fact that a self-organizing network, in contrast to one controlled by outside forces, is capable of quickly evolving to a new state characterized by optimal flexibility via interactions among its component elements. Nowhere has this concept been so taken to heart as within the U.S. Department of Defense (DoD). DoD’s Office of Force Transformation (OFT5) has described networkcentric warfare (NCW) as “an emerging theory of war in the Information Age” that “broadly describes the combination of strategies, emerging tactics, techniques, and procedures, and organizations that a networked force can employ to create a decisive war fighting advantage.” NCW is probably the most ambitious application of network-centric operations in any discipline, and one whose benefits are most evident in the form of enhanced battlefield knowledge and flexibility. This flexibility means that the system is able to rapidly achieve any one of a number of states, thus minimizing response time to any of a number of tactical moves by an adversary. Vice Admiral Arthur Cebrowski, who held a master’s degree in computer systems management from the Naval Postgraduate School, is
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considered to be the father of network-centric warfare (now more commonly known as network-centric operations). He envisioned transforming U.S. defense, using the principles of complexity theory. As related by Dr. James Moffat, “ADM Cebrowski . . . indicated that Network Centric Warfare is an emerging theory of war based on the concepts of nonlinearity, complexity, and chaos. It is less deterministic and more emergent; it has less focus on the physical than on the behavioral; and it has less focus on things than on relationships.” Sensemaking is key to a concept such as this, which offers so much promise in optimizing a combat model. Just as in the Bak-Sneppen evolutionary model, the idea is to allow the battle state to evolve to one that allows maximum flexibility—that is, one that can respond to any of a number of decisions by an adversary. Nevertheless, in response to new information and analysis, commanders can still change the evolutionary path by their command decisions. As related to Congress by the Congressional Research Office, “NCO is intended to increase collaboration through the free flow of information across the battlespace so that acquired data is shared, processed into information, and then provided quickly to the person or system that needs it.” NCO is sometimes viewed as primarily a technological development, one in which networked communications, advanced hardware, and sophisticated sensors provide the ability to create a shared awareness of battle-space conditions. The input to the system is new information, and the output is a decision (e.g., orders). Although all these factors facilitate NCO, it is instead probably the most sophisticated and operational application of complex systems theory in the world. Naturally, creating such shared awareness requires sophisticated technology. As just one example, Battle Management Language (BML) has been described as, “an unambiguous means of describing military operations to people, simulations, and robotic forces” and as a “transformational enabler.”6 (BML is not unlike other extensible languages, such as those used within the financial community to communicate transactions in complex derivative securities.) The nature of modern warfare is also highly path-dependent. In this context, path dependency means that the outcome and the rate of change are highly dependent on the initial conditions. One objective of networkcentric warfare is to allow the system to come to a state that allows optimal starting conditions and rapid response. Sensemaking in all its aspects is, then, critical to such system optimization. Sensemaking within an NCO framework requires that all key factors be identified; this is akin to knowing the who, what, where, when,
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and why. In a technical war, this information might be provided by sensor arrays and other intelligence. The Congressional Research Office report provides an excellent example of how networked forces can spontaneously generate new tactics in response to nontraditional threats in the field. In OIF [Operation Iraqi Freedom], U.S. Army forces utilized movement that was described by some as “swarm tactics”. Because networking allows soldiers to keep track of each other when they are out of one another’s sight, forces in Iraq could move forward spread out in smaller independent units, avoiding the need to maintain a tight formation. Using “swarm tactics,” unit movements are conducted quickly, without securing the rear. Network technologies enable all units to know each other’s location. If one unit gets in trouble, other independent units can come quickly to their aid by “swarming” to attack the enemy from all directions at once.
In another natural experiment, Israel reportedly benefited from such an approach in its short clash with Syria- and Hezbollah-supplied troops in 2006. The future of conflict seems to be shaping up as network-versusnetwork warfare. The Congressional Research Office report also noted a number of NCO-like efforts by state and nonstate actors. The European equivalent of NCO is network-enabled capability (NEC). NEC is defined as the coherent integration of sensors, decision makers, and weapons systems along with support capabilities to enable superior decision making. NATO has established the Network Centric Operational Industry Consortium to define open standards and allow collaboration between allies. The United Kingdom (a single, generalized network architecture called Global Information Infrastructure, with a specialized application for battlefield applications), Australia (an innovative networked sensor technology and the use of unmanned vehicles that maximize the country’s small force), Germany (a future soldier system named Infanterist der Zukunft, or Infantryman of the Future), and France (a system called Guerre Infocentre or Infocentric Warfare, which emphasizes information flows rather than the network) all have ongoing efforts in this direction. China’s focus is somewhat different, with an emphasis on disruptive technologies. As the Congressional Research Office report indicates, China is emphasizing the development of new-concept offensive tactics such as electromagnetic pulse (EMP) systems that can jam its adversaries’ networks, and defensive tactics such as separate GPS networks that might immunize its military from a failure of other satellites and networks.7
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As the report also indicates, “Recent publications from China and national defense policy use terms such as ‘informationalization’ and ‘Integrated Network-Electronic Warfare’ (INEW), while describing how warfare is becoming more information oriented. Chinese military officials have stated that the INEW concept is comparable to U.S. Net Centric Operations. However, while INEW involves acquiring both defensive and offensive information operations capabilities, there is a premium placed on developing active strategies for offensive information operations.” NCO is, of course, vulnerable to deficiencies in communications and computing. An enemy could profit either from deceiving or blocking the sensor arrays that gather data or from interfering with the transmission of information between the nodes of the network and the automated sensemaking and decision support systems. NCO relies on the heavy use of technology to facilitate communication between nodes. Although on its surface NCO speeds information and sensemaking, its more subtle benefit is the ability to allow optimal self-organization at a local and system level, that is, to allow emergent behavior of the network to deal with emergent threats. We may see more examples of both emphasis on the development of technology to defeat others’ NCO and tests (satellite or commercial network attacks) that might be field tests. Some theorize that the rapid increase in sustained intelligencegathering cyber attacks directed against the Pentagon and other military networks (such as an extended and successful intrusion into the DoD’s Non-Classified IP Router Network that obtained many terabytes of data) may have originated in China, and in fact may be trial runs for potential offensive actions. Even nonstate actors such as Al Qaeda exhibit some characteristics of NCO, and the cellular structure of their organization enables them to execute tactics locally with little direct C2 communications. This has an additional advantage: it helps Al Qaeda maintain operational security and secrecy. For example, unconventional communications and money transfers can occur via mechanisms such as hawala, an informal money transfer system that involves a large network of money brokers. MODELING CONNECTIVITY In previous chapters, we discussed the dependence of any system on its interconnectivity. For good or ill, connectivity permits the propagation of effects from causes, often in unintended and unpredictable ways. Connections might be direct: a tree might burst into flames if it is in
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sufficiently close proximity to another that is burning. Or, they might be less direct: Russia’s political choices contributed to Long-Term Capital Management’s downfall. We know from systems theory that the presence of complex dynamics and intricate relationships can cause a system to adapt in a manner that is unpredictable without sufficiently robust models. But the task of creating such a model is difficult. Given the number of connections in any complex system, a literal representation of such a system would be computationally intractable and impossible to update, and might introduce additional sources of model risk. Instead, some conceptual representation of the system that includes those and only those variables necessary for identifying extreme scenarios or emergent behavior is ideal. There are a number of methods used by the national security community for informing or validating a network model that might well be adapted to other disciplines. These include the agent-based approaches previously discussed, that is, where the evolution of a system is modeled by specifying the starting conditions and the rules of interaction. Two additional methods that leverage human knowledge and creativity are war games and red-team exercises. WAR GAMES AND RED-TEAM EXERCISES Those who take on the daunting task of specifying a network on the scale of the U.S. military often avail themselves of expert knowledge. Just two of the methods for doing so are war games and red-team exercises, used by the military, intelligence, and homeland security communities. These may be physical exercises (e.g., a simulated attack on the Brooklyn Bridge or a submarine exercise in the North Atlantic), or they may instead be strictly thought experiments. With a proper population of adversaries, and with a structure that provides meaningful results, researchers who study the game can gain insight into the mechanics of drivers, response, and output from field practitioners. War Gaming War gaming is a tried-and-true method of identifying extreme scenarios by letting them play out in a controlled environment. A war game is an artificially constructed microcosm of a system of interest or some subsystem of a larger system. War games measure human responses under tightly controlled conditions, so that all variables other than the human factor are known.
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In the classic form of the exercise, one or more outcomes are generated. They are generally two-player (red team and blue team), zero-sum games conducted in a series of discrete time steps. Given that conducting a war game—even a virtual one—is expensive and resource-intensive, the objective is generally to identify typical outcomes rather than outliers. Generally, the game designer will strive to weed out both gross incompetence and innovative brilliance. This is done because neither of these is likely to occur in practice, and thus they will provide little information about how to tweak the system so that it will prevail in much more likely scenarios. Although identification of many extreme yet plausible scenarios is a worthy goal, war games are usually not the best mechanism for eliciting such scenarios, because they represent just one perturbation of the system. Instead, war games might be more useful as a method for establishing reasonable rules with which to populate an agent-based simulation. And in order to make the situation realistic, great pains must be taken to provide the red and blue teams with only the information that they might have in the course of a campaign, and that they might use to inform their strategic and tactical decisions at each step in the game. In this manner, the information elicited is consistent with that envisioned for a straw man network design. For example, the designer of the war game might ensure that the members of each team are receiving intelligence only from sensor arrays, just as they would in real life. There is a concept called Intelligence Preparation of the Battlefield (IPB) that sets knowledge at the start of the exercise. Then, in a series of discrete time steps, each commander can make both strategic (the plan for the battle) and tactical (e.g., actions such as reassignment of battlefield assets) decisions at each step. The commanders may be uncertain about the reliability of intelligence and therefore their current state of knowledge, and let the odds and their utility function inform each of these decisions. Red-Team Exercises War games are intended to elicit human behavior in the form of command decision making and, if properly constructed, can serve as an exceedingly useful learning exercise. However, because they are intended to play out only the one or two scenarios that are gauged most likely to occur, wargame exercises necessarily suffer from a lack of completeness. That is, they will not—nor are they intended to—generate extreme scenarios. Another method used to do so is the red-team exercise. In such an exercise, a number of subject matter experts are recruited to design
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plausible attack scenarios or otherwise assess vulnerabilities and gauge the quality of defenses to some threat (real or hypothetical). The red-team participants might each create one or two case studies of possible attacks by terrorists: for example, additional attacks using aircraft or attacks on nuclear facilities. Then the group critiques each scenario and brainstorms regarding potential solutions. The final deliverable of a red-team exercise might be a vetted list of feasible yet extreme scenarios, along with recommendations for decreasing their likelihood, our vulnerability to them, or the consequences if they are successful. Agent-Based Approaches When network theory is integrated into the design of a more sophisticated and automated version of a war game, such exercises can yield additional fruit. A red team exercise—like a war game—also suffers from incompleteness because it requires human experts. However, the results of each might be used to inform an automated, agent-based approach that can conduct thousands or millions of iterations, identify all plausible outcomes of interest, and generate useful statistics such as a distribution of the size of cascades of interest.8 MOVING TOWARD A CONNECTIVIST APPROACH IN FINANCE The financial community can take advantage of a connectivist approach that links market drivers to market movements (i.e., cause and effect). Besides providing analytical and forecasting advantages, an approach as rigorous as that of network-centric operations (and the methods used to inform its models) might well reduce risk at both the enterprise and the system level. We might consider a market system to be nothing more than a special kind of ecosystem, one that’s driven by the collective and connected behavior of humans. And what drives humans is not truth, but knowledge; their actions are a function of their own notions of causality, predictability, and uncertainty. In the financial space, connectivism also facilitates the transformation of data to information and information to knowledge via a sensemaking process. For example, in the financial space, historical prices are data, correlation coefficients are information, but cause and effect is knowledge. COMPLEXITY THEORY, COMBAT, AND TRADING The complex systems in which combat and trading occur are not so very different, at least in theory. Table 10-1 reproduces Dr. Moffat’s illustration
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T A B L E 10-1
Comparison of Complexity Concepts to Combat and Trading
Complexity Concept
Information-Age Force
Global Trading
Nonlinear interaction
Combat forces are composed of a large number of nonlinearly interacting parts.
A trading enterprise consists of many diverse trading activities and venues.
Decentralized control
There is no master “oracle” dictating the actions of each and every combatant.
Self-organization
Local action, which often seems “chaotic,” induces long-range order.
Individual traders and units have a great deal of local autonomy with respect to trading decisions. In general, senior management becomes involved only when problems occur or risk limits are violated. As expressed by the efficient market hypothesis, market forces aggregate the effects of all local actions in market prices, which exhibit reasonably orderly behavior.
Nonequilibrium order
Military conflicts, by their nature, proceed far from equilibrium. Correlation of local effects is key.
Adaptation
Combat forces must continually adapt and coevolve in a changing environment.
Collectivist dynamics
There is continual feedback between the behavior of combatants and the command structure.
Market prices exhibit nonGaussian, “fat-tailed” behavior, with occasional volatility spikes and clusters. One initial event may trigger a cascade of similar behavior (e.g., continued selling) by others based on behavioral considerations or risk limits. Traders and their management continually create products, develop models, and avail themselves of advances in technology to obtain a competitive edge. Those participants who are at a disadvantage cease to exist because they cannot match returns. The C-suite (e.g., CEO, CFO, and CRO) as well as traders and portfolio managers are informed in real time about P&L, risk metrics, and other information.
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of concepts from complexity theory and the theory’s suitability for an information-age military force, and includes as a new column the author’s analogs from the world of global trading. INFLUENCING EVOLUTION Previously, we described the evolution of a system in terms of movement toward some attractor: that is, one that causes the system to self-organize to maximum flexibility. However, this evolved state, while having a number of benefits, may not be a desirable one for the humans that live within it or other systems that interact with it. We’ve noted that changing the rules of the game influences the evolution of a system, and this is a role for an exogenous controlling intelligence that might “tune” the system to assist it in reaching some goal (or avoiding an adverse regime shift). Timing is an issue as well; for example, the responsiveness of a controlling intelligence—be it U.S. regulators and policy makers or the Joint Chiefs of Staff—relative to the speed of selforganization may constrain its ability to direct the system toward a goal. SUMMARY In this chapter, we discussed the concept of connectivity as a learning system. We revealed the use of network-centric operations in modern warfare as one of the most sophisticated implementations of such principles, and as a decision-making tool that takes advantage of the self-organizing features of a complex system. We also noted some of the similarities with respect to complexity between an information age combat force and global trading activities, and noted the ultimate use of connectivist approaches: that is, to influence evolution. WHAT’S NEXT The next chapter provides an introduction to the principles of causal inference.
CHAPTER 11
An Introduction to Causality: Theory, Models, and Inference
HISTORICAL VIEWS OF CAUSALITY Causal inference is the process by which causality is determined. But until recently, the notion of causality was more the domain of philosophers than of mathematicians. For millennia, the precise definition of causality has been a philosophical minefield. In 1739, the Scottish philosopher and economist David Hume defined causality this way: “We may define a cause to be an object precedent and contiguous to another, and where all the objects resembling the former are placed in like relations in precedence and contiguity to those objects that resemble the latter.” In other words, Event A can cause Event B only if (1) A precedes B, (2) whenever A occurs, B inevitably follows, and (3) A and B are contiguous (i.e., touch each other directly). In Hume’s world, a set of causal relationships could be inferred by repeated observations that provide a framework for building up a set of causal relationships. This definition is consistent with the human experience, as humans have developed the ability to recognize causality at a very early age. Infancy researchers have shown that even babies younger than 10 months rely on cues from temporal priority, temporal contiguity, or spatial contiguity to infer causality and make decisions. While Hume’s definition seems obvious, it has a number of flaws. Most important, it applies only to deterministic processes—that is, ones that carry the rule of law—with relatively simple forms. In a deterministic system, if Event A is a cause of Event B, then whenever A occurs, so too will B. In such a system, smoking does not cause lung cancer, because not every smoker contracts this disease. But causality doesn’t always run so neatly downstream, either temporally, spatially, or logically. Hume’s definition is rife with opportunities 165
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for both false positive and false negative inferences about causal relationships. Humans often perceive causality where it does not exist (e.g., because two events occurred simultaneously) or miss causality where it does exist because of the complexity of the relationship (e.g., where there are several intermediate steps between the cause and its effect). Hume’s definition does not deal with spurious conclusions, in which both A and B are caused by a common third driver C. Also, there are no constraints on how A and B are defined. If they are unskillfully specified, they may be too all-encompassing: they may skip a number of intermediate causes and thus break the chain between cause and effect. Nor does Hume’s definition deal with counterfactuals. A counterfactual conditional is an “if-then” statement about what would have happened if the antecedent (the “if” part of the logical statement) were true and “if” preceded “then” temporally.1 For example, night follows day. When day occurs, night inevitably follows, and night and day are always contiguous, yet day does not cause night. Hume’s approach does not allow for alternative explanations. Hume’s definition also does not deal with probabilistic causes, for example, those in which A often causes B, but not always. A wet floor often leads to a fall, but not always. In addition to such logical flaws, even assumptions about temporal priority are suspect in modern applications. Besides the astonishing revelations from twentieth-century relativity theory and quantum mechanics, which wreak havoc with our intuitive understanding of cause and effect, practical issues such as feedback loops and the anticipation of future effects require us to consider causality in the context of the system we are attempting to model. For example, in a financial system, prices move in anticipation of an earnings release or employment report, and so the news release and the price movement due to it are not synchronous. In an economic system, forward grain prices reflect anticipated changes in farmers’ planting intentions (for example, a reallocation of acreage from corn to soybeans) when spot prices are high or low. THE UTILITY OF CAUSALITY In spite of such issues, there has been a tremendous surge of interest in causal inference methods and models in the last two decades, addressing such questions in both philosophical and mathematical terms. Today, there are more mathematically rigorous definitions of causality, although this is still a lively area of discussion.
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Much of the theoretical work on this topic has occurred in computer science departments, because its strict enforcement of logical principles has obvious applications in decision theory. Artificial intelligence, like human intelligence, might be gauged by its ability to make optimal decisions without all the facts. Based on such a theoretical framework, there are now a variety of methods for inferring causality, even in complex systems. These are particularly important in dealing with interdependencies that are so complex that they strain human cognitive capabilities. Causal methods are already widely used in fields such as epidemiology, where contagion can be explicitly modeled and the effect of certain intervening actions can be measured. In finance, such models can likewise provide the ideal framework for forecasting—and interfering with—the set of plausible future scenarios. Ultimately, the use of causal methods may enhance the ultimate objective of risk management, that is, enhanced, quantitative decision making under uncertainty. INDUCTIVE REASONING, RISK MANAGEMENT, AND SKEPTICISM Causal models provide a framework that helps to mitigate certain cognitive biases. They also provide a foundation for inferring causality from empirical data alone. As a result, they are particularly well suited to the field of quantitative risk management, in which risk has many sources, many of which interact. Arguably, the most important skill of a quantitative risk manager is the ability to perform inductive reasoning, that is, to employ a rational and logical approach to model building in which all available information is used to create a theory that is consistent with that information and that allows the prediction of future outcomes. Similarly, inductive inference is reasoning about the behavior of objects when they are observed in order to make judgments about the behavior of objects when they are unobserved. Inherent in such reasoning is the requirement that the risk manager be skeptical of any assumption that is explicitly or implicitly contained in a risk measurement model. For example, she must be careful to avoid human biases, such as a predisposition to assume that patterns that existed in the past will continue to repeat in the future. A risk manager cannot assume a stable system—or use statistical methods that implicitly do so—without having validated this critical assumption. For example, intelligence analysts must often rely on inductive reasoning and inductive inference to perform analyses. And the intelligence
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community’s emphasis on all-source intelligence (that is, diverse intelligence from a number of different sources) is consistent with the standard for inductive reasoning that theory must be consistent with all available information. The information used to inform theory may be of various types. It may be completely deterministic, be completely random, or have some functional dependence that includes an element of chance. It may be based on fundamental knowledge of the processes involved, or it may be derived strictly from historical observations. It may be validated using scientific methods, or it may consist only of expert opinion. In practice, interdependence among elements can be expressed in different ways. It may be shown as simple decision tables, linear equations, or continuous functions. Or it may instead include complex dependencies and triggers, nonlinear equations, and noncontinuous functions. Naturally, an analyst will have varying degrees of confidence in these different types of knowledge and their continued reliability into the future. Clearly, deterministic relationships rank highest by this measure and unexplainable correlations lowest. For example, when estimating the probability that an asteroid will hit the Earth, the laws of physics will provide more comfort than will some mathematical curve fit based on the observed path of the asteroid while it is still outside our solar system. While the more complicated representations of knowledge naturally introduce issues with computational tractability, a general approach to theory and model building should allow a framework for including knowledge in as uncompromising a form as possible. Causal inference models provide such a framework; they allow the integration of knowledge of various forms. Such models are also the most general form of model. They allow the inclusion of completely deterministic relationships that lead to certain outcomes, completely statistical models in which every relationship is governed by chance, and anything in between. For example, a Bayesian net can be used to numerically estimate the joint distribution of a number of continuous, independent, random variables with ease, but a statistical function cannot do the same when the variables are not continuous, are not independent, and have a complex interdependency. Causal models’ greatest advantage may be that they enforce a certain amount of intellectual rigor in which critical thinking is required, assumptions are questioned, and all future paths are populated.
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CAUSAL INFERENCE In many cases, causal inference provides a disciplined method for avoiding cognitive biases such as questionable cause, in which a causal relationship is assumed because two events occur simultaneously (e.g., “I wore my lucky socks, and we won the game”). The process of inference merely refers to the solution of a causal model. Consider one of the key questions in causal inference: how can one distinguish between mere correlation and cause and effect? One of the best methods of validating causal relationships is via experimentation, as in drug trials. As will be discussed in Chapter 15, the financial markets—if examined at a sufficiently granular level—can serve as an experimental laboratory that continuously provides us with natural experiments. REPRESENTING REALITY AND CAUSAL INFERENCE Causal inference can occur only after causality is better defined. A more general definition of a cause proposed by economist David Hendry is, “a quantitative process that induces change over time, mediated within a structure.” He goes on to indicate the importance of that last qualifier: “A structure is an entity that remains invariant to interventions and directly characterizes the relationships involved (i.e., corresponds to reality).” In modern applications, causality has been redefined by some to mean that Event A increases the probability of Event B. More specifically, mathematical philosopher Patrick Suppes2 suggests that a test for causality is whether B occurs more frequently when A has occurred, assuming that there is no prior Event C that screens off A from B. That is, if one screens off common driver C by removing it from the process, then A and B will lose their correlation. Contra-examples can show how the results of tests for causality depend on the manner in which cause and effect are defined. Consider the following example from Hendry, who points out the difficulty of specifying root causes. Our everyday thinking is replete with causal assertions: the car stopped because the driver braked; the atom disintegrated because it was hit by the proton; the pressure of the gas rose because heat was applied; output rose because interest rates fell. . . . At one level, such statements seem unexceptional. Consider the first example: the brakes were first applied; the braking system remained intact; the harder the brakes were applied, the more the
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car slowed; the brakes stopped the car (not the car slowing “caused” the brakes to come on). If the brake cables were cut (as in some murder stories), or the brake fluid was too low (as happens in reality) and so on, pressing the brake pedal would achieve little; that system is not invariant to such “interventions.” More fancifully, the car might be attached to a cable, the tightening of which actually “causes” it to slow, so the braking is incidental— causal inference is often based on thought experiments involving counterfactuals. More realistically, it could be argued that the driver caused the car to stop, or even that the trigger for the driver pressing the brakes was the cause. . . . “Causal chains” may have many steps, with the ultimate causes hidden from human knowledge.
In this example, it is clear that an understanding of the physical process that leads from “driver braked” to “car stopped” would greatly aid in measuring the probability that the car stops when the driver brakes. Counterfactuals are key here; a subject matter expert on automotive engineering might construct a set of plausible scenarios under which the first does not inevitably lead to the latter.3 CAUSAL CAPACITY, TIPPING POINTS, AND PREDICTIVE FAILURE In philosophy, causal capacity is sometimes defined as the ability of an agent to make choices, where a number of alternatives are available in a nondeterministic system. In a market system, this might be thought of as the free will of market participants, and its ability to affect outcome. In the context of this book, we will rather freely appropriate this term and redefine it to be a measurement of a system’s capacity for change. In a complex system, causal capacity might be thought of as the spring loading of a fragile or robust system that makes it susceptible to shocks caused by the actions of free agents. In the language of the national security community, causal capacity includes the vulnerability and consequences components of the “threat, vulnerability, and consequences” framework for threat assessment. One might consider causal capacity to be the quantitative measure of systemic risk. Unfortunately, it may be difficult to measure the causal capacity of a system of interest directly. While even a fragile system may appear to be robust for years, its causal capacity may make it extraordinarily vulnerable to a minor or major event that inadvertently or deliberately triggers a cascade of adverse events. Causal capacity need never be triggered; geological stresses under Yellowstone Park have the capacity to cause massive destruction, but have not yet been activated. Even if the level of vulnerability is large, the system may generate no signals until the first domino is tipped. And given the speed with which
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the most catastrophic outcomes can race though a system, warnings might not come in time for any protective actions to be taken. As we now know, there were few market indicators of the high level of financial system vulnerability that led to the credit crisis of 2007–2008. This is so even though, in retrospect, the starting conditions coupled with trigger events make the crisis seem all but inevitable when the causal chain of events is revealed. Unfortunately, working the chain forensically (that is, backward from effect to cause) after the fact is of little immediate value. Instead, a sufficiently realistic causal model may provide forward-looking measures of such hidden risk. Such a task is not easy, but the rewards are large. For example, simulating the effect of a fundamental change in underlying conditions—for example, less restrictive lending practices or the repeal of the Glass-Steagall Act—might have signaled a higher level of vulnerability and also indicated the nature of the events that might trigger a cascade. The same methods can identify optimal changes to the system that humans control. The same methodology might be used to estimate the change in causal capacity as a consequence of a proposed regulatory or policy change. These methods may assist us in creating a quantitative version of “financial Darwinism” not unlike the evolutionary models previously discussed. Historical data and counterfactual reasoning can help us to develop and refine our model of the market system, which we can then use for hypothetical reasoning—the basis for making investments or setting policy. What’s new is that the mechanisms for explicitly representing causal relationships have improved so much over the last two decades (causal networks), as have the mechanisms for drawing inferences from those causal relationships (probabilistic reasoning in a causal Bayesian network). INCLUDING EXPERT KNOWLEDGE Most deep thinkers about causality consider it a representation of reality. We can attempt to add intrinsic or expert knowledge (what experts in cognitive development might call innateness, in contrast to observation) to our model when defining each node of a causal network and its relationships to other nodes. When deterministic factors (with or without an error term) can be separated from or replace stochastic factors, the process benefits. However, the modeler must be careful to validate each deterministic
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assumption so as not to introduce analyst’s prejudice to the network. This is noninductive, top-down knowledge. But even deterministic processes can have complex dynamics. Causality is generally thought of as a one-way process; that is, effect always follows cause. However, determining causality is not quite so simple, even temporally. For example, there are feedback loops that complicate separating cause from effect: a drop in oil prices may induce OPEC to reduce production. Feedback mechanisms that are little understood may sometimes be hidden in empirical data and cannot be disaggregated except via experimentation and simulation. Sometimes, however, expert knowledge can guide the knowledge discovery process, as in the following example. Feedback Mechanisms in Dynamic Systems: The Cobweb Model Consider the cobweb model (see Figure 11-1) that is often applied to explain cyclical prices in agricultural commodities. The current price of a given commodity is determined by supply, but supply was in part determined in the past based on the previous crop year’s price. This is so because farmers can allocate the acreage available for planting to corn, wheat, or soybeans at the last possible moment based on their relative profitability. The U.S. Department of Agriculture regularly reports on planting intentions in its monthly Crop Production Report, and the report’s release is a major driver of grain prices. According to economic theory, the intersection of the supply and demand curves reveals the equilibrium price of the commodity. Assume that the supply and demand functions for soybeans remain constant. Then, if there is a poor harvest (the quantity is low, as for xaxis intercept Q1), the price of soybeans will rise to y-axis intercept P1. But if in the following year, farmers plant soybeans instead of corn to take advantage of higher prices, supply increases to Q 2 and price decreases to P2. Based on this dynamic, prices may oscillate from cycle to cycle. Depending on the relative slopes of supply and demand, the cycles may exhibit convergent or divergent behavior. If the slope of the supply curve is greater than the absolute value of the demand curve, then the magnitude of the fluctuations in price will decrease with each cycle. (If plotted over time, they would form the spiral from which the cobweb model takes its name.) If the opposite is true, then the magnitude of the fluctuations will instead increase with each cycle.
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Supply
P1
Price
P2
P3
Demand
Q1
Quantity Q2
Q3
Figure 11-1 Cobweb Model
Of course, this dynamic is made more complicated by adaptive behavior (e.g., “All the other farmers will be increasing their soybean production because bean prices are high, so I’ll plant corn instead”) and by other factors (e.g., crops must be rotated periodically to increase yield; some crops are more vulnerable to weather conditions than others). Furthermore, real-life boundary conditions (e.g., the maximum number of acres available for planting) impose limits on divergent behavior. Complex relationships such as these—particularly those with a lead or lag involved—can complicate the process of causal inference and require a theoretical framework that is capable of including such real-life behavior. Nevertheless, causality is clearly present, and explicit inclusion of cause and effect can greatly enhance a predictive model and serve to identify worst-case scenarios such as divergent behavior, even if they have never previously been observed in history.
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SUMMARY Much of this chapter was closer to philosophy than to mathematics. Nevertheless, explicit modeling of causality is likely to reduce uncertainty relative to its poor cousin correlation, and such notions as causal capacity provide a language and intuitive understanding that is useful in thinking about risk and vulnerability. WHAT’S NEXT In the next chapter, we will provide detail about the graphic language of causality: the dynamic acyclic graph as used to represent Bayesian inference networks.
CHAPTER 12
Bayesian Inference Networks: Estimating Vulnerability, Consequences, and Likelihood
The discussions in this chapter are intended to serve as a brief introduction to the theory and applications of causal inference, and to show that the creation of a financial world model is tractable and beneficial for real-life trading and risk management applications. The reader who is not mathematically inclined may choose to skip ahead to the conclusions of this chapter. However, those with sufficient mathematical background to follow this discussion may benefit from understanding the fundamental differences between causal inference and statistical models and methods. REPRESENTING REALITY Extreme risk management in any field requires a framework that facilitates identification of the most adverse outcomes and scenarios. That outcome may be loss of life in medicine, loss of key assets in the military, or bankruptcy in finance. But risk measurement is not risk management. Once the sources and the magnitude of risk are known, it’s also the responsibility of a risk manager to recommend the optimal actions to take to mitigate this risk. For a portfolio manager, such actions might include reducing position size, modifying portfolio composition, or revising counterparty exposure rules—all while leaving the basic investment strategy intact. So, the ideal framework for a risk management system is one that enhances quantitative decision making and portfolio optimization based on our best-informed beliefs about reality.
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DECISION ANALYSIS, BELIEF NETWORKS, AND DECISION NETWORKS Decision analysis (DA) meets this criterion. Closely related to the fields of game theory and artificial intelligence (AI), decision analysis is concerned with identifying the relevant issues that are material to a given decision (including the decision maker’s utility function with respect to risk) and mathematically determining the optimal decision. It can also be used to better communicate with stakeholders about risk—for example, to provide the likelihood of some aspirational event such as a 10 percent return on equity. Within the general category of decision-theoretic models are belief (Bayesian) networks (also known as causal probabilistic networks or Bayes nets for short) and decision networks (also known as influence diagrams). Both of these network models are expressed in a well-defined graphic form (a directed acyclic graph, or DAG) that consists of a set of nodes that represent variables and links that express the variables’ conditional interdependencies. Nodes can represent observable variables, latent variables (i.e., variables whose nature can only be inferred from observable variables with which they interact), unknown variables, or simply hypothetical functions. A Bayesian belief network is so named because it aggregates a set of beliefs about reality. Recall that to a Bayesian, there is no such thing as absolute truth. Beliefs can be informed by observational data or expert opinion, and they can be modified as new empirical evidence becomes available or opinion changes. Bayesian networks are the perfect fusion of decision theory and graph theory. A Bayesian network is a directed graph combined with a set of conditional probability tables associated with each of its nodes. It explicitly models cause-and-effect chains of events and systematically generates each possible outcome and its likelihood and consequences. Named after Reverend Bayes by Judea Pearl because they depend on Bayes’s simple but powerful equations for calculating conditional probabilities, Bayesian networks can be used to infer and predict information about the system, its drivers, and its future behavior. A special form of a belief network is a causal network, in which the relationships are causal (have an explicit directionality). In most applications, the directed arcs in a Bayesian network represent causal relationships, and each node includes a list of possible states (outcomes) and the probability of each, conditioned on the state of its predecessor nodes (causes).
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The primary purpose of building a belief network is to facilitate the process of causal inference, that is, the process of evaluating the network model. In this process, the probabilities of each possible state are calculated, using the evidence provided to the network and the relationships between variables. Therefore, causal inference is a method for identifying every possible state of a system (implied by the information with which it is provided) and, by inference, excluding all impossible states. Every Bayes net is complete, in the sense that it automatically creates every possible state and prohibits certain situations such as infinite loops. A Bayes net therefore imposes discipline, completeness, and logical rigor on the system. Such evaluation is particularly useful when attempting to identify all important outcomes or scenarios, their relative likelihoods, and their primary or contributory causes. In particular, they may provide their greatest value when revealing extreme but plausible outcomes contrary to the intuition of the modeler, and allowing her to trace back the causal chain. Bayes nets are commonly used in such fields as epidemiology in medicine, operational risk in financial institutions, and even robotics. The network can be used to both analyze and visualize many real-life problems: for example, H1N1 contagion in epidemiology, a chain of credit losses in the financial sector, or natural evolution in biology. A decision network (also known as an inference diagram) is a belief network that is configured to assist in decision making under uncertainty. In practice, it includes two additional types of nodes: decision variables, in which an outside agent can control the outcome of the process, and utility variables, in which the utility function (i.e., preferences) of the agent is included in the optimized decision-making process. A decision network is the more general case of a belief network. For example, a belief network might be used to estimate possible future outcomes for a contagious disease, while the inference network might be given the task of determining the efficacy of certain intervening decisions, such as providing vaccines to certain populations, closing borders, or hedging a portfolio with an options position. A belief network that models sequences of variables is a dynamic Bayesian network. For example, such a network has applications in speech recognition, because a sequence of sounds gives rise to logical interpretation. Advances in decision theory since the 1960s have made causal inference models easier to express and to implement. A decision network allows a parsimonious expression of all possible influences on a decision, and as such is often an alternative to a decision tree, in which every possible
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set of alternatives is displayed (and which is therefore subject to exponential growth in the number of branches). Furthermore, if properly formulated, a decision network has the additional computational advantage of allowing decision fragments to be solved independently, and then be brought together again to create a group decision. These networks are sometimes compared to neural nets, which have a similar graphical structure. However, neural nets rely on data mining, in which knowledge is inferred from a set of data values and then used to create predictive models. Compared to Bayesian nets, neural nets are relatively unconstrained (by exogenous knowledge) in the manner in which they populate the network and, therefore, may be less likely to provide an accurate representation of the interactions in a real system. Neural nets represent subsymbolic reasoning; the individual nodes are not intended to correspond to any particular concept. Conversely, Bayesian nets represent symbolic reasoning, in which the individual nodes do have meaning. Even if equally useful, Bayesian nets therefore enhance transparency regarding the mechanics of cause and effect. Bayesian networks have some additional advantages over other inferential methods. They allow for such real-world problems as incomplete data sets (missing information). Similarly, they also permit the process of inference to run both forward and backward, facilitating calibration with observational data or solving for unknown variables. (This is akin to calculating implied volatility from an option price, even though volatility is an input and price is the output of the Black-Scholes option-pricing formula.) In the following discussions, the terms decision network, influence diagram, and influence network will be used synonymously to emphasize the network’s utility in quantitative decision making, and belief network will be used synonymously with Bayesian network to emphasize the philosophical aspect of decision theory and the implicit acknowledgement of model risk. SPECIFYING A BELIEF NETWORK A belief network consists of the following elements: • A set of variables (portrayed as nodes in the graph) • A graphical structure that represents the interdependencies between the variables (portrayed as links between the nodes) • A set of conditional distributions (information carried within each node)
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The nodes represent random variables1 that may be observable variables, latent (hidden) variables, decisions, or unknown parameters. GRAPHICAL REPRESENTATIONS OF INFLUENCE NETWORKS Graphical representations of an influence network are economical, elegant, and revealing. Consider the graph of Figure 12-1, which reflects a decision (influence) network for a sports wager on either Team A or Team B. In this network, squares are used to represent decision nodes, circles to represent chance nodes, and the diamond for an end (results) node.2 The directions of the arrows indicate the direction of influence: the payoff is completely determined by the wagering decision and the game outcome, and the payoff cannot affect either the wager or the outcome. In such a diagram, each of these nodes contains all information regarding any dependence on its parent nodes. Assume that the two independent variables have only discrete outcomes. The decision node “Make Wager” has three possible values for the size of the wager: Bet on Team A ⫽ $100, Bet on Team B ⫽ $100, or No Bet ⫽ $0. The chance node “Game Outcome” has two possible values: “Team A Wins,” which is 30 percent likely, or “Team B Wins,” which is 70 percent likely. Compare the compact and informative influence diagram to its decision tree equivalent,3 as shown in Figure 12-2, which details every possible outcome. Without the inclusion of a utility function, the decision
Game Outcome Make Wager
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Figure 12-1 Simple Influence Diagram for a Sports Wager
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Figure 12-2 Decision Tree for Sports Wager
tree has solved for the path of the optimal decision (i.e., “Bet on Team B,” shown as True) that maximizes the expected Payoff (i.e., $40). This influence diagram is a trivial example in which each node was specified using tables of discrete outcomes. However, it could easily have used more complex functions and dependencies. The chance nodes might have been represented by a continuous probability distribution, the decisions made on the basis of complex and customized rules, and the decision controlled by a utility function rather than by simple maximization of the end result. The influence diagram of Figure 12-1 is an example of a directed acyclic graph. The “directed” component of the name refers to the fact that the arrows point in one direction, while the “acyclic” component refers to the fact that there is a clear endpoint (i.e., the graph contains no closed loops). Directed graphs, especially DAGs, have been used for years to express causal or temporal relationships and have come to be known as Bayesian networks, a term coined by Pearl in 1985 to emphasize both the subjective nature of knowledge and the dependence on Bayesian rules regarding conditional probabilities for solutions. When these networks are used to infer new information, they are referred to as Bayesian inference networks (BIN). Thus, a Bayesian network is a carrier of conditional relationships along the order of construction. The order of construction might be logical (e.g., in order of causal chain reactions) or temporal. In fact, for a forecasting application, it might be implicitly or explicitly ordered in both causal and time order.
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W
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Figure 12-3 Graphical Representation of Directed and Bidirected Edges
Graphical Notation and Terminology Graphs are the language of causality. Given the lack of symmetry with respect to cause and effect, only a graphical representation of variables and the dependencies between variables will do. Current convention has strict construction rules. For example, Figure 12-3 portrays an influence diagram as a set of nodes (vertices) and a set of links (edges) that connect some pairs of nodes. The nodes in the graphs correspond to variables, while the links denote the relationships between pairs of variables.4 The links may be directed (with an arrow that indicates temporal or causal order) or undirected. An arc is a link with a single arrowhead. A directed graph is a special case in which all links are directed. Even in such a graph, causality need not run downstream. While a directed graph may contain directed cycles (e.g., X : Y and Y : X) to indicate a feedback process, it cannot contain circular loops (e.g., X : X). An acyclic graph is one that contains no directed cycles (that is, that has no closed loops). A graph that is both directed and acyclic is a directed acyclic graph. This discussion provides only a cursory view of DAGs. There are a number of graphic conventions used to provide additional knowledge about the system, and the interested reader is encouraged to pursue this topic in more depth. For example, so-called bidirected links (generally indicated as dotted curved arcs, as shown in Figure 12-3) are used to denote the existence of confounders, or hidden causes that affect both nodes, and whose nature might be reverse-engineered to great advantage.
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Some experts question the universality of the DAG notation and approach, contending that it cannot always satisfy a Markov condition unless the net is deterministic. Nevertheless, most concede that it provides a framework that can enhance knowledge discovery. Hierarchical Structure The hierarchical language of kinship is a convenient semantic used to describe the direction of influence. A family is a set of nodes containing a given node and all its parents. Within that family, terms such as parent, child, ancestor, and descendant all provide an intuitive feeling for the nature and closeness of a relationship. A node in a directed graph is called a sink if it has no children and a root if it has no parents. Every DAG has at least one root and one sink. Two special cases of DAGs that will be familiar to financial engineers are the tree (a connected DAG in which every node has at most one parent) and the chain (in which every node has at most one child).5 A path in a graph is a sequence of links—again, a term familiar to those who are expert in path-dependent derivative securities such as “down-and-out” options6 and strategies such as the delta hedging of options.7 SPECIFYING A BELIEF NETWORK The construction of a belief network involves both science and art. Just as in an econometric model, the analyst must include all the relevant variables and should exclude the irrelevant. The ability of the model to include all plausible scenarios and exclude the implausible depends such selectivity. To create a belief network, an analyst follows a process in which she rigorously and logically defines all the distinct elements of the network and the relationships between them. This is essentially a bottom-up process, in which specific variables and the relationships between small sets of them are included or excluded one at a time. With this procedure, a complex network can evolve in a manageable manner. The following steps describe the general process of creating a belief network: 1. Identify all the variables that are important to the system or situation being modeled. 2. Assess the prior probabilities for root variables. 3. Define any causal relationships between the variables, and specify all links from parents to children.
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4. For each of the child (dependent) variables, define all of the possible states that it might take, that is, the “mutually exclusive and exhaustive” set. Specification of the Nodes In a belief network, each node contains information about a single variable that is important to system behavior. When creating the network, the analyst specifies all the variables, as well as the possible states of each variable and their probabilities. The states of such nodes (known as nature nodes, because they provide information about the nature of the system) can be discrete (e.g., have Boolean values such as true or false, or userspecified states such as high, medium, or low) or continuous (e.g., be a normal probability distribution specified by its mean and variance). These probabilities can be derived from observational data (e.g., historical price behavior), be derived from expert opinion (e.g., the effect of a regulatory change on investor behavior), or even be left as unknowns. One of the most powerful features of a belief network is the ability to specifically incorporate lack of knowledge. SOLVING BAYESIAN NETWORKS A properly specified network can be used to generate all possible final states of the system or to solve for a missing element of the system. If additional nodes such as decision nodes are also included, they can be used to identify optimum decisions, their consequences, and the sensitivity of the system to both exogenous variables and the decisions themselves. A Bayes net has an efficient hierarchical structure that takes advantage of probability theory. Once the network is built, the structure reveals all relationships. For example, if there is no link between two nodes (either directly or indirectly), the variables represented by the nodes are conditionally independent; that is, the likelihood of one variable does not depend on the likelihood of the other. A link connects and describes the causal relationship between a logical or temporal antecedent (the parent) and its subsequent consequence (the child). EFFICIENCY AND THE BAYESIAN NETWORK The well-defined structure of a Bayesian net, in which each variable depends only on its immediate parents, creates efficiency by taking advantage of the chain rule of probability calculus.
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Since the likelihood of the child node (the influenced variable) depends only on the likelihood of its parent nodes (the influencing variables), such a structure facilitates economical calculations; there is no mathematical reason to reach farther back than the child’s parents to calculate the joint probability distribution. Although the inference diagram can be converted to a decision tree in which every possible outcome is determined (which would require an astronomical number of calculations if the number of variables and possible states of each is large), the process of inference does not proceed in such a tedious manner. Instead, the process of causal inference takes advantage of the structure of a DAG and of the chain rule to greatly speed the calculation of the final states. The Chain Rule of Probability Theory The chain rule of probability theory allows the calculation of a joint probability distribution from a set of conditional probabilities. In a DAG, each node contains a complete set of conditional probabilities, from which the probabilities of every possible end state can be computed. Suppose we seek to determine the probability distribution P, which is a function of n variables. The chain rule of probability calculus always permits us to decompose the final distribution P as the product of n conditional distributions: n
P(X1 = x1, Á , Xn = xn) = q P(Xi = xi |Xi - 1 = xi - 1, Á , X1 = x1) i=1
For example, with just two variables, the probability of a state in which both A and B occur is the product of the probability of A conditional on B and the (unconditional) probability of B, as follows: P(A, B) = P(A | B)P(B) If we assume that, in the general equation, the conditional probability of some variable Xj is not sensitive to all the predecessors of Xj, but only to a small subset of those predecessors (in the case of a Bayesian net, only its parents, denoted as PAj), we can instead use the following expression of the previous product: P(xj | x1, Á , xj - 1) = P(xj |paj)
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We assume that Xj is independent of all other predecessors. Use of this minimal set of predecessors considerably simplifies and reduces the amount of information required and the time required to calculate the final states. Bayesian Filtering Another technique that leverages the power of a Bayesian network is Bayesian filtering. In this context, filtering is the process of estimating the current value given past observations. For a dynamic system (one that changes over time), sequential Bayesian filtering is used to estimate the real value of a variable that evolves over time. An estimator is a filter that incorporates new information, modifying prior knowledge and creating posterior knowledge as new information becomes available. Dynamic Bayesian filtering is essentially a connectivist learning system and a sensemaking tool, that is, one that incorporates all relationships to facilitate the creation of knowledge. Such filtering is already widely used in a number of applications. For example, for e-mails, the occurrence of certain key words that are not often found in non-spam (e.g., “Viagra”) or a combination of such words can facilitate accurate spam filtering. One of filtering’s most exciting applications is in robotics, where such methods are used to enhance incremental learning by artificial intelligence. Such methods can fuse information from various sources, including the integration of dynamic sensor data, temporal sequencing, hierarchical taxonomies relevant to the process, and methods for identifying and categorizing the current situation. Other Numerical Methods There are a number of numerical methods by which the most efficient form of an inference engine might be created, depending on the system model type and the problem. Figure 12-4 shows a hierarchical ranking of various Bayesian formalisms, ranked in general-to-specific order. The more specific approaches are useful in systems whose theoretical behavior is restricted in some way. For example, a Kalman filter may be used for a dynamic, linear system. C⫹⫹ code for many filtering methods is commercially available. Gibbs Sampling and Computational Efficiency As previously discussed, Monte Carlo simulation is widely used in stochastic modeling. For example, Monte Carlo techniques are often used for derivative instruments such as collateralized debt obligations
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More General Bayesian Programs
Bayesian Maps
Bayesian Networks
DBNs
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Particle Filters
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Figure 12-4 Probabilistic Modeling Formalisms in General-to-Specific Order
(CDOs) with complex features such as “nth-to-default” tranches (in which a payoff occurs upon the nth default in a market basket of various names). Because one of the risks inherent in such instruments is so-called correlation risk, quantitative modelers often use Cholesky decomposition (a method used in simulating systems with multiple correlated variables) to generate random numbers for the Monte Carlo simulation. Causal models have equivalent numerical solutions. For example, they can use Gibbs sampling, a technique for generating random numbers that have the required properties with respect to causality rather than correlation. Gibbs sampling is particularly well adapted to sampling the posterior distribution of a Bayesian network. COMPARISON WITH STOCHASTIC MODELING PROBLEMS Clearly, a Bayesian network that is entirely consistent with any stochastic model can be built. Indeed, this is only reasonable, since Bayes’s Theorem is the foundation of all statistics. In the limit, the number of possible values for each node could approach infinity (approximating a continuous variable), and the network could have multiple dimensions. Furthermore, if no limiting causal relationships are specified (e.g., if all dimensions of risk factors are orthogonal),
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then such an approach could be used to approximate complex statistical functions. For example, although this is computationally impractical for all but the smallest networks, a Bayesian network could substitute for a copula approach in calculating a joint distribution from its component distributions. BAYESIAN NETWORKS AND EXTREME SCENARIO GENERATION Bayesian networks can be used to explicitly generate every possible scenario and estimate the likelihood and consequences of each. Unlike classical inference models, Bayesian inference models allow the introduction of prior knowledge and expert opinion into the calculation. The same types of models might be used to model the set of market indicators consistent with each extreme outcome for use in warnings. A Bayesian approach has limitations, the greatest of these being the availability of data regarding the vulnerability of assets and the lack of certain historical precedents that can be used to define the presence or effect of a primary influencer. For example, the cause of an earthquake (leading to a scenario in which a building collapses) can be stated only with some degree of uncertainty. And vulnerability data are required to assess the probability that a particular building will collapse, to estimate the first-order loss resulting from the collapse, and to estimate any secondorder losses (such as loss of business continuity), which may be larger than the physical loss. The analytical foundation for such an approach is a dynamic, object-oriented Bayesian network, in which causal relationships are explicitly modeled. Because the network can be informed by both facts (where they exist) and expert judgment (where they do not), such an approach is appropriate for modeling low-probability/high-consequence events, particularly events that have never before occurred and/or events for which few data exist. Relying as it does on expert opinion, this analytic approach represents the degree of belief that a threat is plausible. This is not unlike financial risk metrics, which—although they purport to represent the probability that a financial threat is likely—actually represent belief as well. This is so because many financial models implicitly contain the modeler’s assumption that the future is well represented by the period of the past data that he has included, and/or that no model error exists. Since to a Bayesian all probabilities are nothing more than subjective degrees of belief, Bayesian networks provide a natural framework for combining “known” probabilities (degrees of belief that we can agree on,
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such as the probability that a coin will land on heads) with more subjective probabilities (degrees of belief that are a matter of opinion, such as those elicited from subject matter experts). To properly model very low-probability events, such belief networks are necessarily large and complex. However, because these networks can include diverse drivers, they may permit relatively easy integration of financial data and drivers. In fact, Bayesian networks are already used in the financial community to estimate operational risk. Many of the largest operational risks—for example, the risk of loss due to accounting fraud, as in the case of Enron—could not have been accurately modeled using only historical precedents. SUMMARY For purposes of extreme risk management, specifying a Bayesian inference network assists both in measuring risk by identifying plausible scenarios with the most adverse consequences and in mitigating risk by providing a decision-making framework to minimize the likelihood or consequences of those scenarios. While such an approach can be used to reproduce (albeit inefficiently) any of the stochastic methods already used to estimate joint probability distributions, the converse is not true: only such a network allows complex, noncontinuous, and nonlinear dependencies with ease. There is also well-developed theory and numerical methods that can be leveraged for new applications and that facilitate computational tractability. WHAT’S NEXT In the next chapter, the theories of this chapter are extended to financial and other threat applications. A special version of a Bayesian inference network, the risk inference network, will be discussed.
CHAPTER 13
Securities Valuation, Risk Measurement, and Risk Inference Networks
BAYESIAN INFERENCE NETWORKS IN FINANCE Simply put, causality makes risk actionable. In any domain, transparency with respect to threats, vulnerability, and consequences allows optimum decision making at both a strategic and a tactical level. Because they explicitly include chance, Bayesian inference networks (BIN) are ideally suited for representing many types of financial problems. While a directed acyclic graph (DAG) can be used to represent a simple statistical operation (for example, a joint probability distribution), it is far less limited in representing reality and can be used as a general framework in which stochastic, causal, and deterministic dynamics might all be present. Causal inference methods might be used to value complex securities and to measure risk in the financial space, akin to evaluating the likelihood and consequences of plausible threats in the national security space. Such methods are already used by financial institutions for the estimation of operational risk, but they are less common for the estimation of market, credit, and other such risks. As a case in point, some financial models require automated decision making, because the value of many path-dependent derivative securities is based on the premise that the owner of the security will make the optimal economic decision at each point in time. For example, the value of an American-style option is generally calculated with the aid of a binomial decision tree,1 in which the owner’s decision to exercise the option or not is simulated at each branch of the tree. Likewise, estimating realistic market risk often requires the inclusion of complex dynamics. As discussed in the context of dynamic value at risk (VaR), even a random change in price can force position liquidation and trigger a cascade of monotonic changes in subsequent prices. A BIN 189
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can be used to model the changes in price that such a dynamic generates and to estimate multiday losses more realistically. The DAG for each of these examples would include both chance nodes and decision nodes, in which decisions (to exercise the option, to sell part of a portfolio) are fully determined by rules (optimal economic action, required by firm management). Table 13-1 shows a number of common financial applications and the benefits of using a causal approach rather than a stochastic approach. So, the use of causal inference methods and models might assist in managing risk and also generate trading opportunities. But even more important, such use enhances transparency. A DAG’s graphic representation T A B L E 13-1
Benefit of Bayesian Inference Networks in Financial Applications
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Comment
Securities valuation
BIN can include complex interrelations and automated decision making BIN can reflect causation rather than correlation between elements in a portfolio
Risk measurement
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BIN can be used to systematically generate and evaluate extreme scenarios
Portfolio optimization
BIN can include latent nodes, which might represent optimal additions to the portfolio
Principal component analysis (PCA)
BIN might be used to identify principal causal components from a number of possibly correlated variables BIN can include or infer behavioral effects BIN can include more complex dynamics between strongly or weakly correlated alternative investments
Behavioral studies Capital allocation
Benefit Better estimates of value and hedging strategies Better estimates of magnitude and sources of risk, as well as identification of “hot spots” and extrema Better estimate of economic capital Extends the efficient frontier by identifying nontraditional methods for optimizing the portfolio Greater transparency, model simplification
Input to alternative investment strategies Creates a better schema for risk-based capital allocation by a financial institution or fund of funds
(Continued )
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T A B L E 13-1
(Continued)
Application
Comment
Benefit
Evaluation of model risk
BIN can evaluate model risk (e.g., uncertainly regarding stochastic parameters)
Enhances risk measurement and evaluation of the quality of the models used
Evaluation of policy and procedures
BIN can model the consequences of current strategies
Warnings of risk regime change
BIN might aid in identifying changes in system drivers
Evaluates risk management protocols and helps ensure that they achieve the desired results Earlier warning of a shift to a higher-risk regime
of interconnectivity, dependence, and causality can be used to vet the model (e.g., by revealing constructs that are inconsistent with expert knowledge), disclose the presence of feedback loops (both positive and negative), and illuminate the paths that lead to the most adverse outcomes. Recall the Basel Committee’s comments related in Chapter 4, in which it identified the inability of risk managers to justify the plausibility of extreme scenarios to senior management. Likewise, such graphic representations of cause and effect can suggest where intervening actions might be optimally inserted, can be used in an agent-based simulation to test various interventions, and might even be used to infer the presence and nature of certain hidden drivers. In the case of threats against an embassy, the intervening action might be the hardening of a target, while in the case of counterparty credit risk, the intervening action might be the purchase of a credit default swap (CDS) contract. There are few limits on the problems that such an approach can handle, and simplifying assumptions are generally unnecessary, particularly compared to stochastic approaches. Processes can be dynamic and time-sensitive. And, for financial markets, the accuracy of the network dynamics can be tested against historical data for explanatory power. THE GENERAL APPROACH Creation of a Bayesian inference network requires an integrated view that includes a world model, a domain model (i.e., how things work in the problem space), and subject matter expertise regarding specific drivers.
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For a financial engineer, a domain model might include knowledge of securities valuation models and the dynamics of the parameters on which they depend. For a risk manager, a domain model might include knowledge of risk management protocols, margining rules, and behavioral effects. For an economist, a domain model might include knowledge of major economic and financial drivers of systemic and specific risk and their causal interactions. In the first of the following two examples, domain expertise in financial engineering is used to create an alternative option-pricing model. In the second, domain expertise in risk management is used to create an alternative estimate of multiperiod VaR. An Valuation Example: Option Pricing with Uncertain Mean In the following example, we estimate the value of a European-style option, where the standard deviation is known but the mean is uncertain. The three distributions of Figure 13-1 show the distribution of values for three typical European-style options: the first at-the-money, the second with a strike price one standard deviation out-of-the-money, and the third two standard deviations out-of-the-money. Each has a fixed standard deviation of 1.0 but uncertain mean. The mean is expressed in turn as a Gaussian distribution with its own mean of zero and standard deviation of 0.1. In such a BIN, mean becomes a chance node, and the estimated value of the option increases due to the asymmetry of the calculation. Figure 13-2 shows the sensitivity of the option’s expected value to its strike price and to the standard deviation of mean. Note that when we add uncertainty with respect to model parameters, option value increases, as does the ratio of the value of this alternative formulation to the option value estimated only at the fixed maximum likelihood estimates. In a sense, this is an example of explicit estimation of model error for a one security portfolio with respect to one input parameter. In point of fact, standard deviation is uncertain as well, and an alternative model in which the standard deviation is uncertain and the statistical parameters for the mean are a function of the standard deviation would create yet different estimates of option value or model risk. Risk Example: Estimation of Multiperiod VaR In the following example, the BIN of Figure 13-3 specifically includes discrete temporal components: five successive days. In this model, rather than assuming that each day’s movement is independent of the others, each is positively correlated to the next. Each of the chance nodes is
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Figure 13-1 Distribution of Values for European-Style Option with Uncertain Mean 193
Figure 13-2 Sensitivity of European-Style Options to Out-of-the-Moneyness
Figure 13-3 Bayesian Inference Network and Serial Correlation 194
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represented by a Gaussian distribution, but only the first day’s node is independent of the others. Such a dynamic is meant to simulate memory in prices. Such memory might be an artifact of a fundamental driver that takes days to be fully discounted by the marketplace, a carryover in market sentiment and psychology, or even forced position liquidation. The resultant distribution of Figure 13-4 shows the fat tails typical of empirical market data and suggests that the presence of de facto memory might explain such tails. From the distribution of changes in price (which maps directly to P&L in a single-security portfolio), VaR can be estimated empirically. COMPUTATIONAL TRACTABILITY IN FINANCIAL APPLICATIONS Previously, we discussed the fact that a BIN is efficient because it is constructed in a manner such that each node is dependent only on its immediate parents. Furthermore, this hierarchical approach also lends itself to a variety of ancillary benefits, such as the separation of various systematic and specific risks. In essence, we have used some of the principles of
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causal reasoning to ignore observations without degrading the quality of the results, thus creating efficiency and tractability. Furthermore, with appropriately clever design, a BIN can benefit from an object-oriented design. A BIN can be built in network fragments (to be joined later), in which each fragment might include other models (e.g., structural models used in credit analysis that measure the probability of default as a function of capital structure) or exogenous rules that are subject to change (e.g., margining and clearance rules). But most important, the fragments can be built by subject matter experts in the domain of the fragment. Although these techniques are mathematical, they include an element of art as well, and they are ideally guided by those with expert knowledge and intuition with respect to actual market behavior. THE RISK INFERENCE NETWORK (RIN) One approach that is finding wider acceptance in the homeland security community is that of Bayesian risk inference for purposes of modeling threats. Although the examples in this chapter involve threats to national security, they are no different in principle from other forms of operational risk in the financial space, stemming, say, from failure to prevent a rogue trader or a cyber intrusion. In this methodology, risk is considered to be a function of likelihood, susceptibility, and consequences. All three are important. For example, a target, no matter how “soft,” is unlikely to present much risk if a successful attack would fail to match a terrorist’s objective. One special case of a Bayesian inference network that integrates such an approach is the Bayesian risk inference network (RIN). A RIN2 is a network that is specifically designed to identify and quantify various sources of risk in a systematic and objective manner, and to suggest solutions that might mitigate those risks. A RIN specifically allows the inclusion of knowledge of various types. Its original application was for physical threats (e.g., an attack on a nuclear power plant by terrorists, or a cyber attack by an unfriendly state actor). Naturally, since there is little or no history on such attacks, a stochastic approach is inappropriate. And even if such history did exist, it might be worse than useless; previous vulnerabilities would have been eliminated, and malevolent actors could be assumed to have moved on to exploiting new and different vulnerabilities. So, while some risk influencers can be described probabilistically, an expert opinion is required for others. The latter is not necessarily the
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second-best choice; in a changing environment like counterterrorism, a forward-looking expert opinion might serve the process better than an unjustifiable statistic based on limited or unrepresentative historical data. Therefore, a RIN that is used in national security must include expert knowledge. A systematic process can be used to guide the expert and elicit a formal representation of his knowledge while minimizing cognitive biases. This process is akin to developing any expert system (i.e., a system that mimics the actions of human experts) used in the field of artificial intelligence. Like any other BIN, a RIN can include stochastic and causal elements. For example, an initial cause such as an earthquake may lead to an effect such as a building collapse. The probability of the earthquake may be estimated from historical data, while the consequences of the earthquake (building damage or building collapse) might be modeled from expert knowledge elicited from a structural engineer. BAYESIAN RISK MODELS AND METRICS Bayesian risk metrics represent the degree of belief that a threat is plausible. As shown in the following examples, the analytic foundation is a dynamic, object-oriented Bayesian network in which risk is a function of likelihood, susceptibility, and consequences. The domain model and the RIN implicitly represent causality. Expert judgment is included where appropriate and is essential to completeness. Building a RIN: Comments on Notation There are a number of commercially available services that assist with the construction of a Bayesian net, but practical considerations have allowed more than one convention in how such networks are depicted. Consider the simple storm indications and warnings network of Figure 13-5. In it, the arrows are drawn from the two indications and warnings of an impending storm; that is, dark clouds (node A) and high winds (node B) are two indicators that it’s going to storm (node C). In this hierarchical depiction, nodes A and B are the parents of node C. However, nodes A and B may not be the only parents of node C; there might be other indicators, such as a drop in barometric pressure, an increase in humidity, or cows lying down in the fields. It might take a sizable effort to elicit from expert meteorologists how the likelihood that it’s going to storm depends on each of these indicators (or any combination of them if they’re not independent).
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Node A
Node B
Dark Clouds
High Winds
Node C It’s Going to Storm
Figure 13-5 Storm Indications and Warnings Network
An alternative approach to depicting the network involves drawing the arrows in the causal direction (i.e., from cause to effect). In the previous network, dark clouds and high winds don’t cause a storm; instead, it’s the other way around. Using this convention, the network looks like that of Figure 13-6. The process of Bayesian inference can run from either cause to effect or the reverse, so the choice of notation is up to the user. The only exception is when there is some dependence between nodes (for example, when the likelihood of a storm may depend to some degree on a
Node C It’s Going to Storm
Node A
Node B
Dark Clouds
High Winds
Figure 13-6 Storm Indications and Warnings Network (Causal Direction)
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combination of dark clouds and high winds). If this is in fact the case, then it is more appropriate to keep the arrows pointing toward C, as in the first network. In that case, node C consists of a prior probability table, that is, the probability that it’s going to storm. The depiction in Figure 13-5 might be preferred by those who are building networks that are intended to provide warnings of an event, whereas the depiction in Figure 13-6 might be preferred by those who are attempting to generate and evaluate all possible outcomes that might result from one or more drivers based on the system specifications. CASE STUDY: THE USE OF RISK INFERENCE NETWORKS IN COUNTERTERRORISM One might characterize attacks by terrorists as a special case of operational risk. The following examples from the homeland security community will illustrate the process of creating a conceptual model for the purpose of risk assessment within a Bayesian framework. In order to evaluate a Bayesian network, there must be a probability table (or some other expression of uncertainty) for each chance node. Each node can therefore have multiple states (discrete or continuous), so a node in a Bayesian net that has many parents can quickly expand to many permutations, that is, for all possible combinations of all those parent states. The network must often be populated by eliciting expert opinion from subject matter experts, and a binned approach is often used. For example, these experts might be asked to rate on a scale of 1 to 5 terrorist access to a certain type of weapon. Figure 13-7 shows a fragment of a risk inference network, where the risk is of terrorist attack. The choice of orientation in this fragment is from cause to effect. USE OF RISK INFERENCE NETWORKS FOR PURPOSES OF INDICATIONS AND WARNINGS An indicator is defined as an event (including a null or missing event) or combination of events that provides important clues about current conditions and suggests a path toward an eventual end state. Warnings are signals of a change in state. As time passes, additional signals may indicate progress along that path, and thus validate or modify the expected end state. In a field such as counterterrorism, indicators may provide links back to a nefarious state or nonstate actor, based on the character and capabilities of the suspect organization. For example, Al Qaeda might be the
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Figure 13-7 Risk Inference Network Threat Fragment Source: Digital Sandbox, Inc.
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logical suspect when indications of a physical attack jibe with its capabilities and intentions—for example, an attack on an iconic target such as the Statue of Liberty, where the gain is primarily in propaganda value. Conversely, a state actor might be the logical suspect when the resources required or the gain realized at the end state is consistent with the intent and capabilities of such an actor. In a field such as finance, indicators might instead point to a progression of events that is not orchestrated by financial actors, but instead provides insight into a path and end state that are increasingly likely to occur. Just as a flood might establish one of multiple paths over a rocky incline until a single river is formed, so too might indicators taken over time revise or confirm progress toward a particular financial outcome. For example, an initial triggering event might be dampened and dissipate because of large positions by hedge funds that trigger profit taking. Or, it might instead gain momentum as market psychology or one of a hundred other drivers amplifies the original trigger event. Such indicators can be used alone or in combination to create warnings of specific events. These can be either top-down warnings, in which the entire universe of events of interest is monitored, or bottom-up warnings, in which indicators of specific scenarios (e.g., a dirty bomb attack) are identified and monitored. In the top-down case, a sensemaking effort is employed that infers the end event from the indicators, while in the bottom-up case, all the indicators already point to a specific end event. Bottom-up warnings are therefore of potentially more operational value if they are well specified. Figure 13-8 shows a fragment of a RIN that is geared toward providing indications and warnings of possible terrorist activity. MODELING SYSTEMIC AND SPECIFIC FINANCIAL RISK IN RIN In a properly defined structure and in the language of a directed graph, a root (a node with no parents) might be a fundamental driver, such as an economic indicator or earnings report, while a sink (a node with no children) might be the price of a security. Some of the roots might express systematic drivers, while others might express increasingly more specific drivers. Between the roots and the sinks might be nodes that model the influence of each driver on each instrument in a portfolio. The probability of some nodes can be expressed in terms of a probability distribution, whereas others can take on only more discrete values (e.g., a credit event happens or it does not). And
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Surveillance [Yes] [No] [Don’t Know]
Acquisition
24.3 74.7 1.0
[Yes] [No] [Don’t Know]
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Prepositioning [Yes] [No] [Don’t Know]
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Elicitation Organizational Intent [Very High] [High] [Moderate] [Low] [Very Low]
Indications and Warnings
1.00 9.00 20.0 30.0 40.0
[High] [Moderate] [Low]
13.4 37.7 48.9
[Yes] [No] [Don’t Know] Goes from direction of cause to effect. Organizational intent is plan to create attack, and I&W is corollary effect (can’t avoid allowing some I&W identifiable by IC to leak out).
24.3 74.7 1.0
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Training [Yes] [No] [Don’t Know]
Other Suspicious Activity
Recruiting [Yes] [No] [Don’t Know]
21.9 77.1 1.0
Goes from direction of cause to effect. Recruiting is considered an effect, as the master plan requires recruiting to make it operational.
Figure 13-8 Risk Inference Network Threat Indications and Warnings Fragment Source: Digital Sandbox, Inc.
[Yes] [No] [Don’t Know]
Propaganda [Yes] [No] [Don’t Know]
21.9 77.1 1.0
21.9 77.1 1.0
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unlike in a copula approach, extreme movements—even in a random variable—might be allowed to lead to certain events that more moderate movements cannot. For example, a chain reaction of credit failures might be modeled only if credit spreads suddenly widen precipitously or exceed some barrier value. A properly designed RIN will also include feedback mechanisms, since these are often the primary drivers of regime change. THE ROLE OF FEEDBACK IN REGIME CHANGE It’s particularly important to include any feedback mechanisms in the design of a risk inference network, since these mechanisms may be responsible for either prolonging the current risk regime or generating the “tipping point” that leads to regime change as a system adapts to change. Self-organization is achieved via a number of mechanisms. Numerous small-scale interactions can drive change, but that change can be dampened or amplified by a feedback process, negative or positive. In fact, positive feedback is sometimes referred to as cumulative causation, because the effect of one cause starts a process in which subsequent effects are in the same direction as the first effect. For example, A creates more of B, which in turn creates more of A. Conversely, a system that responds in such a way as to force correction of the first cause is said to exhibit negative feedback. A system that exhibits positive feedback in response to any change in its current state is said to be in unstable equilibrium, whereas a system that exhibits similar negative feedback is said to be in stable equilibrium. Feedback in Economic Systems Even though Adam Smith’s invisible hand may eventually cause the global economic and financial systems to self-organize and find a new state of equilibrium, statistical examination of the current state cannot in and of itself provide evidence that this state is either stable or unstable. The system may exhibit highly optimized tolerance (HOT) and be both robust and fragile. It might alternate robust and fragile behavior: first unstable, and then, as new mechanisms and human preferences finally kick in, stable. The former, unstable phase is the source of scenarios that, although extreme, are plausible because of the positive feedback mechanism that generated them. The latter, stable phase represents tremendous opportunities for profit by those who can accurately model the end of the threat.
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This is not unlike the task of intelligence analysts who model threats from state actors, both friendly and unfriendly. It’s as important to them to identify the cessation of an existing threat (irrespective of saber rattling and excessive rhetoric) as it is to identify the commencement of a new threat. This is so because their analyses serve to assist the decision-making processes of senior government officials with respect to foreign policy and both strategic and tactical actions. In intelligence terms, such analysis is referred to as deciphering the “intent and resolve” of those state actors and might lead to actionable intelligence. REPRESENTING A MARKET NETWORK In previous examples, we created fairly limited models with specific purposes. But in order to measure systemic risk, a much more ambitious task is required. A systems model of the capital markets might be specified in a number of different ways, depending on one’s intuition and purpose. For example, if we are attempting to model the consequences of a credit shock, the network representation might be literal: each node might be any individual institution that acts as counterparty or guarantor to a financial contract (e.g., banks, broker-dealers, hedge funds, or exchanges). The interactions that link the nodes might be performance on those contracts (e.g., payment of swap fees or delivery of a futures contract) or intermediate calls for capital (e.g., margin calls). The network representation might also be more abstract, limited only by the creativity of the modeler. It may be that the data needed to properly inform some versions of such a model aren’t readily available. However, a well-specified network model also reveals the information required to inform it, irrespective of whether that information is available. (This is consistent with the principles of conceptual model design in Chapter 7, in which one first decides what information is required for the model rather than working with whatever information is readily available.) In order to produce the desired results, a great deal more transparency and information sharing may be required than was available in the past. For example, a model of systemic credit risk might require details of individual or net exposures for each pair of entities in the network. Since it’s unlikely that any enterprise or exchange would voluntarily share this information, the collection and analysis of such data might be the responsibility of a government regulator. This body might be the only entity that is able to view the system as a whole, as required in systems thinking.
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An even more sophisticated version of the system model (one that is allowed to interact with other systems) might also ideally reflect the interconnectivity of all the subsystems involved, and the potential that each has to provide a trigger event. For example, geopolitical events such as military action or an embargo can clearly trigger extreme market events. Although a fully formed market and world model would be extremely complex and ambitious, even nascent forms of such models might provide useful information and insights. Furthermore, the computational efficiencies that leverage the chain rule, as well as the ability to implement an object-oriented approach that combines RIN fragments from diverse subject matter experts, make the creation of a market RIN more feasible than the scale of the domain alone suggests. SUMMARY In this chapter, we discussed the utility of using Bayesian inference networks to model a number of financial and threat problems. In particular, the role of the Bayesian risk inference network to identify the likelihood, susceptibility, and consequences of all plausible scenarios was illustrated. Although there are substantial challenges related to using such methods to identify systemic and specific market risk, there are some efficiencies that make the effort less daunting than it first appears. WHAT’S NEXT In the next chapter, a framework for integrated enterprise risk management that reconciles stochastic and causal approaches is discussed.
CHAPTER 14
Risk Fusion and Supermodels: A Framework for Enterprise Risk Management
THE PERSISTENT TENSION In the introduction of his excellent book, Against the Gods: The Remarkable Story of Risk,1 written in 1998, Peter L. Bernstein says, “The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the patterns of the past, and those who base their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved.” In the more than a decade since Bernstein wrote these words, the line between these two points of view has started to blur. A connectivist approach toward all the drivers of a system may allow a fusion of the best of each, and it provides a path toward supermodels that include interdependencies among all sources of risk. Today, analysts are recognizing that subjective degrees of belief are present even in quantitative models. Even the language of risk modelers more explicitly reflects the presence of belief; for example, financial engineers now say “volatility forecast” rather than “volatility” when discussing one parameter for a risk model. ENTERPRISE RISK MANAGEMENT Enterprise risk management (ERM) is the management of all sources of risk to the enterprise, irrespective of source. ERM requires appropriate aggregation of market, credit, liquidity, operational, reputational, legal, and other sources of risk into a single framework. Some of these risk elements are highly subjective and explicitly belief-dependent (e.g., legal or 206
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reputational risk), while others are estimated using highly quantitative models and methods. However, just as in a securities portfolio, these diverse risks cannot be added to measure enterprise risk. They are generally calculated using different methods (e.g., stochastic methods for market risk and Bayesian inference networks for operational risk) and are interrelated in a complex and causal fashion. For example, an operational failure such as a lost trading ticket has no economic consequence if market prices haven’t moved. Conversely, a failure to collect margin has profound consequences if the counterparty goes bankrupt. A stochastic approach is insufficient; only a causal approach allows proper integration of all such causal relationships. Previously, we discussed how risk management is more than risk measurement, but this is particularly true at the enterprise level. ERM typically involves identifying particular events or circumstances that are relevant to the organization’s objectives (risks and opportunities), assessing them in terms of their likelihood and the magnitude of their impact, determining a response strategy, and monitoring progress. When C-suite executives can view their enterprise’s integrated risk in a framework that enhances transparency, they are far better equipped to optimize their decision making, with the assistance of the quantitative tools that such an approach facilitates. For example, in such a supermodel, they might explicitly include a utility function when they are optimizing the allocation of capital among business units, or include aspirational goals that might be reverse-engineered for required capital or risk appetite. Similarly, an integrated ERM model might be used to analyze internal policy (e.g., how position limits are determined or how employees are rewarded) or the effect of proposed changes in regulatory policy (e.g., a change in margining or give-up protocols). DECISION SUPPORT AND THE FINANCIAL COMMUNITY The highest goal of any ERM system is decision support. Even a simple metric like value at risk (VaR) that quantifies the magnitude of risk (if not its sources) can inform a management decision to reduce gross risk, to reallocate risk to activities with more reward, or even to reward those traders with the best risk-reward ratio rather than merely the largest profit. Yet, how much more richly informative is a picture of cause and effect described by a risk inference network (RIN)! It provides transparency into the potential paths that might lead to catastrophe (or phenomenal
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returns). No longer must senior executives rely on the indecipherable products of analytic black boxes in making fateful decisions. A RIN may provide indications and warnings (I&W, in the parlance of the intelligence community) that facilitate dynamic adjustments (to positions or strategies) when a warning sounds. It might even be used to dynamically reset the parameters of algorithmic trading engines; for example, if a market shock is on the horizon, the scaling strategy must adapt to a change in volatility or the possibility of a tipping point. It can also be used to identify any hidden minefields by identifying hot spots, or combinations of conditions that lead to an adverse outcome, but do not necessarily occur at market extrema. CREATING A COMMON FRAMEWORK As economist David Hendry pointed out, “Causality is a property of nature, not of a model.” A risk modeler who ignores causality runs the risk of simulating a system that is unrepresentative of reality, and therefore is unlikely to provide meaningful assistance in decision making. A common risk framework that is suitable for modeling enterprise risk is one that can integrate stochastic measures with expert opinion. A Bayesian risk inference network is one such framework that is mathematically tractable. Indeed, all statistics is based on Bayes’s Theorem, and many statistical results could be computed (albeit imperfectly and inelegantly) using a Bayesian network. Such a framework allows (but does not require) causal relationships. Furthermore, it allows features such as granularity and asymmetry that often represent the real-life behavior of market prices more accurately. For example, portfolio risk might be calculated using a RIN in which there is no causality (except via correlation coefficients). By using many nodes, the RIN might serve to approximate a continuous distribution of outcomes, just as a histogram might approximate a Gaussian distribution. However, the success of such an approach depends in large part on the way the RIN is structured. In the intelligence space, where such methods are widely used, the greatest amount of effort goes toward specifying a hierarchical inheritance structure. For example, in a threat assessment problem, means of attack might include Humvees, which inherit certain characteristics and vulnerabilities from land vehicles, which in turn inherit the same from the class of all vehicles. And by analogy, a common framework for the financial sector requires that systematic and specific risks be separately categorized and understood in a fundamental fashion. Fortunately, the financial community has a
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number of rich ontologies and taxonomies that are already hierarchical in structure. As just one example, the Global Industry Classification Standard (GICS) is one such taxonomy created by Standard & Poor’s (S&P) and Morgan Stanley Capital International (MSCI). In it, all public companies are organized according to their business activities: into sectors (10), industry groups (24), industries (68), and subindustries (153). For example, the Energy industry group is the parent of Oil, Gas, and Consumable Fuels, which in turn is the parent of Oil & Gas Drilling (which contains 64 members). When inferring causality, such hierarchical data might be used to isolate drivers based on their effect on specific peer groups and provide an approach to estimating specific risk at various hierarchical levels. Similarly, supply-chain data (also readily available) might be used for the same purpose. SHIFTING KNOWLEDGE IN THE GLOBAL CAPITAL MARKETS In the global capital markets, belief changes. One particular challenge in creating an enterprise risk management model is to keep up to date as theory or experience drives belief. Knowledge is knowledge only until a better sensemaking model comes along. Knowledge changes over time, and it sometimes takes years to converge on truth. For example, in the late 1970s, so-called standby commitments in GNMAs traded at a fairly constant 1/4 point per month. At that time, the Black-Scholes option-pricing model was yet not widely used, and little attempt was made to quantitatively value these securities (if it had been, they would have been seen to be significantly underpriced). These contracts were essentially one-month, at-the-money options that allowed a lender to protect itself from a decrease in mortgage rates after it had made a mortgage commitment to a borrower. Experience and theory both triggered sophisticated dynamic valuation models just a few years later. Likewise, consider the yield spreads at which corporate debt traded more than a decade ago. All else being equal, these bonds and notes traded at relatively stable spreads over comparable Treasury issues, based on the credit rating assigned by the ratings agencies. However, by the late 1990s, credit derivatives were becoming more widely traded, and structural credit models (which considered the capital structure of a particular company2) were used to estimate statistics such as probability of default in a much more sophisticated manner.
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The graph in Figure 14-1 seems to indicate a sea change in the behavior of credit spreads, commencing in late 1998 (at about the same time that these new models became commercially available), when the use of credit derivatives became more widespread and sophisticated. Although market events such as the collapse of LTCM triggered increased volatility, credit spreads appear to henceforth exhibit new patterns of behavior relative to other ratings buckets; for example, there was more differentiation between rating categories after 1998 than before for investment-quality ratings. In a market system, it is human knowledge, preferences, and biases that define the nature of interrelationships. Even in high-frequency trading, humans design the algorithms, set limit and margining rules, and write the computer code that generates automated orders. Market prices therefore reflect consensus opinions, risk preferences, and cognitive biases—accurate or not, rational or not, stable or not. Sometimes the market provides warnings of an incipient risk condition. There are few true complete surprises. And although the first event may be minor or may be dampened by the system, the same may not be true the second time around. Such a warning was provided in 2005, and it provides an example of shifting and valuable knowledge about system vulnerabilities. An Example: Correlation Risk in CDS Indexes Two years before the credit crisis, the June 2005 issue of Risk magazine related the difficulties in hedging a credit default swap (CDS) market basket or index. As the author, Navroz Patel, stated, “Market dynamics have prompted multi-million dollar mark-to-market losses on structured credit trades. Idiosyncratic risk has exposed the frailty of hedging in an imbalanced correlation market.” The article related an anecdote about the type of widespread loss that shocks market participants into new models and new solutions: The downgrade of Ford and General Motors (GM) to junk status by Standard and Poor’s last month was widely anticipated in the credit markets. What was not understood—by most, at least—was that the ratings action would prompt an unprecedented period of stress in the singletranche credit market. Risk managers at some dealers, hedge funds, and other investors were left reeling, with commonplace hedging and investment strategies suffering multi-million dollar mark-to-market losses. “To be frank, much of the market was caught out. They didn’t think that the downgrade of Ford and GM would cause such a significant impact on correlation,” says Robert McAdie, global head of credit strategy at Barclay’s Capital in London.
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Figure 14-1 Credit Spreads by Ratings, 1995–2003, from AAA to B
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The article goes on to discuss the accuracy of correlation models. In fact, credit derivatives traders estimate implied correlation in a way similar to that that option traders use to calculate implied volatility (both of which are statistically based measures). It points out that in the period between April 29—the last trading date of that month—and May 11, one iTraxx credit derivatives index blew out from 29 basis points (bp) to 53 bp. (Although this doubling was extreme at the time, it was dwarfed by levels in 2008.) Furthermore, the implied correlations in U.S. equity tranches had been volatile as well, moving from a level of around 24 percent in midApril to around 12 percent on May 10. Such movements are important to P&L: theoretically, higher correlation increases the value of an equity tranche to a seller of protection. However, using a statistical measure such as correlation for measuring the value or risk of such instruments is intrinsically flawed. If there is any type of financial crisis that is capable of causing a chain reaction, it is a credit crisis. And perhaps the least acceptable assumption of all is the fact that proper use of correlation coefficients requires that there be a linear relationship between the two variables. This certainly cannot be assumed for the single-name credit derivatives in the index. And even if such a linear relationship exists, recall that this coefficient intrinsically depends on a least-squares fit—that is, one in which the sum of the squares is minimized. Use of this objective function makes the solution far more tractable and is a holdover from an era long past in which such calculations might have been performed by hand. If one were starting from scratch today in defining this objective function, one might very well pick something else to minimize. The article goes on to state: “The losses have certainly raised questions about the accuracy of correlation models,” says Andrew Feldstein, a New York based founder of BlueMountain Credit Alternatives, a hedge fund with $2.7 billion worth of assets under management. . . . But not all funds active in the credit space are hurting. Dealers tell Risk that the larger, more sophisticated funds that incorporate fundamental analysis into their approach are weathering the storm best. “Idiosyncratic risks have caused many credit funds problems, but some of the major structured players are doing OK,” says one dealer.
The article goes on to describe the need for a sea change in risk management methods:
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Irrespective of whether or not the market tumult prompts any dealers or hedge funds to exit the structured credit market permanently, it will certainly have an impact on how they choose to risk manage them from now on, say observers.
This clear warning obviously wasn’t heard by all market participants. Case Study: A RIN for Dynamic VaR In the simplified risk inference network of Figure 14-2, a model of dynamic VaR is illustrated. In it, a random price movement in a particular security triggers an increase in VaR, which in turn causes position liquidation by some traders who hold that position. Case Study: Testing Regulatory Rules When a shock to the system has occurred, the first reaction is often to make dramatic changes in regulatory policy and extensive changes in protocols and procedures. However, based on systems theory, we need to ensure that the cure is not worse than the illness. A network model might be used to analyze such potential solutions. For example, if over-the-counter (OTC) positions in certain derivatives
Figure 14-2 Dynamic VaR Model
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instruments must be “given up” (i.e., transferred) to an exchange,3 the risk that one party will not perform on the contract is transferred from two individual counterparties to one counterparty and the exchange’s clearing corporation. The purpose of such a protocol is to allow netting of positions in order to reduce systemic credit risk. However, the clearing corporation that guarantees the exchange’s performance consists of a number of major financial institutions, most of which take substantial risk positions in those same derivatives themselves. And although there may be less systemic risk under normal conditions, analysis of the network may indicate that there are certain scenarios (e.g., a very large trading loss by one of the members of the clearing corporation) that jeopardize the creditworthiness of the clearing corporation and trigger a cascade of credit failures systemwide. LESSONS LEARNED: THE IMPLICATIONS OF SELF-ORGANIZATION In creating a systems model or an enterprise risk model, it’s important to be aware of the dependency of the enterprise on the self-organizing nature of the broader system within which it operates, and its ability to organize to a new state. Such self-organization is a source of model risk for any ERM model, and it makes continuous monitoring of the system for indications of such a shift exceedingly important. In Chapter 10, we discussed the implications of a self-organizing system and network-centric operations in warfare. There are historical studies that indicate that in combat situations dating back centuries, casualties follow a power-law function. However, it would be wrong to assume that the power law is an intrinsic feature of a self-organizing system. It has certain features (such as critically important “breakthroughs,” often geographic) that may not have a direct analogy in the financial space. We’ve shown that more realistic representations (e.g., trees that grow in clusters rather than being evenly spaced) may exhibit some recovery features (the ability to regrow locally) that produce other distributions (e.g., a Poisson distribution). This ability to recover spontaneously is more similar to the birth and death of hedge funds than it is to warfare, and the importance of feedback loops in financial actions and prices may tend to prevent some outcomes. So, in order to understand the evolution and dependencies of a system, it’s important to (1) create realistic representations of the system, its interconnectivity, and its responses, (2) use agent-based or other simulation tools to reveal the emergent behavior of a system and analyze its
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sensitivities to assumptions, and (3) study historical price movements to determine (similar to the historical studies of combat casualties) whether the network model represented reality in the past. We might create mathematical metamodels that are intended to describe the dynamics and sensitivity of the system more clearly. If, in an agent-based simulation (in which adversary agents collect intelligence and act on it to their own benefit), the network can be represented in terms of a relatively few meaningful variables, then such metamodels can create transparency and provide guidance to those who would manage the system (e.g., a systemic risk regulator) or those who would control their own risk (e.g., hedge funds) as a mere element of the larger system. Such systems thinking has implications even for users of statistical methods. It can assist in identifying the point in time when a regime shift occurred and define new protocols for normalization of key parameters so that they do not include data from previous regimes that are unlikely to be representative of the future. SUMMARY In this chapter, we discussed the usefulness of a RIN as a framework for enterprise risk management, not only because it can measure all integrated sources of risk, but because it creates transparency and can better assist C-suite executives in decision making and in meeting aspirational objectives. Furthermore, such a framework promotes systems thinking and makes all market participants aware of the self-organizing nature of a changing marketplace. WHAT’S NEXT In the next chapter, we discuss methods for inferring causality from market data alone, as an additional technique for more easily creating and automating a model of enterprise risk.
CHAPTER 15
Inferring Causality from Historical Market Behavior
CAUSALITY AND PREDICTABILITY Determining causality is a worthy goal with abundant rewards. Causality implies predictability—especially about situations that are unlike any that occurred in the past. Predictions based on causality may be discrete and certain in the case of an inevitable consequence, or they may be continuous and uncertain in the case of a distribution of possible outcomes. They may provide targeted warnings of systemic or specific risk if the observed behavior deviates from that predicted. Or, they may instead simply signal anomalous behavior— for example, when a causal relationship starts to fail—indicating the possible presence of an important new driver of change. But for all their elegance and utility, causal inference models present new challenges. Unless causality either is known with confidence (e.g., deterministic margining rules), can be elicited from subject matter experts (e.g., the effects of an attack on a nuclear facility), or utilizes shortcuts (e.g., substitutes statistical for causal representations of relationships), such models may be difficult to design and populate. This is particularly true for complex systems that exhibit emergent behavior. Although chaos is a cryptic form of order, it may be difficult to deconstruct the component dynamics of such a system. And in finance, the myriad drivers (both systemic and specific) that affect each security can make it difficult to identify the physics of a causal cascade that leads to extreme outcomes. Fortunately, the advances in both market technology and decision theory now facilitate the discovery and expression of causation.
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THE DISCOVERY OF CAUSES Scientific approaches for discovering causes from data are relatively young. As Judea Pearl points out, “The possibility of learning causal relationships from raw data has been on philosophers’ dream lists since the time of Hume (1711–1776).” He also points out that “that possibility entered the realm of formal treatment and feasible computation in the mid-1980s, when the mathematical relationships between graphs and probabilistic dependencies came into light.” But, as discussed in Chapter 11, a precise definition of causality has been a philosophical minefield for millennia. As humans, we have an intuitive notion of causality: if X causes Y, then every time that X occurs, so too will Y. We also gauge causality by temporal order: if Y follows X, then Y could not have caused X. But such intuitive rules are insufficient. To paraphrase computer scientist John Sowa, three generally accepted conditions for causality (at least until the mid-twentieth century1) were 1. There is some law that dictates that the occurrence of X results in the occurrence of Y, where X and Y may be objects, phenomena, events, or situations. 2. The cause must be prior to or simultaneous with the effect. 3. Cause and effect must be connected; they must either be in direct contact or be connected via an intermediate chain of connections. Recall that the first condition describes deterministic causation, in which Y inevitably follows X. However, it doesn’t consider probabilistic causation, in which the occurrence of X merely increases the probability of Y. When probabilistic causation is observed, it may be evidence of a causal system that includes chancy components. Or, it may merely be an artifact of a deterministic system that is insufficiently well specified. The objective of much recent work is to define a scientific framework for inferring or validating causal relationships from empirical data. MINING FINANCIAL DATA FOR CAUSALITY Some experts in causality question the utility of using historical data for the purpose of identifying or validating a causal relationship. They are of the opinion that only experimental research, in which variables are carefully controlled (for example, as in medical research), is a legitimate method of isolating a single cause and measuring its resultant effect.
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Such a method is certainly not an option in the financial sphere; we cannot shock, say, the U.S. dollar and observe its effect on gold. But we do have access to millions of natural experiments. Every day, events small and large drive market prices. For example, Figure 15-1 shows daily spot gold prices tagged with major economic and financial events.2 In the past, such low-frequency (i.e., daily) pairings between an event and a price had limited use; many events occur over the span of a trading day, and inferring causality from such data was the equivalent of trying to gauge the efficacy of a single drug in a patient who’s taking 10 different drugs. But today, advances in trading technology give us the mathematical equivalent of a more tightly controlled experiment. Zooming in on a microscopic view of trading activity, we can identify periods of time (perhaps seconds, perhaps minutes) during which there was only one important driver. The price of a single stock may have been influenced by many events in the course of a single trading day: information that is specific to the company, its industry, the supply chains on which it depends, and the general state of the economy. However, usually just one of these factors was the dominant driver for prices, say, between 10:33 and 10:35. In a sense, the data space was “excited” by a piece of news, and this provides us with a de facto natural experiment. And because there are thousands of important events each day (important to some securities and sectors, if not to the broad markets), even a few years of high-frequency data may be the experimental equivalent of millennia of daily data.
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The task is made easier because lags between cause and effect are minimal.3 As a result of global market connectivity, today’s market prices react universally and instantaneously to a shock anywhere throughout the system. We now have the requisite data to uncover causal structures. We can obtain pricing data that are accurate to within a few milliseconds, thanks to the technology built to support algorithmic trading. And commercial information services are now accurately time-stamping events, and even tagging them with keywords that help identify their importance and influence.4 So, the nature and timing of individual events (both scheduled events such as the release of economic indicators and unscheduled events such as news) can be categorized and synchronized with high-frequency pricing data. We can, therefore, create highly granular and reliable time stamps for both events and market prices to establish temporal order and observe reactions. Cause and effect can now be directly linked. A Low-Frequency Example: Monthly Unemployment Statistics This synchronization process is not unlike the ones used to measure the market’s reaction to scheduled events such as the monthly unemployment report. As shown in Figure 15-2, experts are polled on their expectations for the headline statistics (such as the month-over-month change in nonfarm payroll), and the survey results are widely reported. Market prices anticipate this change, and generally react only if the actual value deviates widely from the survey. With these data, an analyst can compare immediate price reactions (say, in the first minute after the release) as a function of forecasting error and measure the magnitude of the bond market’s reaction as a function of survey error (implicitly assuming that little else of importance is happening between 8:30 and 8:31 on the first Friday of each month).5
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Figure 15-2 U.S. Employees on Nonfarm Payrolls, Total Month over Month Net Change Source: Bloomberg, L.P.
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Figure 15-3 Implied Probabilities of Multiple Paths for Fed Funds Rate over Time (December 18, 2009) Source: Bloomberg, L.P.
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Such information might provide bond traders with actionable intelligence. For example, if history showed that, on average, long bond prices could be expected to drop 1 percent if the actual number released were 100,000 higher than the survey average, a trader might profit from anomalous price behavior in postrelease trading. A Forward-Looking Example: Implied Probabilities of Future Fed Action The previous example measured an expected reaction; we can also observe the uncertainty about the expectation. Because of the abundance and variety of derivative securities (many of which have a temporal component), we can obtain distributions of expectations about the future directly from market prices—again, at very high frequency. As in the previous example, we might measure the effect of an event on consensus forecasts—in this case, for a number of horizon dates. Figure 15-3 shows both the expected fed funds rate and the probabilities of various alternative levels, as reverse-engineered from options on fed funds futures. It shows the asymmetrical distribution of outcomes and multiple paths to those outcomes over time. A Higher-Frequency Example: News on Venezuela Consider also a higher-frequency example in which price change is triggered by geopolitical action. On January 8, 2007, Hugo Chavez of Venezuela suddenly and unexpectedly nationalized a number of companies, including telecommunications provider Compania Anonima Nacional Telefono de Venezuela (CANTV). CANTV is a public company that traded both in Caracas and in New York (as an ADR). As shown in Figure 15-4 (which shows the price of CANTV in one-minute intervals), its price dropped about 14 percent in just seven minutes before trading was halted in New York. Certainly, this was anomalous behavior, given the stock’s price stability before the news. (One didn’t have to wait the full seven minutes, either, to see that something was up.) If the tagged news and price action were matched, cause and effect would be clear. Even without access to any news, a market observer might reasonably conclude that an exogenous event was the cause of CANTV’s precipitous change in price; however, he could not conclude whether the root cause was a telecom-related event, a Venezuela-related event, or something else. However, if CANTV and other companies were tagged with characteristics such as “telecom” or “Venezuela” or “large cap,” similar price movements in multiple companies all tagged with “Venezuela” might have pointed conclusively to an action by the Venezuelan government.
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Figure 15-4 Price Activity in CANTV, January 8, 2007 Source: Bloomberg, L.P.
Such an inference process might be automated, and the nature and likelihood of even a hidden event might be estimated by observing which securities moved and which did not. Clearly, such an analysis would be even more credible with more granular data, and this is not unlike the methods used by some high-frequency hedge funds. Knowledge Mining Knowledge mining is the process by which data are converted to knowledge that is suitable for inclusion in a sophisticated model. There are a number of mathematical methods used to perform such mining and software products6 that attempt to assist in the conversion of empirical data to knowledge about causality. Knowledge mining is a form of data mining, which attempts to identify patterns (e.g., patterns in consumer behavior) from raw data. In an exceedingly complex system such as the financial system, relatively unconstrained methods, such as those that employ neural networks, can suffer from too having many degrees of freedom, including nonlinear and noncontinuous relationships and the like. However, knowledge mining guided by expert knowledge exogenous to the data might produce repeatable patterns. Similarly, if the choice of data is carefully controlled (e.g., if different states are identified, and data from all but one state are filtered out), such methods might be used to identify expected behavior under normal or extreme conditions, and separately identify patterns of behavior for each.7
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ANALYZING THE NATURAL EXPERIMENTS Most predictive models in economics and finance rely on statistical methods either to serve as the foundation of the model or to create the parameters that inform it. Nevertheless, they often explicitly or implicitly account for causality, albeit in a form that does not account for the direction of cause and effect. Stochastic risk measurement models and econometric models are two such examples. The former are generally used to predict a distribution of possible outcomes, and the latter are generally used to predict the most likely outcome. Implicit Causality in Stochastic Models Even stochastic risk measurement models reflect expert opinion regarding causation. For example, certain parametric value at risk (VaR) models are informed by correlations between securities and fundamental economic risk factors, rather than by correlations between all securities. For a stochastic model, the metric of causation is the correlation coefficient; a high value implies a direct or indirect causal relationship. Theory is implicit in the choice of risk factors; otherwise, such correlations would be spurious if one could not assume that the factors served as proxies for market drivers that would continue to force such mathematical relationships in the future. Thus, human experts select the exogenous risk factors, and endogenous ones as well. The more sophisticated stochastic models— for example, those that model dynamic volatility—may implicitly reflect human behavior, which is, of course, influenced by recent patterns of price activity. As we’ve previously noted, there is nothing inherent in the structure of a bivariate distribution to indicate which of the variables is the dependent variable and which is the explanatory variable (nor if both variables are dependent on a third). But given the nature of the data, we can assume a kind of implied directionality. It’s unlikely that changes in market prices are the major driver of economic risk factors; instead, knowing what we know of investor behavior, it’s far more likely that economic conditions drive investor actions. Explicit Causality in Econometric Models The field of econometrics combines economic theory with quantitative methods in order to reveal economic relationships. Applied economists use mathematical methods to identify the causality that they seek to
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reveal. Such relationships can, in turn, be used to forecast future economic states. Thus, understanding causality in this field takes the form of (1) identifying exogenous variables and characterizing their interaction with the system, 8 and (2) testing for causality in a mathematically rigorous manner. Econometricians often employ statistical methods applied to macroeconomic time-series data, because they, too, are constrained from identifying causality through the use of controlled experiments. In time-series data, both the value of the observations and their order have meaning. But they might also use data without an explicit temporal component, such as cross-sectional data (in which information about some phenomenon is observed and aggregated at a single point in time) and panel data (in which such data are observed over multiple periods of time). Identification of Causality via Simultaneous Equations In economics, statistical parameters such as correlation may hint at causality, particularly if the process was guided by the expert knowledge of an econometrician. But the concept cause does not exist in statistics. Nevertheless, complex system dynamics can give rise to a situation in which statistical methods are insufficient to reveal causality—even deterministic causality. In such a case, econometricians use alternative methods to establish causality, including techniques to identify the presence of more complex relationships, such as the existence of simultaneous equations, and to estimate their parameters. For example, consider the cobweb model of Figure 11-1. In the graph, the supply and demand curves for a given commodity have slopes of opposite sign, and their intersection reveals the commodity’s equilibrium price. Assume that we have historical data on the price and traded amount of this commodity that are exactly represented by the theoretical model (that is, there are no error terms). If we attempt to solve for price as a function of quantity traded using a linear regression, we will fall afoul of the parameter identification problem that can be present in the estimation of simultaneous equations with a variable in common. A bivariate regression can produce only a single fitted line, not the two (supply and demand) that are required to properly represent price dynamics. Econometricians instead use alternative methods (for example, the introduction of additional variables) to identify the two simultaneous
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equations that are required to properly portray these price dynamics. Estimation theory is a fusion of statistics and signal processing that might aid in estimating the values of parameters from empirical data. Granger Causality One of the most popular tests for causality is one formulated by Nobel Prize winner Clive Granger. Granger argued that a set of statistical tests on time-series data might reveal the presence of a causal relationship for certain classes of problems. The Granger causality test is a test of whether one time series is useful in predicting another. In Dr. Granger’s own words, In the early 1960’s I was considering a pair of related stochastic processes which were clearly inter-related and I wanted to know if this relationship could be broken down into a pair of one-way relationships. It was suggested to me to look at a definition of causality proposed by a very famous mathematician, Norbert Weiner, so I adapted this definition (Wiener 1956) into a practical form and discussed it. Applied economists found the definition understandable and useable and applications of it started to appear. However, several writers stated that “of course, this is not real causality, it is only Granger causality.” Thus, from the beginning, applications used this term to distinguish it from other possible definitions.
Although the correlation coefficient of two time series X and Y may hint at a potential causal relationship between the two variables, it provides no information about whether knowing X enhances our ability to forecast Y. In a Granger causality test, a time series X is said to “Grangercause” Y if Yt occurs before Xt ⫹ 1, and if the information contained in Yt is uniquely useful in forecasting Xt ⫹ 1 (that is, if it contains information that is not found in other variables). As Dr. Granger described, the process goes as follows. First, we attempt to forecast Xt using only past terms of Xt and Wt , where Wt is a Wiener process (i.e., Brownian motion). Then, we again try to forecast Xt ⫹ 1, this time using past terms of Xt, Wt, and Yt. If the second forecast has greater predictive ability than the first (using standard statistical tests), then it appears that Y is uniquely useful and “Granger-causes” X. However, such a test has its limitations. Its quality may depend on the intuition of the economist; if she does not test the appropriate variables, then causality may not be accurately identified. Likewise, issues such as anticipation can invalidate the test. And most important, if the data sampled come from two different economic regimes, then the method may likewise be inappropriate.
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THEORY-DRIVEN VERSUS DATA-DRIVEN APPROACHES There are two primary paths to the discovery of knowledge about causality: the theory-driven approach and the data-driven approach. In each case, both factors of influence and interference and their functional relationships are surmised or revealed. In the theory-driven approach, the analyst hypothesizes some model of a system and then attempts to determine whether observational data bear out or contradict that theory. Conversely, in the data-driven approach, a modeler assumes no prior knowledge about systems behavior, and instead attempts to infer causality from empirical data alone. The Theory-Driven Approach When early astronomers validated Newton’s law of motion via planetary observations, they were using a theory-driven approach. In a Bayesian analysis, a set of observations should be seen as something that changes an opinion, rather than as a means of determining the ultimate truth. In a theory-driven approach, theory is the prior opinion of how a dynamic system works, and theory modified by testing against reality is the posterior opinion. This approach requires an iterative process, in which prior knowledge is refined to posterior knowledge as theory and experience merge. A theory-driven approach has the advantage of inserting expert knowledge at each step in the process; that is, each successive iteration of the model is guided by expert intuition as new information is revealed. Such an approach has a number of advantages. First, testing a theory against historical data is far easier than trying to extract the theory from the data. Second, this process is guided by expert knowledge. And third, second- and higher-order effects might be identified after filtering for firstorder effects. The Data-Driven Approach A data-driven approach relies on inductive reasoning, that is, the process of transforming data to theory that allows the prediction of future knowledge. In an article in The Economist, Dr. Judea Pearl has suggested that by analyzing scientific data using a Bayesian approach, it may be possible to distinguish between correlation (in which two phenomena, such as smoking and lung cancer, occur together) and causation (in which one actually causes the other). Fortunately, present theory is well developed (much of it by Pearl in the early 1990s) and now includes methods that are well suited for
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financial problems. For example, there are now mathematical criteria used to establish various types of causality, including potential causes, genuine causes, spurious association, and genuine causation with temporal information. Supported by such theoretical foundations, methods now exist for inferring causal structures as well as studying the relationships between statistical relationships and causal connections. For example, under certain conditions, one might be able to recover a directed acyclic graph (DAG) structure or even to recover a latent structure (one in which certain elements are hidden from view). As noted by Pearl, “With the added assumption of stability [of the distribution], every distribution has a unique minimal causal structure . . . as long as there are no hidden variables.” Although a discussion of such methods is beyond the scope of this book, the hierarchical approach to building Bayesian inference models is ideally suited to the task of decomposing chaos into a set of manageable fragments that can later be recombined in useful ways. Since it is now possible to better synchronize market movements with market drivers (and, by doing so, meet temporal conditions), it may be possible to establish some elements of causation from market data alone without expert knowledge. Likewise, these same synchronized data are ideally suited to testing and refining theoretical models. THE RELIABILITY OF HISTORICAL INFERENCE In previous chapters, we argued that the global financial system is inherently unstable. We described its evolution over time as occurring via a number of jumps from one state to another, triggered by endogenous or exogenous events. And although a process of self-organization might inevitably generate a new version of a stable system—at least until the next change in state—we’ve seen that even sophisticated market participants such as Lehman Brothers and Bear Stearns may not survive a tumultuous transition period. We have further made the point that it is difficult to identify an unstable system solely from historical statistics. The astute reader might reasonably ask whether this is also an issue with causality inferred from historical data. The answer is a qualified yes. In spite of the fact that the global financial system continually evolves in small ways and large, historical data can nevertheless provide evidence of causality. Although old cause-and-effect relationships may change and new ones form, there are still carryovers from state to state, not the least of which are behavioral effects. Human
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nature is one of the few constants, and human preferences—especially with respect to risk aversion—are one of the major drivers of market prices, perhaps even more important than any invisible hand. A firm that recognizes the causal capacity of the current state—and then first notices indicators that may trigger a chain reaction that uses that capacity—can beat the crowd by initiating changes in strategy that mitigate loss or generate profit. Thus, statistical representations of a system’s current state tend to be reasonably stable, until they are not. And parameters based on a single state, or even parameters that span data from multiple states, may not adequately represent the extrema that might occur during a transition period. The pendulum might also swing too far during the transition period between two locally stable states; if new events and drivers don’t create extrema, behavioral effects such as extreme risk aversion, forced position liquidation, and new investor preferences will create consequences that irrevocably change the system before a new equilibrium is achieved. Nevertheless, the current state, even if it appears to be stable, contains the seeds of the next state, in that it contains some causal relationships that even a completely unexpected event or driver might trigger. For example, it’s clear in hindsight that the extension of mortgage lending to the less creditworthy, coupled with massive credit exposure in the form of mortgage and credit default swaps, increased causal capacity long before the chain of events that created the credit crisis of 2007-2008 commenced. However, it took expert knowledge of the underlying conditions and market protocols (for example, the size and nature of major financial institutions’ derivative positions) and a deep understanding of the interrelations among all the players (from individual mortgage holders to hedge fund managers) to forecast the conditions under which a meltdown might occur. Such information cannot be inferred from statistical examination of the well-behaved price activity prior to the start of the crisis. At most, such an examination can provide indications and warnings of an impending change in state when such models start to fail. Nevertheless, even an apparently stable system contains clues to its own potential instability and, more important, to the nature of the extreme scenarios that might occur. And examination of historical data by other than statistical methods may assist in the creation of models that systematically generate the most extreme scenarios, their consequences, and even their leading indicators.
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SUMMARY In this chapter, we discussed methods for inferring or testing hypotheses regarding causality from data, using a theory-driven or a data-driven approach. We also discussed techniques from other disciplines that are used to establish causality in economic and financial models, and compared the efficacy of stochastic and causal models. WHAT’S NEXT The next chapter discusses techniques for identifying anomalous market behavior and engaging in sensemaking for purposes of warnings.
CHAPTER 16
Sensemaking for Warnings: Reverse-Engineering Market Intelligence
INSIDER TRADING BY ADVERSARIES Immediately after the 9/11 attacks on New York and Washington, it was widely reported that there had been an unusually large amount of buying of put options on American Airlines and United Airlines on the last trading day prior to the attacks. This anomalous trading activity raised suspicions that someone with advance knowledge of the attack had engaged in insider trading based on that knowledge. While the official 9/11 Commission Report did not identify such insider trading, the reports nevertheless prompted widespread discussion of whether such insider trading was indeed possible and whether, if detected in advance, it could lead to the prevention of another such attack. Since then, extensive research and development has been devoted to both the modeling of such behavior by insiders and the detection of their actions in a timely manner. A recent Barron’s article1 indicated, “In February, India’s national security advisor, M.K. Narayanan, said at a security-policy conference in Munich that India had evidence of ‘isolated incidents of terrorist outfits manipulating the stock markets to raise funds for their operations.’” And Christopher Cox, former chairman of the Securities and Exchange Commission, indicated that “the intelligence reports [by the CIA] offer the SEC a ‘somewhat sharper focus’ to an ‘underworld of murky, illegal dealings that threaten the world capital markets.’” Whether or not terrorists or their confidants actually engaged in insider trading, the possibility illustrates the potential for live sensemaking using open-source market data. Whether for purposes of enhancing national security, protecting the financial system, or merely reducing 230
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portfolio risk, market data can be used to reverse-engineer warnings of systemic or specific risk. TRADECRAFT AND MARKET INTELLIGENCE The intelligence community and the financial community have much in common. Each community seeks to obtain key data and perform analyses that give it an edge in decision making. Toward this end, each can benefit from the use of market intelligence2 (MARKINT). In this context, market intelligence is defined as the systematic collection and analysis of open-source information from the global capital and commodities markets in order to derive actionable intelligence from the activities of market participants. In this new field, “tradecraft” has a double meaning. Insider trading rings have been known to use disposable cell phones and dead drops (e.g., messages left in trash barrels) to relay confidential market information and illegally profit from that information. The legitimate trading community similarly uses techniques that are not fundamentally different from those used in military and intelligence activities. As Reuters described it, Snipes, sniffers and guerillas3 are lurking in the stock market. So are dark pools, daggers, boxers, slicers and nighthawks. Reflecting the nature of the struggle for ascendance in algorithmic trading—or simply, the algo wars— investment banks and hedge funds have been giving military monikers to their increasingly complex and machine-driven trading strategies. The battlefield names may well be suitable, given that many of the strategies seek to disguise a trader’s real intentions, deflect the strategies of rivals and take advantage of them, or capture fleeting anomalies in market behavior.4
U.S. Army Captain Tim Hsia further described the similarities between trading activities and combat operations: Stocks are traded and bought based on intelligence. Any individual trader can access a plethora of information from open sources: basic charts showing a company’s past performance, insightful analysis of the company from several analysts, company key leadership, income streams and expenditures, blogs by other traders, and future projected earnings. . . . Additionally, traders with insider information can profit spectacularly by making bets that a certain company will move forward on a certain course of action. The stock market mirrors combat and counterinsurgency operations primarily because intelligence is the driving factor in both realms. Without proper intelligence, commanders are likely to make decisions that do not
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accurately match the historical patterns and events of the local area. By accessing a geointel site they can quickly sift thru actions made by previous commanders and assess the effectiveness of certain actions.
TAPPING THE ULTIMATE COLLABORATIVE ENVIRONMENT MARKINT thus provides access to the ultimate collaborative environment. The global capital and commodities markets serve as intelligence aggregators, reacting in real time to new information (either public or confidential), expert analysis, and changing risk preferences, as revealed by trading activity. MARKINT is a way to tap into the collective wisdom of market participants, weighted by the size of their bets (which correlates with the quality of their resources and knowledge). Since market prices change continuously, MARKINT is the equivalent of an automated, real-time poll of global subject matter experts (friendly or unfriendly), weighted by their seniority, skill, and confidence in the quality of their intelligence. And this poll can be taken again milliseconds later. THE THEORETICAL FOUNDATIONS FOR MARKINT There is a sound theoretical foundation for MARKINT. Recall that, according to the efficient market hypothesis (EMH), the market price of any security or commodity reflects all information known about that security or commodity at that particular point in time. EMH’s complement, behavioral finance, posits that market prices are not a mechanical composite of all drivers; instead, they also reflect individuals’ preferences and biases, rational or not. The source of this knowledge may be global, well funded, and proprietary research performed by major financial institutions, or it may be insider information known only to those who are privy to market-moving events such as an upcoming large-scale terrorist attack or military invasion. Thus, the market price of a security reflects implied forecasts—both of the expected future price and of the level of uncertainty about that forecast. Both are useful for purposes of warnings: a merger may or may not occur; a military invasion may or may not succeed. Fortunately, at the point when an expert or insider attempts to monetize his information (by executing a transaction), his knowledge enters the public domain. Every new transaction leaves its fingerprints on market prices, and anomalous changes in market price can be observed and interpreted.
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More than just the “wisdom of crowds,” MARKINT principles allow analysts to reverse-engineer the changing consensus opinions, forecasts, and even level of risk aversion of experts or insiders, weighted by the amount of money that those investors are willing to bet. Furthermore, the nature of such changes (at a country, industry sector, company, or other hierarchical level), alone or in combination with other observed changes, can be reverse-engineered to provide actionable intelligence on a realtime basis. There are a number of clues that might assist in a sensemaking effort. The manner in which the trade was executed, the venue selected, and even attempts at obfuscation may all assist the astute observer in deciphering the identity, motive, and intent of the executing party. Even trading by a state actor or its confidants can reveal that actor’s intent and resolve during a geopolitical conflict. And detection of such “insider trading”—either individual or statesponsored—is an old and well-developed skill on Wall Street. There is a saying, “There are no secrets on Wall Street.” U.S. exchanges, regulators, and oversight agencies and the surveillance officers of broker-dealers, assisted by sophisticated quantitative models and technology, are all skilled in the detection of unusual patterns of behavior. And irrespective of the marketplace in which a trade was executed— e.g., on a Chinese exchange, on a U.S. or European exchange, or in a private over-the-counter trade—the interconnected global market ensures that market flows anywhere in the world and in any form are almost instantaneously reflected in prices around the globe. For example, if an over-thecounter trader in London executes a transaction with a secretive hedge fund, his hedging activities (say, on a Chicago futures exchange) can be instantly observed globally. Arbitrageurs’ actions will ensure the efficient transmission of information throughout the global market system. Even more to the point, such methods are tried and true, at least in the financial community. Some hedge funds use variations of such models to detect insider trading and profit from it within seconds, using algorithmic trading models and systems that identify signals from real-time market data and execute transactions designed to profit from such signals automatically and without human intervention. (In fact, such activities serve to amplify small but anomalous signals until they are more easily detectable.) Often, the signal detected indicates insider trading and foreknowledge of an upcoming market event, such as a takeover or an earnings announcement. Piggybacking off such a signal is legal and is not considered to be insider trading if the trader is not privy to the inside information itself.
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In the specific case of a state actor such as China, insider trading might be either state-sponsored or private. For certain events or drivers (e.g., a hypothetical invasion of Taiwan), the Chinese central bank might take certain actions to mitigate China’s financial and economic risk from upcoming events. In such a case, large flows—even if executed slowly and methodically—might easily be observed because of the massive size required. Derivative instruments such as options on equities or credit default swaps provide a particularly rich source of intelligence, and provide even more insight regarding how investors gauge the probability and timing of certain extreme events. For example, as of December 8, 2008, the CDS markets implicitly estimated5 (correctly or not) that the probability of default by the United Kingdom on its sovereign debt within the next five years was greater than that of Hong Kong and Shanghai Banking Corporation (HSBC). Similarly, the very low yields on short-term Treasury bills6 imply that a massive “flight to quality” has occurred, reflecting extreme levels of risk aversion.7 Options are similarly useful, because the insider’s choice of strike price and expiration date provides valuable information about the expected magnitude of the event (if a far-out-of-the-money option is selected) as well as temporal information (the event is expected to occur before the expiration of the option). GENERATING INDICATIONS AND WARNINGS The most useful application of MARKINT for either financial or intelligence purposes may be to either (1) provide indicators that quantify threat levels or (2) provide warnings of imminent events. Each community is already familiar with such metrics. What the intelligence community calls a “threat metric” for a state actor, the financial community calls “country risk.” And what the intelligence community calls “indications and warnings” (I&W), the financial community calls “anomaly detection.” For the financial community, such I&W might be of increased levels of risk aversion (the indication) or trading patterns consistent with insider information about an upcoming event (the warnings). For the intelligence community, they might be of state actor intent and resolve during a current geopolitical crisis (both indications and warnings). In the financial community, such indicators already exist—generally, for broad market risk. For example, the IMF uses the levels of the volatility index (VIX), euro—U.S. dollar swap spreads, and the TED spread8 as indicators of risk. Similarly, the Westpac Strategy Group creates a Risk Appetite Index, calculated from market prices.
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Similarly, warning systems exist. For example, credit rating agencies use automated means to identify anomalous stock price behavior consistent with an important company event. (Such warnings trigger an investigatory phone call to company management.) CONCEPTUAL FRAMEWORK Making market intelligence actionable requires a structured approach to building a conceptual model of reality. As previously described in Chapter 7, a conceptual model is a collection of knowledge and interdependencies used to represent the dynamics of a real-life situation. With such a model, MARKINT can be created using either a bottom-up or a top-down approach. MARKINT can be used to answer either broad or narrow questions, and, as always, the quality of the answer depends on the quality of the question. Such questions can be exceedingly specific (e.g., warnings of the target, means, and timing of a terrorist attack; indicators of vulnerability in the health-care sector) or quite broad (e.g., measurement of a state actor’s intent and resolve during a geopolitical crisis; indicators of increased systemic risk). In a bottom-up approach, an analyst might generate a particular threat scenario. In the financial community, this might be a sovereign default by Dubai. The analyst would attempt to anticipate the causal chain of micro shocks that would trigger such a default, and set a MARKINT model to looking for such indictors. In a top-down approach, all relevant markets are monitored for anomalous behavior. Then, based on knowledge of common links or dependencies, a sensemaking engine might be used to put the pieces together to point to some theoretical scenario. That is, a number of isolated signals (and lack of others) might allow a model to triangulate in on some hypothetical future event. The bottom-up approach has the advantage of being extremely specific, so that if signals are generated, they are more likely to have value. However, this approach has the disadvantage of signaling only known scenarios. For example, only a scenario that anticipated using planes as weapons might have provided warnings of September 11. Conversely, the top-down approach has the advantage of being allencompassing and not requiring preliminary scenario generation. However, it is far more vulnerable to accidental correlation and false positives. In practice, both approaches are useful. At the very least, the most extreme scenarios to which an enterprise is exposed should be modeled.
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For example, a financial institution might include the scenarios that it uses to estimate economic capital and ensure its continuing survival. THE GLOBAL MARKETS AS PREDICTION MARKETS At the heart of MARKINT is the fact that the financial markets are a portal into changing global opinion, implicit intelligence and forecasts, and state actor intent and resolve—benign or malevolent. In a sense, the global capital markets are prediction markets, except that the predictions must be inferred using expert analysis. THE DEPARTMENT OF DEFENSE AND PREDICTION MARKETS Impressed by the ability of consensus opinion to outperform expert opinion, the intelligence community has looked at prediction markets before. Between 2001 and 2003, the Defense Advanced Research Projects Agency (DARPA9), an agency of the U.S. Department of Defense, funded FutureMAP (Futures Markets Applied to Prediction), which was intended to be a market-based decision support tool. Like the Iowa Electronic Markets—an Internet-based futures market in which anyone can participate (albeit for no more than $100)— FutureMAP’s Policy Analysis Market (PAM) was a prediction market. However, unlike Iowa, PAM participants bet on the probability of events such as a North Korean missile attack or the assassination of Yasser Arafat rather than on who was likely to win an Academy Award. As shown in Figure 16-1, DARPA’s concept was that a market-based method might outperform other predictive methods, such as a poll of experts or more traditional analyses. The DARPA FutureMAP project was terminated in 2003, after an article in the New York Times subjected it to intense scrutiny. (Among other objections by Congress to FutureMAP was the hypothesis that someone might in fact carry out some of the hypothetical scenarios, such as assassination, in order to profit on the exchange.) Although the DARPA initiative may have been flawed, the basic premise was correct: that useful intelligence can be inferred using only publicly available data. Although the consensus market opinion regarding a specific question of interest may not be as easy to obtain as it would be if one could ask that question directly, it may nevertheless be possible to infer threat metrics or warnings of an upcoming event by analyzing market expectations as reflected in market prices.
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Figure 16-1 DARPA FutureMAP Concept
The following two examples—one from the intelligence community and one from the financial community—illustrate the use of MARKINT principles for purposes of warnings. Intelligence Example: Venezuela and Sovereign Debt Yields Venezuela is a dollar-based economy that is highly dependent on sales of oil and gas (which make up nearly 90 percent of its exports), which it exports primarily to the United States. Therefore, it might be considered anomalous if Venezuela were to dramatically shift its foreign exchange reserves out of U.S. dollars. Although Venezuela’s reserves cannot be directly monitored on a live basis, yields on U.S. and Venezuelan sovereign debt can. All else being equal, one would expect the two time series to move more or less in parallel, given the economic links between the two nations. However, as shown in Figure 16-2, yields (for five-year notes, in this example) have diverged at times, moving in nearly opposite directions during the threemonth period June 30, 2005, to September 30, 2005 (the left box). Conversely, previous to June 30 and during the four-month period February 28, 2006, to June 30, 2006 (the right box), the two series more or less moved in tandem.
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Anomalous Behavior: Move Out of U.S. Reserves Venezuelan Yields Drop while U.S. Treasury Yields Rise
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Clearly, an inverse relationship between the yields of these two notes is highly anomalous, especially if it is sustained for a three-month period. At the beginning of the third quarter of 2005, U.S. five-year notes were trading at about 115 basis points (bp) lower than Venezuelan five-year notes; however, by the end of the quarter, the two were at parity. Without knowing any additional details, a bond trader might surmise that a large-scale selling program was underway—that is, selling U.S. Treasuries and/or purchasing Venezuelan sovereign debt. This proved to be the case; at the end of September 2005 (at the apparent end of the reallocation period), Venezuelan President Hugo Chavez revealed in an off-the-cuff comment on his weekly radio show that Venezuela had transferred about half of its $30.4 billion in foreign currency reserves out of U.S. Treasury securities and banks and into European banks. Domingo Maza Zavala, a director at Venezuela’s central bank, shortly thereafter verified that, over the previous four months, 50 percent of the bank’s roughly $24 billion in operational reserves, or $14.4 billion, had been liquidated and the funds deposited in the Bank for International Settlements (BIS) in Basel, Switzerland. Because such a large and rapid shift seemed to have little economic justification, many surmised that this action was taken for political purposes—either to use the cash to effect political change elsewhere in the region (e.g., by lending money to Argentina), or to reduce Venezuela’s financial exposure to the United States in the event of hostile actions ordered by Chavez. [Chavez later nationalized a number of companies, some of which were at least partially owned by U.S. interests, and exited from the World Bank and the International Monetary Fund (IMF) in 2007.] Of course, there might be other reasons for such anomalous behavior, and false positives must be eliminated. For example, during the height of the credit crisis in September 2008, U.S. yields dropped dramatically, while Venezuelan yields nearly doubled (from about 2.5 percent to over 5 percent). However, this can be explained in large part by a decline in the price of oil, to which the Venezuelan economy is extremely sensitive, from over $140 per barrel in July to under $40 per barrel by December. Investors recognized the strong link between Venezuelan credit quality and oil price, while political scientists recognized the threat to Chavez’s “twenty-first-century socialism.” Financial Example: Goldman Sachs and Patterns in VaR MARKINT can also be created for strictly commercial purposes. In a bottom-up approach, warnings of specific risks can be generated, and
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this approach can even provide market timing signals. But anomalous patterns in performance can also provide trading I&W. In one application, monitoring the behavior of a risk metric such as value at risk (VaR) can provide warning of a change in risk regime and assist an enterprise in avoiding high-consequence events. For example, consider the anecdote reported on January 4, 2009, by Joe Nocera in the New York Times Magazine.10 How then do we account for that story that made the rounds in the summer of 2007? It concerns Goldman Sachs, the one Wall Street firm that was not, at that time, taking a hit for billions of dollars of suddenly devalued mortgagebacked securities. Reporters wanted to understand how Goldman had somehow sidestepped the disaster that had befallen everyone else. What they discovered was that in December 2006, Goldman’s various indicators, including VaR and other risk models, began suggesting that something was wrong. Not hugely wrong, mind you, but wrong enough to warrant a closer look. “We look at the P&L of our businesses every day,” said Goldman Sachs’ chief financial officer, David Viniar, when I went to see him recently to hear the story for myself. (P&L stands for profit and loss.) “We have lots of models here that are important, but none are more important than the P&L, and we check every day to make sure our P&L is consistent with where our risk models say it should be. In December our mortgage business lost money for 10 days in a row. It wasn’t a lot of money, but by the 10th day we thought that we should sit down and talk about it.” So Goldman called a meeting of about 15 people, including several risk managers and the senior people on the various trading desks. They examined a thick report that included every trading position the firm held. For the next three hours, they pored over everything. They examined their VaR numbers and their other risk models. They talked about how the mortgagebacked securities market “felt.” “Our guys said that it felt like it was going to get worse before it got better,” Viniar recalled. “So we made a decision: let’s get closer to home.” In trading parlance, “getting closer to home” means reining in the risk, which in this case meant either getting rid of the mortgage-backed securities or hedging the positions so that if they declined in value, the hedges would counteract the loss with an equivalent gain. Goldman did both. And that’s why, back in the summer of 2007, Goldman Sachs avoided the pain that was being suffered by Bear Stearns, Merrill Lynch, Lehman Brothers and the rest of Wall Street.
For Goldman Sachs, anomalous discrepancies between P&L and VaR implied a breakdown of the assumptions inherent in the VaR calculation:
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the forecasts for volatility and correlation were substantially flawed. In a portfolio as diverse as Goldman’s, such a pattern was indicative not of isolated failures, but rather of some more fundamental change in market conditions. The composition of the firm’s portfolio, together with its proprietary risk measurement methodologies, may have inadvertently replicated an indicator of systemic risk. Goldman’s response was not unlike the “situational awareness” of a military commander on the battlefield. In the parlance of the intelligence community, Goldman used “all-source intelligence” that ranged from the most quantitative models to the subjective feel of line practitioners. Anecdotally, Goldman was not the only firm to observe such patterns. Starting in about 2006, other enterprises also observed year-over-year increases in the number of VaR violations (that is, the number of times that losses exceeded VaR). In retrospect, such a pattern established the start of the shift to a new risk regime. RISK REGIMES AND WARNING SYSTEMS As the Goldman anecdote illustrates, the complexity of the financial system makes the interpretation of anomalous patterns difficult. As Professor James Moffat eloquently stated, “Complexity explains why interventions may have unanticipated consequences, but also explains why combat effects follow from these consequences. The intricate interrelationships between elements of a complex system give rise to multiple chains of dependencies. Change happens in the context of this intricate intertwining at all scales. We become aware of change only when the pattern changes.” And the first indicators of trouble can be subtle. By the time a change in risk regime is apparent, it may be too late to substantially mitigate risk. Broad metrics (which are easily visible to all and sundry) are not likely to provide actionable intelligence and a competitive advantage. For example, what is particularly disturbing to many is that, previous to the worst market shock in decades, there were few obvious indicators or widespread fear of imminent trouble. For example, once again consider the chart of Figure 8-11, which displays the daily price history for the VIX.11 Recall that this index provides a forward-looking estimate of shortterm volatility,12 based on traded prices. Because it is a market price, it reflects traders’ consensus forward-looking expectations and is often a component of risk indexes. Nevertheless, on August 28, 2008, just two weeks before Lehman’s bankruptcy, the VIX was trading at a typical implied volatility level of
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19.43 percent, off from its recent highs and not much different from its two-year average of 16.66 percent. But by November 20, 2008 (only three months later), the VIX had more than quadrupled to an all-time high of 80.86 percent. MAKING MARKINT ACTIONABLE Thus, standard risk indexes and analyses of historical VaR cannot be counted on to provide actionable intelligence. Instead, a MARKINT model might provide a signal that the first domino has tipped. In such warning systems, it’s not about the magnitude of market movements, but about their patterns. Stated more formally, MARKINT might identify those micro shocks that might touch off a cascade, and a systems approach might indicate to which of those shocks the system is vulnerable. Fortunately, the financial community is rich in hierarchical taxonomies and ontologies that can be used to organize data. Thus, using Bayes nets, agent-based simulations, or even war games, an enterprise might be able to simulate the chain reaction of events and model its consequences. Sometimes the revised prior information supplied by even a minor indicator can greatly change the posterior distribution and indicate both system vulnerability and the start of a causal cascade. MARKET INTELLIGENCE AND NATIONAL SECURITY Although market intelligence is clearly useful to the financial community, it may be equally useful to the intelligence community. Both MARKINT and the more traditional “INTs” can inform a model of fused intelligence. In intelligence analysis, there are likely to be situations in which corroborating or contradictory answers to the same question exist: one from MARKINT, and one from more traditional sources of intelligence. MARKINT may be a particularly useful addition to the mix. Like its close cousin signals intelligence (SIGINT), MARKINT provides a method for transforming massive amounts of real-time market data into market intelligence that has a place in an intelligence analyst’s toolkit. Such market intelligence will be entirely orthogonal to other, more traditional sources of intelligence, and may also have a temporal component (often not available in any other way), which is necessary to trial world constructs. Such intelligence may be timelier, as well. Market prices—and consequently the intelligence that can be derived from them—are updated at very high frequencies: turnaround time for market data is measured in
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milliseconds. The ability of market participants to handle data at such speeds is testimony to the technical capabilities of their automated sensemaking tools. To summarize, MARKINT can provide content, both raw data that might provide critical links and knowledge in the form of answers to broad and narrow questions and warnings. It may provide answers to highly specific and nonfinancial questions (e.g., the status of the Chinese defense industry or the progress of U.S. black programs) or to broad questions (e.g., consensus estimates of country risk) that have profound financial and geopolitical ramifications. It can answer questions that serve many different kinds of missions, and it is uniquely capable of assisting with financial and economic threats and warfare. MARKINT can also leverage sensemaking methods and models used by the financial community that might be adapted for the missions of the intelligence community. The models are diverse, ranging from automated anomaly detection and pattern recognition models to sophisticated risk measurement models. Such models might be easily retasked for intelligence purposes and, to use a military analogy, reduce the fog of war. SUMMARY OF MARKINT ADVANTAGES MARKINT has a number of advantages that are unlike those of more traditional sources of information: • It is orthogonal to intelligence from other sources. • It provides forward-looking information and metrics. • It may provide unique intelligence (e.g., temporal information from an options expiration date) that is not available via other means. • It can provide real-time, quantitative I&W/metrics (e.g., of “country risk” or industry sector risk). • For concurrent events, it can provide an estimate of the magnitude of an event’s importance. • It may be the only method for gaining some measure of transparency into sovereign wealth funds and other state actors or pseudo-governmental financial entities. • It is required for any serious defense against economic/financial warfare and protection of critical U.S. assets. • It provides a framework for working with and leveraging the knowledge and capabilities of regulators and the financial community.
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SUMMARY This chapter described the field of market intelligence, with which indications and warnings that are useful to both financial and intelligence analysts can be reverse-engineered from market prices and converted to actionable intelligence. The global capital markets were described as the most efficient intelligence aggregators, reacting in real time to both new information (either public or confidential) and analysis. WHAT’S NEXT The next chapter goes on to describe the United States as an enterprise, discusses the use of a risk-based approach to its major vulnerabilities, and describes the implications for national security and policy.
CHAPTER 17
The United States as Enterprise: Implications for National Policy and Security
The United States is essentially a meta-enterprise, and one whose existence—at least in its present form—is constantly at risk from threats both old and new. Systems thinking that integrates all the important drivers—geopolitical, financial, and economic—can aid in reducing its vulnerability to the most extreme outcomes. PUBLIC- AND PRIVATE-SECTOR APPROACHES TO SYSTEMIC RISK Although it is not a new threat, the importance of systemic risk originating in the financial sector is being newly appreciated because of its intersection with other missions that are critical to national security. Both the short-term and the long-term consequences of the 2007–2008 credit crisis continue to play out in the natural laboratory that is the global capital markets, and to provide evidence in a thousand ways that shocks to financial and economic systems pose an extreme threat to the United States and other nations. Both the public and the private sectors are concerned about the magnitude of systemic risk and are taking new actions to measure and manage it. All areas of government are attempting to meet this challenge. The U.S. Treasury is endeavoring to prevent a shock to the system triggered by a bank failure. In February 2009, it required the 19 largest U.S. banks to pass a stress test, in which each estimated the impact of specific economic conditions on the institution.1 Treasury Secretary Timothy Geithner also proposed a new “super regulator,” who would be given the task of managing systemic risk. And regulatory capital requirements and the manner in which they are calculated are under intense scrutiny. 245
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Further, the intelligence community is involved as well. Recent events have brought home the interconnectivity of the geopolitical and financial spheres, and the Central Intelligence Agency is making use of market experts who transferred their skills from Wall Street to Langley. One can directly observe the connections between national security and economic conditions. For example, as a consequence of recent events, Venezuela is now experiencing 29 percent inflation, and Hugo Chavez’s hold on the hearts and minds of his fellow citizens is much diminished, as social spending can no longer be subsidized by high-priced oil. “Regime change”—the term that economists use to indicate a sudden shift in an economic system—may be a more prescient term than was originally intended. National security, then, may depend in large part on the ability of a super regulator and others to manage systemic risk. But in the current environment, managing the risk of any enterprise—let alone that of a meta-enterprise like the United States—is a daunting responsibility. For the foreseeable future, the economic and financial environment is vulnerable to discontinuous and disruptive shocks; the danger that the United States passes an irreversible tipping point without clear warning is real. It is at risk from friendly fire, as well: those who, with the best of intentions, intend to cure the system may inadvertently trigger new shocks. At best, regulators and legislators might modify the financial infrastructure in such a way as to cut off a number of adverse outcomes. At worst, they may open new paths that either lead to unintended consequences or increase vulnerability to events that are outside their control. Therefore, those with the power to affect the system must be as confident as possible that any actions that they take will mitigate systemic risk rather than contribute to it. Treating the global capital markets as an experimental laboratory is exceedingly risky. Like that of any other enterprise risk manager, the ultimate objective of some theoretical national chief risk officer (NCRO) is to ensure the continued existence of the enterprise, and her primary analytic goal is the creation of actionable foresight that might be used to guide decision makers. As the global economic system continues to evolve, the numbers of links and interdependencies have continued to increase. Trading that was previously conducted by open outcry is now electronic, and many stock and commodity exchanges have now joined with exchanges abroad. For example, in 2007, the Chicago Mercantile Exchange partnered with Dubai
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Holding to create the Dubai Mercantile Exchange. In the same year, the Deutsche Börse’s Eurex subsidiary acquired the U.S. International Securities Exchange (ISE). This evolutionary path may have increased the vulnerability of the United States on a number of fronts. Therefore, a quantitative, networkcentric approach to enterprise risk management that explicitly accounts for the interdependency between all such threats might be as suitable for the United States as it is for a financial institution. DRIVERS, TRENDS, AND THE O/DNI’S VISION 2015 The intelligence community is well aware of the drivers of globalization and how they add complexity to its missions. Periodically, the Office of the Director of National Intelligence (O/DNI2) creates a vision statement that provides guidance to all U.S. intelligence agencies concerning the changing state of risks to national security. As shown in Figure 17-1 (reproduced from Vision 2015), the drivers and trends that must be included and fused for optimal sensemaking are diverse and require analysts with deep subject matter expertise.
Figure 17-1 Vision 2015 Drivers and Trends Source: Vision 2015
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This document acknowledges the complexity of the analytical task when dealing with a complex, dynamic, self-organizing system. Vision 2015 touches on the emergent behavior of such a system when it says, “Each driver and trend independently produces unique changes and challenges; those points where factors intersect often reinforce and amplify the effects of change and create a series of complex and often unpredictable threats and risk that transcend geographic borders and organizational boundaries.” UNRESTRICTED WARFARE Systemic risk and national security most obviously intersect in the area of unrestricted warfare. Unrestricted Warfare (literally, “warfare beyond bounds”) is a book written in Chinese in 1999 by Colonels Qiao Liang and Wang Xiangsui of the People’s Liberation Army that contains a comprehensive description of such warfare. The authors focus on unconventional means for defeating a militarily or technologically superior opponent such as the United States without the need for direct military action. The book, which received wide attention, discusses a number of unconventional means by which to engage in warfare, including using international law to the disadvantage of an enemy. However, the type of unrestricted warfare that the authors favored and that received the most attention was financial warfare. As the two colonels related, “So, which [of many unconventional means], which seem totally unrelated to war, will ultimately become the favored minions of this new type of war—‘the non-military war operation’— which is being waged with greater and greater frequency throughout the world? . . . Financial War is a form of non-military warfare which is just as terribly destructive as a bloody war, but in which no blood is actually shed. Financial warfare has now officially come to war’s center stage.” Many in the West found these concepts particularly striking, given the relatively primitive state of the Chinese capital markets in 1999 and the fact that the authors were military officers. ECONOMIC AND FINANCIAL WARFARE The purpose of economic warfare is to so damage an enemy’s critical economic resources as to provide some strategic or tactical advantage. Tools used in economic warfare include embargos, blockades, and preclusive purchasing. Conversely, the purpose of financial warfare is to disrupt a financial system.
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However, financial warfare may lead to economic consequences more profound than those that any traditional economic attack might have. As Paul Bracken, professor of management and political science at Yale University, said, “Financial warfare has greater targeting accuracy than the classic economic warfare of trade sanctions, embargos, and blockades, which have an overly diffuse impact on whole populations. For this reason, its use is likely to increase, just as precision military strikes replaced carpet bombing two decades ago.”3 Financial warfare is nothing new. The United States has engaged in financial warfare before to great effect. For example, in the 1956 Suez crisis, Britain and France (both NATO allies of the United States) landed troops to prevent nationalization of the Suez Canal by Egypt. President Eisenhower, who condemned this action but could not confront Britain and France militarily, ordered the U.S. Treasury to dump massive quantities of British pounds on the open market, which of course depressed the currency’s value and impeded the ability of Britain to pay for imports. Britain got the message and, along with France, soon withdrew its troops. Today, however, a financial attack can be far more destructive and far-reaching, and be initiated in a far less transparent manner. In decades past, financial warfare could not be effectively conducted against those nation states (e.g., China and Russia) that did not have capital markets. But today, one can hypothesize many modern versions of such an attack, conducted by either state or nonstate actors. For example, a financial attack might be executed physically—say, via a cyber attack on vulnerable elements of the global financial network—and take advantage of electronic trading, money transfer, and securities clearance systems. Unrestricted Warfare by State and Nonstate Actors Although economic warfare is almost exclusively the purview of state actors, financial warfare does not require their level of resources and sophistication. For example, a nonstate actor (Al Qaeda) carefully selected its two primary targets on September 11 (the World Trade Center and the Pentagon) to be an attack on both the U.S. government and the country’s financial system. In fact, three years before September 11, Unrestricted Warfare referred to means for such an attack, saying, “Whether it be the intrusions of hackers, a major explosion at the World Trade Center, or a bombing attack by Bin Laden, all of these greatly exceed the frequency bandwidths understood by the American military.”
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There is some tendency in the United States to concede Al Qaeda’s competence in attack planning using such means as bombs, beheadings, and terror plots, but to dismiss its members as being insufficiently sophisticated to influence or profit in the financial markets. On the contrary, there is evidence that real jihadis are highly conscious of the impact of their actions on the financial markets. In the infamous “dinner conversation tape” released in November 2001, Bin Laden himself discussed the exact dollar value of stock market declines after September 11. CYBER ATTACKS AND FINANCIAL WARFARE Hacking into Web sites and targeting financial institutions are two of the methods proposed by Qiao Liang and Wang Xiangsui, in keeping with, “The first rule of unrestricted warfare is that there are no rules, with nothing forbidden.” This is network-centric warfare in both the literal and the figurative sense. Threats to the Military Infrastructure Air Force General Kevin Chilton (the head of the Pentagon’s Strategic Command) warned Congress that the United States is vulnerable to cyber attacks on both the public and the private sector, which could “potentially threaten not only our military networks, but also our critical national networks.”4 There have been recent instances of successful intrusions into military networks. In November 2008, the Global Information Grid (GIG) a system composed of 17 million military computers, many of which house classified or sensitive information, was penetrated. Similarly, in June 2009, the Pentagon took an estimated 1,500 computers offline after it had detected penetration of an unclassified e-mail system used by the office of the secretary of defense (OSD). As reported by the Office of the National Counterintelligence Executive (NCIX) in 2006, the United States continues to be besieged by efforts to obtain critical U.S. assets: Entities from a record number of countries—108—were involved in collection efforts against sensitive and protected US technologies in FY 2005 [from 1 October 2004 to 30 September 2005], according to evidence amassed by the Counterintelligence (CI) community. A relatively small number of countries, though—including China and Russia—were the most aggressive and accounted for much of the targeting.5
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Threats to the Private Sector The collection efforts that are of greatest concern are those made by foreign state-sponsored actors that target sensitive U.S. technology, both classified and proprietary: “Again in FY 2005, foreign collectors targeted the entire range of items on the Military Critical Technology List (MCTL).” NCIX’s report enumerates a number of collection methods, including the efforts by individuals such as academics working in U.S. research institutes. However, as the report indicates, Of major concern is the fact that the nations best poised to use cybertools to access US technologies are the countries that traditionally have been the most aggressive collectors in the United States.
Cyber-Related Sensemaking Challenges Sensemaking with respect to adversaries’ collection efforts is made more challenging by the fact that the specific instigator or target of the intrusion— or even the fact of the intrusion—may not be known: Detecting the origin of such attacks—even determining for certain whether they originate outside the United States—is difficult, since the probes can be routed through multiple foreign countries. And the real concern for the CI [Counter Intelligence] community is how many such attacks may have been undetected.
The difficulty of sensemaking efforts will only increase in the future, and the utilization of certain types of financial data in an automated and structured fashion will become increasingly important. As the report goes on to note: Cybertheft appears to be on the rise. . . . The creation of international supply chains—where foreign firms become the major providers of key software and hardware components—opens the door to even greater possible vulnerabilities.
Cyber Attacks on Financial Markets A cyber attack on financial markets might be most effective if it leveraged the connectivity and automation that are now present in U.S. markets. Rather than involve traditional types of attacks such as of denial of service or commercial espionage, it might instead take other forms. For all intents and purposes, today’s global trading environment is already nearly indistinguishable from a virtual world. Each trader already
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has access to global trading venues, and physical exchanges such as the NYSE’s trading floor are rapidly giving way to strictly electronic venues where buy and sell orders are matched in an automated process. Today, a trader’s portal links him to both the visible and invisible worlds of trading, providing both raw and transformed data according to his specific needs and preferences. For example, one form of attack might be interference in “straightthrough processing” (STP), that is, settlement of transactions without human intervention at any step along the way. Similarly, another form of attack might be a flood of illegitimate orders into an electronic exchange with the intent of driving down prices, causing exchanges and other financial institutions to suffer extreme damage. The chain reaction from such an action would be far-reaching, especially if it were discovered to be deliberate. Commodity brokers, brokerdealers, hedge funds (especially algorithmic traders), and foreign exchange dealers would all be affected. The markets would lose liquidity, as well. Credit spreads would probably widen (more volatile markets imply greater credit risk), and brokerdealers might reduce lines of credit for all but the most creditworthy overthe-counter counterparties, just as occurred after the Long-Term Capital Management failure. Anecdotally, the financial markets have experienced several benign instances of such cascades in the futures markets. For example, in 1999, a junior trader at a French bank entered a market order in a relatively illiquid futures contract (French franc futures) via an electronic order system, but didn’t quite understand the units in which the order was to be entered and added a few zeroes to the size of his order. The market in the French franc suddenly plummeted for no apparent reason. This price action was noticed by every professional trader, whether involved in the Forex markets or not—if not directly, as soon as the trader grapevine distributed the news. This error cost the young trader’s firm a great deal of money, but it also created a chain reaction of gains and losses worldwide. For example, a trader involved in the French franc–Swiss franc cross trade might have arbitraged the discrepancy in exchange rates, thus moving the Swiss franc. A NET-CENTRIC APPROACH TO FINANCIAL WARFARE Economic warfare—offensive or defensive—might well be waged in a network-centric manner, much as military actions are conducted today.
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The synergy between economic/financial and military views of information and interactions (i.e., in terms of nodes and links) is inescapable. Bracken expresses the reason why financial warfare may be more effective than economic warfare from a network point of view when he says, “Knocking out key nodes is much more difficult than it first appears because activity automatically shifts to other nodes and sectors.” This is so because the flow of financial assets dwarfs the flow of economic assets. Money finds its own level by moving around the globe in search of maximum risk-adjusted returns. Bracken also points out a physical point of vulnerability when he notes, “Financial warfare also has a deep connection with information operations and network-centric warfare, which points to a new type of conflict against computing and network infrastructures in the financial sector. When these networks are cut off or compromised, money stops flowing. The ability to do this—offensively and defensively—has enormous political consequences.” Analysis of a financial network—whether to protect it or to literally find its weakest links—is an exercise that is well worth conducting. Fortunately, in addition to developments in network and systems theory, there are additional quantitative methods for the analysis of economic and financial warfare. Academics have been considering this specific problem for some time. In 1965, Oskar Morgenstern (the co-inventor of game theory, along with John von Neumann) described modern economies as “highly compressible”;6 that is, even if some key nodes in an economic system can be destroyed, this need not irrevocably lead to system collapse. Activity can be shunted around them to other nodes. Von Neumann, the author of perhaps the most important work in mathematical economics, dealt with the topic in 1944 in The Theory of Games and Economic Behavior. As Paul Samuelson observed: “the incomparable Johnny von Neumann . . . darted briefly into our domain, and it has never been the same since.” Morgenstern said, “The topic is a large one that continues to trouble my mind.” This relates to the concept of the “removable player” in game theory discussed by Morgenstern and von Neumann, and was a natural extension to the gamesmanship of unrestricted warfare. Together, Morgenstern and von Neumann formalized Bernoulli’s work in 1944 as the von Neumann-Morgenstern Expected Utility Theory, which discussed choices under uncertainty.
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MARKINT AND A MISSION-BASED FOCUS Financial warfare is arguably one of the types of unrestricted warfare for which the United States is least prepared and to which it is most vulnerable. However, while markets may contain the seeds of their own destruction, they may also contain the means for generating warnings to protect them. As Bank of China Vice President Zhu Min said in discussing the risks of the surging demand for derivatives at a panel discussion on the global economy at the Davos World Economic Forum in Davos, Switzerland, on January 24, 2007, “You can easily get liquidity from the market every second for anything.” Fortunately, a market intelligence (MARKINT) corollary to this statement might be, “You can easily get intelligence from the global capital markets every second for many risks.” Ideally, the intelligence community might leverage the intelligencegathering and assimilation capabilities of the global financial community and the hundreds of thousands of subject matter experts that it includes. For example, so-called emerging markets traders and the firms that employ them have their own intelligence-gathering resources, which may be different from those of more traditional human intelligence (HUMINT). MARKINT provides a method for leveraging the expertise of market experts, with or without their explicit participation. Because MARKINT relies only on open-source data, it may be possible to extract such information without risking a breach of U.S. security and without violating U.S. law. Market data can be used to infer intelligence that is of use for specific missions, both old and new. As further described in Vision 2015, an enhanced and collaborative mission-based focus can serve the intelligence enterprise. “Given these challenges, the analytic community has no choice but to pursue major breakthroughs in capability. Applying the principle of Collaborative Analytics, analysts will be freed to work in a fundamentally different way—in distributed networks focused on a common mission.” Figure 17-2 identifies the persistent threats and emerging missions identified in Vision 2015 for which MARKINT might have utility. These include applications in nearly every type of significant threat and mission, such as cyber threats, counterintelligence, terrorism, insurgencies, rising powers, energy, rogue states, financial, space, and failed states. FINANCIAL DRIVERS AND TRENDS Market intelligence, then, can provide intelligence that is relevant to a variety of threats and missions. But one of the most important—and the one to which MARKINT is uniquely qualified to contribute—is in the area of financial drivers and trends. There simply is no substitute (e.g., via HUMINT or expert analysis) that reproduces MARKINT.
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Figure 17-2 Vision 2015 Persistent Threats and Emerging Missions
Of all the important drivers and trends mentioned in Vision 2015, the one with which most members of the intelligence community have the least familiarity is “financial.”7 Recent economic events have shown the power of financial events as a driver of world change in every way— economically, socially, geopolitically, and militarily. For example, the exposure of financial firms to esoteric derivative instruments such as the aforementioned credit default swaps has caused, in short order, the failure of major financial institutions such as Bear Stearns and Lehman Brothers, a global recession, a change of administration in the United States, increasing tensions between Ecuador and its neighbors,8 a drop in oil prices from nearly $150 per barrel to under $40 per barrel, and large reductions in the defense budgets of oil producers such as Russia. It has also allowed quasi-governmental entities such as China Investment Corp. (China’s sovereign wealth fund) to attempt to acquire significant stakes in critical U.S. infrastructure at levels that probably would not have been permitted had it not been for the financial crisis. MARKINT also provides the ability to quantify financial risk to the United States as an enterprise—individually, or relative to other state
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actors. For example, the price of insurance (against default on debt obligations) on U.S. sovereign debt increased from a minimal 8 bp (0.08 percent) per year at the beginning of 2008 to a high of 100 bp per year9 by February 24, 2009 (see Figure 17-3). Over the same period, the price of similar insurance on Russia’s sovereign debt increased from about 88 bp (just under 1.00 percent) per year to 1117 bp per year (high on October 24, 2008), indicating a high probability of default over the next five years. (This is about the level at which Enron protection was trading before trading ceased.) Note that the price of insurance on the two countries’ debt reached their peaks on dates four months apart, providing some insight about the drivers of increased perception of credit risk. Although MARKINT may often have value by itself, its maximum utility is achieved when it is fused with other intelligence. As a completely
Figure 17-3 CDS Spreads: Russia, All Sovereigns, and the United States
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orthogonal and open source of intelligence, MARKINT is potentially of very high value in a cognitive analysis portal as a source of critical links, a method for validation of other intelligence, and sometimes the only source of temporal or other information that enriches existing intelligence. MARKINT can, therefore, serve the intelligence community by applying the models, methods, and tools of the financial community in order to provide a sensemaking capability that serves as an analytical bridge between subject matter experts and mission-based analysts. In Table 17-1, a number of hypothetical attack scenarios are listed. Although most experts separate such attacks into only two categories, economic warfare and financial warfare, a third category called “market warfare” has been added here by the author for additional clarity. T A B L E 17-1
Sample Attack Scenarios by Category
Hypothetical Attack Scenarios
Economic Warfare
State actor, via its state-sponsored sovereign wealth fund, has substantial control over U.S. or foreign companies that supply critical assets to U.S. commercial or defense interests.
X
State actor, via private or public companies with which it is closely aligned, stockpiles key commodities (e.g., copper or oil) or other assets.
X
State actor or terrorist organization engages in cyber attacks on critical infrastructure in the United States (e.g., the power grid).
X
State actor or terrorist organization engages in cyber attacks on critical financial infrastructure in the United States (e.g., the SWIFT messaging network or the “Fed Wire” for funds transfer and securities clearing), severely damaging the ability of financial and other institutions to conduct normal business.
Financial Warfare
Market Warfare
X (Continued )
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T A B L E 17-1
(Continued)
Hypothetical Attack Scenarios
Economic Warfare
Financial Warfare
Market Warfare
State actor or terrorist organization, via covert agents in place within the information technology departments of exchanges and/or major financial institutions, disables normal safeguards with respect to electronic trading, allowing a flood of illegitimate orders designed to wreak havoc with market prices and trigger a cascade of credit failures.
X
State actor, via its sovereign wealth fund or a cutout financial institution, takes market positions designed to profit from an upcoming event that is under its control. For example, Russian interests might take highly leveraged long positions in wheat futures just before the country announces an increase in taxes on exports; Saudi interests might short crude oil futures just before OPEC announces an increase in output.
X
The People’s Republic of China (PRC) informs the president of its intent to dump much of its U.S. holdings via global trading channels if the United States supports Taiwan in a future military confrontation.
X
X
The PRC deliberately produces false crop reports on its corn production in order to drive prices lower and to obtain needed supply at those levels.
X
X
HOT SYSTEMS, ROBUSTNESS, AND FRAGILITY We have good reason to believe that John Doyle and Jean Carlson’s highly optimized tolerance (HOT) model may—at least at times—be representative of the global capital markets. Doyle and Carlson suggest that when systems are made too efficient, they have no natural or designed tolerance;
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it’s in the nature of a HOT system to be both robust and fragile. If this is so, we may need to expect occasional large-scale shocks. As they warn us, such a system may appear to be stable for some time while it’s in its robust phase. Nevertheless, it may contain a ticking time bomb in the form of sensitivity to a stressor that’s not apparent except by analysis of a sufficiently representative model. One such manifestation of the robust stage may be what appears to be a thriving economy and marketplace. As economist Leo Tilman pointed out, it’s also in the nature of the financial markets that, as they mature, traders reach for diminishing returns, taking the system to the threshold for failure. For example, with easy credit and liberal risk-taking policies, larger and larger positions were taken prior to the credit crisis for less and less incremental profit, which caused the system to butt up against boundaries at which the reward-to-risk ratio approaches zero. If the markets are in such a state, then major changes cannot be made without careful and comprehensive modeling of the consequences, using a causal approach in order to identify “hot spots.” Even so, change is best made in small doses, like a physician who prescribes a minimum dose of a medication and studies the consequences before increasing the dose. Such methods also help to ensure that regulatory reform first does no harm. For example, consider a regulatory requirement that all standardized credit default swap contracts be cleared via an exchange. As previously discussed, this has obvious benefits, such as netting of standardized transactions and a strictly enforced margining protocol. However, to each position holder, this is really an exchange of one credit risk for another: rather than having a single name guarantee performance, the members of the clearing corporation jointly do so. But there are scenarios in which the clearing corporation might be less creditworthy than the best single names, in which market volatility is so large that margin is inadequate, or in which one or more members of the clearing corporation have very large risk positions. Careful modeling might prevent contagion that reaches, say, the grain markets and beyond. Doyle and Carlson suggest a new viewpoint on systemic failure that is appropriate to financial crises, that is, that failure will occur, but that it’s necessary to plan for such failures. Quick fixes and reactive rather than proactive responses bring a new set of risks to the table. Overly heavyhanded regulatory reform or an emphasis on solutions that address only previous failures may introduce a new vulnerability to the system—one with which we have no previous experience, and one that’s not obvious in a complex, adaptive system. And finally, some excess capacity needs to be
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built into a system, whether in the form of regulatory capital or through the ability to increase government spending in the event of a bad surprise from any source. CONCLUSIONS In this book, we’ve articulated many types of risks and focused on those both extreme in magnitude and difficult to anticipate. Some modeling approaches are better at discovering risks, while others better at quantifying risks. Complex adaptive system models are good at discovering the unrecognized properties of a system and are therefore a rich source of discovered risks. For example, it’s possible to repeatedly analyze a network representation of a system in order to get a sense of the robustness of the risk and to identify the general conditions that lead to (that is, indicate or predict) systemic failure. Bayes conditional probabilities are uniquely useful to bifurcating systemic and specific risks in a financial portfolio. However, such models are not particularly useful in quantifying risks. They may still require expert judgment to analyze results, to identify cause-and-effect relationships, and then to extrapolate to the real world. Such discovered knowledge may then increase the expert knowledge base and eventually find its way into a useful representation of the system in a model such as a Bayesian network. In addition to forecasting, intelligence analysts have two other jobs; they must both explain a situation (in causal terms) and identify how a policy maker can influence a situation (also causal). For example, war games are used to discover underlying causes and agent-based simulations using toy models to discover outcomes. Bayesian networks can be used for both discovery and quantification. Often, when an intelligence analyst builds even the most trivial toy network, the model results can be surprising. The output here is lessons and knowledge, not probabilities. But other times an analyst may build a Bayesian network to estimate the probabilities of various outcomes. These networks take a great deal more effort to build, and the analyst must endeavor to ensure that the conditional probabilities match “real-world” relative frequencies where those exist. When used for either purpose, such methods can assist those in the financial space with both recognizing and quantifying the most extreme outcomes. In a perfect world, regulators and policy makers would be aware of the paths to the most adverse scenarios, and would act in such a way as to
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cut off these paths or mitigate their consequences while minimizing interference with less adverse outcomes. The same forces of financial innovation and new technology that create efficiency can also open up new channels of communication throughout the financial network, allow information to flow from one end of the system to the other at lightning speed, and facilitate self-organization, adaptation, emergent behavior, and evolution to unanticipated states. However, scientific disciplines such as decision science have approaches that are useful in systemic risk management. We can retask the analytical and operational framework of network-centric operations (such as those used for military operations) to further enhance the strategic decision making of those who defend the United States from all types of threats. Such a framework has the added benefit of adding transparency to the process; there are no black boxes here. Such clarity leads to solutions. Decision trees allow the insertion of “interveners” that cut off the most adverse paths or that simply reduce system scale, complexity, vulnerability, or consequences. In a physical threat model, this might take the form of hardening a target. In a financial infrastructure model, it might take the form of circuit breakers such as short-sale rules or even legislative changes such as reinstitution of the Glass-Steagall Act. These analytical methods provide a virtual laboratory in which the effects of changes can be simulated before the changes are implemented. This same systems thinking should guide policy makers, as well. Consistent with the structured approach to the creation of conceptual models suggested in Chapter 7, such models can also aid in defining and justifying regulatory reporting and other data requirements. Like an intelligence analyst, a hypothetical NCRO can obtain from the field any missing information that she needs to inform the models (and justify the need). The NCRO might also conduct red-team exercises or financial war games, a method commonly used by the intelligence community to simulate scenarios and gather expert opinion. Causal methods can assist with contingent planning as well. Events have the potential to unfold rapidly and catastrophically as well as irreversibly, and not every driver can be defused. Economic and financial warfare (in the form of cyber attacks on the U.S. power grids or banking systems) is such an event, and it requires a rapid and suitable response. These methods might also help alert the United States to such events. They facilitate the creation of indications and warnings derived from open-source information obtained from the global capital markets.
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And finally, risk management of any type requires risk metrics, used both to provide decision makers with metrics of current threat levels (not unlike the risk metrics used by the financial community) and as an objective and scientific method of feedback over time. Modern theory makes feasible the fusion of the best methods of the public and private sectors and of the financial and intelligence communities, to their mutual benefit. And, like one of the stated objectives of A-Space, discussed in Chapter 7, an ideal collaborative environment in which all might participate is one that might “transform the analytical process by creating a workspace that integrates virtual worlds and . . . to dynamically exploit context and time.”
NOTES
CHAPTER 1 1. A very few best-of-the-best hedge dealers and hedge funds use some of these methods in automated high-frequency trading, but they are not often used for lower-frequency trading and investment activities. 2. In principal component analysis, the number of candidate variables that may be intercorrelated is reduced to a set of independent variables called principal components. 3. Generalized autoregressive conditional heteroskedasticity is a method for dealing with data that exhibit volatility clustering, or periods of high volatility among periods of relative calm, and jumpdiffusion processes, in which a sudden jump in volatility diffuses over time. 4. This is a model of price behavior over time in which some measure of volatility, such as standard deviation, is itself a random variable. 5. See Christina I. Ray, The Bond Market: Trading and Risk Management (New York: McGraw-Hill, 1990) for an explanation of the behavioral effects that can cause serial correlation over time in both the magnitude and the direction of market prices. 6. A collateralized debt obligation (CDO) is a structured instrument whose value derives from that of a portfolio of fixed-income securities. Some structures contain tranches with a defined priority for recovery; for example, one might own the first-to-default tranche, which has its own particular risk and return characteristics. CHAPTER 2 1. Peter Bernstein, Against the Gods: The Remarkable Story of Risk (New York: Wiley, 1996). 2. Bernoulli, Daniel, “Specimen theoriae novae de mensura sortis,” Commentarii academiae scientiarum imperialis Petropolitanae, 263
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3. 4. 5. 6.
7.
8.
9.
10.
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5 (1731) 1738, pp. 175–192. Translated by Dr. Louise Sommer as “Exposition of a new theory on the management of risk,” Econometrica 22 (1) (January 1954), pp. 23–36. Available on JSTOR. The only other translation of Bernoulli’s paper was into German in 1896. The topic of quantitative decision support is developing quickly as a subspecialty of computer science. A risk premium is the premium over fair market value that an investor requires to purchase a risky asset. In economics, utility is a measure of the relative satisfaction with an outcome, and a utility function describes relative preferences mathematically. Bernoulli even suggested a form for the utility function: “In the absence of the unusual, the utility resulting from any small increase in wealth will be inversely proportional to the quantity of goods already possessed.” Value at risk, or VaR, is a risk metric that indicates the magnitude of loss at a given confidence level over a certain horizon. For example, if one-day, 99 percent VaR is $1 million, this indicates that the probability of a loss greater than $1 million within one day is only 1 percent. Bernoulli was doubtless aware of contemporary banking practices. As early as the fifteenth century, the Medici Bank in Florence, founded in 1397, had become the greatest of the banchi grossi (“great banks”) by subverting prohibitions on the collection of interest, similar to today’s Sharia (Islamic banking) prohibitions. The Medici essentially created a book of foreign exchange transactions (bills of exchange), which were the economic equivalent of loans, but on which exchange fees were charged rather than interest. The Medici diversified within the asset classes of the day (e.g., silk, wool, and ships), geographically and internationally, and via numerous individual transactions. This diversification was important to their continued existence, since they were heavily leveraged, by some accounts having only about 5 percent of the capital that they required. The Medicis later fell afoul of concentration and credit risk by lending for political purposes. The Medici bank dissolved not long after, in 1494. Its decline was hastened by (somewhat forced) large loans to secular rulers who had little motive to repay. Jean-Michel Courtault, Yuri Kabanov, Bernard Bru, Pierre Crepel, Isabelle Lebon, and Arnaud Le Marchand, “Louis Bachelier: On
Notes
11.
12.
13.
14. 15. 16. 17. 18.
19.
20. 21.
22.
23. 24. 25.
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the centenary of theorie de la speculation,” Mathematical Finance 10, no. 3 (July 2000). This form will be familiar to students of options theory, in which the variance of a normal distribution increases linearly with time to expiration. A European-style option can be exercised only on its expiration date, in contrast to an American-style option, which can be exercised at any time. While European options can be priced analytically with an equation, American options require the use of a binomial tree or some other numerical method that permits simulation of the option holder’s right to make the optimal decision (exercise or not) at each step in time. Eugene Fama, “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance 25, no. 2 (May 1970). Classically, via patterns in graphs of price history, such as support lines, channels, and head-and-shoulders formations. Paul Samuelson, Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, 1947). Harry Markowitz, “Portfolio Selection,” Journal of Finance 7, no. 1 (March 1952), pp. 77–91. In 1990 Markowitz shared the Nobel Prize in Economics with William Sharpe and Merton Miller for their work in portfolio selection. The two-stock case permits only one return for each value of risk and vice versa, whereas with more than two stocks, there may be more than one portfolio with the same characteristics. In finance, volatility is annualized standard deviation, generally of returns (percentage changes). For comparison, the VIX volatility index had roughly similar volatility in 2003–2006, with a low value of 9.89 percent on January 24, 2007. Extreme value theory is used to model “fat” right and left tails of a distribution as an alternative to theories that assume a normal distribution. Sharpe’s coauthor, John Lintner, had passed away previous to Sharpe’s award. Portfolio volatility is usually calculated as the standard deviation of daily returns. A fat-tailed distribution indicates a higher probability of extreme moves than does a normal distribution.
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26. Such skewness is present even in forward-looking prices. For example, out-of-the-money puts in equities tend to trade at higher levels of implied volatility than do calls, since risk-averse investors prefer to buy protection rather than to sell it. Conversely, the volatility “smile” (i.e., implied volatility as a function of out-of-themoneyness) in bond options is more symmetrical, since bond traders find it as easy to be long as to be short. 27. Burton Malkiel, A Random Walk Down Wall Street (New York: W.W. Norton & Co, Inc., 1973). 28. The OCC is the world’s largest derivatives clearing corporation, guaranteeing performance on a wide range of derivative products. Participant exchanges include the American Stock Exchange, Chicago Board Options Exchange, International Securities Exchange, NYSE Arca, Philadelphia Stock Exchange, and others. 29. Kahneman received the Nobel Prize in Economics in 2002 (in spite of being a psychologist) for his work in prospect theory, in which he dealt with decision making under uncertainty where probabilities were known. CHAPTER 3 1. If xt and xt ⫹ 1 represent two successive changes in price, then ln(xt ⫹ 1/xt) is the continuously compounded return (in percentage terms) over the period. If returns are normally distributed (as is often assumed in financial models), then changes in price will be lognormally distributed. 2. This was not strictly true, in that securities and commodities exchanges might provide closing prices at different points in time, and that OTC markets might choose different times yet for end-ofday marks and data collection. However, since most economic news releases were made early in the day (often before certain markets opened), even closing prices gathered between, say, 3 p.m. EST and 4 p.m. EST were reasonably synchronized. 3. The rate at which homeowners prepay their mortgages (e.g., when they refinance their mortgage, sell a home, or suffer a foreclosure). 4. This is so because the mortgage holder has the right to refinance a mortgage and prepay the old one if rates drop—to his benefit, but to the detriment of the owner of the debt. So, the principal amount remaining of a mortgage-backed security stays high when its coupon rate is below market, but declines when its rate is above market. The
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price of mortgage-backed securities such as those issued by the Government National Mortgage Association (GNMAs) therefore depends on this implicit option embedded in the mortgages of which the securities are comprised. Similarly, if the mortgage is guaranteed by the Federal National Mortgage Association (FNMA) and the mortgage holder defaults, then the FNMA pays off immediately at 100 cents on the dollar, or par. Such optionality is an important driver of the average expected life of the mortgage and thus affects its theoretical value and price. 5. The percentage of assets recovered after a credit event such as a bankruptcy. 6. A credit default swap (CDS) is a contract that insures the owner of the swap against an adverse credit event such as a bankruptcy or credit downgrade. CHAPTER 4 1. These positions were converted on the basis of duration, or the sensitivity of the price of an issue to a change in interest rate. So, for example, a $100 million face amount of 5-year notes might equate to a $30 million face amount of a given 30-year bond, because each would generate the same P&L for a unit change in interest rates. 2. The confidence interval for VaR is expressed as both the probability within the distribution (e.g., 99 percent) and that outside it (e.g., 1 percent). The meaning should be clear in either case, since VaR is meant to measure the consequences of only extreme events.” 3. VaR can alternatively be expressed in terms of return. 4. This misunderstanding is no doubt due to the history of VaR. In the early 1990s, J.P. Morgan’s risk unit published its VaR methodology (based on the variance-covariance model used to generate the 4:15 report), making it an industry standard and creating a commercial software product from it. By 1998, Morgan spun off the solution provider as RiskMetrics Group: now publicly traded on the NYSE. 5. Although classic modern portfolio theory assumes that the variances and covariances for each security in the portfolio are used, in practice, statistics for representative bins (e.g., an equity bin in a particular country) are often used instead. 6. Variance-covariance VaR is the only common VaR methodology that can be directly calculated from a closed-form solution (that is, using equations rather than simulations or other numerical methods).
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7. That is, using equations rather than simulations or other numerical methods. 8. This curve-fitting methodology is the most commonly used application of EVT and is an example of a peak over threshold (POT) model such as those used in the insurance industry, in which only losses that exceed a deductible need be estimated. 9. J.P. Morgan/Reuters Technical Document, 4th ed., 1996 (available at RiskMetrics.com). 10. Gilles Zumbach, A Gentle Introduction to the RM2006 Methodology, RiskMetrics Group, January 2007 (available at RiskMetrics.com). 11. At the time, RiskMetrics had found its previous EWMA method too sensitive to recent history and created an alternative model that included long volatility “memory.” 12. This number is half of 4802, since the matrix is symmetrical. 13. This three-dimensional representation is a volatility surface. Many firms create one or more standard surfaces (e.g., by country) for common use across the enterprise. 14. In 1995, Nick Leeson caused the collapse of Barings Bank (the U.K.’s oldest bank) by conducting unauthorized speculative trading on the Singapore International Monetary Exchange (SIMEX). Leeson was able to hide the positions because he was allowed to settle transactions while functioning as chief trader, a violation of standard operating protocols. 15. In a trading context, the term liquidity risk refers to the latter. 16. Systematic risk is not to be confused with systemic risk, which is the risk of the financial system as a whole. 17. The Basel Committee on Banking Supervision, located in Basel, Switzerland, is an organization made up of the G-10 nations. Its purpose is to recommend best practice in banking supervision. 18. The astute reader will notice that no simplified measure for estimation of market risk exists in Basel II. This is so because, based on the mathematical principles of portfolio theory and the nonadditive nature of market risk, such a measure would be ripe for gaming by banks attempting to minimize their capital requirements. 19. Basel Committee on Banking Supervision, Revisions to the Basel II Market Risk Framework, Bank for International Settlements, July 2009. 20. In more sophisticated backtests, the entire distribution is tested, instead of just a specific risk level. 21. Basel Committee on Banking Supervision, Principles for Sound Stress Testing and Supervision, May 2009.
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CHAPTER 5 1. Some hypothesize that a rogue wave on Lake Superior was the cause of the destruction of the SS Edmond Fitzgerald on November 10, 1975. RMS Queen Elizabeth 2 is also reported to have “surfed” a nearly vertical 95-foot wave during Hurricane Luis in 1995 to avoid capsizing. 2. Napoleon III engaged city planner Baron Haussmann to create a vast new infrastructure. While it created the Paris that is so beloved today, certain features, such as widened streets, were intended to discourage revolution by preventing citizens from erecting barricades of the sort that had helped bring Napoleon III to power. 3. Because they receive option fees as revenue but incur no losses from option exercises. 4. Feedback describes a situation in which an event (or information about the event) in a causal system affects the same process that generated the event in the present or future. Feedback can be positive or negative; it might tend to force equilibrium by putting a particular process (say, price generation) into a loop, or it might magnify the effect of the process. 5. Leo Tilman, Financial Darwinism: Create Value or Self-Destruct in a World of Risk (Newark, N.J.: John Wiley & Sons, Inc., 2009). 6. A full discussion of this model is outside the scope of this book, but the interested reader is encouraged to review the literature on this model and other topics relating to self-organizing systems. A Java applet and demonstration of a Bak-Sneppen application can be found at cmol.nbi.dk/models/bs/bs.html. 7. Bak first described this state as self-organized criticality (SOC) in 1987. SOC is a concept taken from statistical physics to describe a class of dynamical systems that have a critical point as an attractor. 8. These assets need not be physical assets; they can, for example, be information or cyber assets. 9. Although the temporal dimension might theoretically be considered just another dimension, it is unique in that information cannot flow across this dimension (i.e., the present cannot communicate with the past). 10. Serial correlation is correlation between successive observations in a time series. For financial data, it can take the form of correlation with respect to direction (e.g., up days tend to be followed by up days) or with respect to magnitude (large movements tend to be followed by large movements, irrespective of direction).
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11. Stephen Mihm, “Dr. Doom,” New York Times Magazine, August 15, 2008. CHAPTER 6 1. https://www.newyorkfed.org/registration/research/risk/Daula_slides .ppt#611,2,Systemic Risk. 2. In location arbitrage, a security is bought at one location and sold at another for a profit. 3. High-water-mark rules are often present in hedge fund compensation rules. Profit is calculated from a previous high-water mark to prevent an investor being charged performance fees for a large gain in net asset value following a large decline. 4. Burton Malkiel, “Risk-Taking Reined In Needed to Restore Markets,” Bloomberg News, December 30, 2009. CHAPTER 7 1. The definition of model risk is often interpreted to include other sources of error, such as data or coding errors. However, in this discussion, these sources of risk will be considered to be operational risk rather than model risk. 2. A more complete discussion of A-Space can be found in Analytic Transformation: Unleashing the Potential of a Community of Analysts, Office of the Director of National Intelligence, September 1, 2008; available at odni.gov/content/AT_Digital%2020080923.pdf. 3. Additional material on this subject can be found at www.omnisinc.com. 4. Holographic four-dimensional displays (where the fourth dimension is time) are being utilized for some applications in which the time dimension adds clarity or insight. 5. A technology developed by Systems Research and Development (SRD), which was acquired by IBM in 2005. 6. See the Wikipedia.com entry for “Decision Tree” for additional illustrative examples. 7. That is, if X occurs, then there is a P percent chance that Y will occur. 8. Recall that Dubai and Abu Dhabi are two of the seven emirates of the United Arab Emirates (UAE), and the only two with veto power over UAE policy. Dubai receives only about 6 percent of its revenue from gas and petroleum and is far more dependent on real estate and construction.
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9. The fact that Dubai’s CDS spread had come off its high substantially before February 23 may be an indicator that the upcoming bailout was known or surmised by sophisticated investors. 10. Anecdotally, the London Metal Exchange (LME) also had a series of technical glitches when trading resumed, which impeded London traders’ ability to manage their exposure. 11. For comparison, this level is just slightly worse than that of the sovereign debt of Pakistan, which closed at 687.5 bp on the same day. 12. Laura Cochrane, “Dubai Default Swaps Rise to Two-Month High on Debt Request,” Bloomberg News, November 25, 2009, 13:49 GMT. 13. Laura Cochrane, Haris Anwar, and Vivian Salama, “Dubai Credit Risk Rises First Time Since June as Debt Comes Due,” Bloomberg News, November 25, 2009, 03:31 GMT. 14. Tal Barak Harif, “Dubai Woes May Reach ‘Sovereign Default,’ B of A Says,” Bloomberg News, November 27, 2009, 16:17 GMT. 15. Ayesha Daya, “Abu Dhabi to ‘Pick and Choose’ Dubai Debt Support, Reuters Says,” Bloomberg News, November 28, 2009, 9:56 GMT. 16. They often use exponential weighting to give recent experience far more weight, in a concession to changing market conditions. CHAPTER 8 1. Judea Pearl, Causality: Models, Reasoning, and Inference (Cambridge: Cambridge University Press, 2000). 2. To convert standard deviation to volatility, we multiply the standard deviation by the square root of 260 (assuming that there are 260 trading days per year). 3. As indicated by the “hat” over each variable. 4. The vertical bar notation in the equation for L means “given”: that is, the likelihood of a given pair of values for mean and standard deviation given the set of test data x. 5. The values for likelihood are scaled to have a value of 1 (on the z axis) for the maximum likelihood mean and standard deviation. 6. In reproducing the calculation, note that each value of the standard deviation has two roots for the mean: the positive and the negative. 7. Recall that the mean is expressed in terms of daily return, so a mean of 0.0356 represents quite a significant drift. The price at the end of 100 days Pt ⫽ 100 is equal to (1 + m)100 Pt ⫽ 0. 8. Changes in standard deviation for a constant mean can be shown to follow an inverse chi-squared distribution.
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9. Although they might impose arbitrage-free conditions, such as an assumption of future prices consistent with the spot price and the net cost of carry. 10. It should be noted that, since the underlying instrument of the VIX is the S&P 500 Index, it is likely to exhibit somewhat lower volatility than some of the index’s component securities, making any shifts in volatility all the more significant. 11. Specifically, GARCH(1,1), where GARCH(p,q) has lag p ⫽ 1 and order q ⫽ 1. 12. It should be noted that there was a change in the manner in which VIX was calculated in 2003, although not one that would account for the decline observed.
CHAPTER 9 1. A collateralized debt obligation is a structured security backed by a portfolio of other debt, such as secured or unsecured bonds issued by corporate or sovereign obligors or loans made to corporations by banks. 2. Richard Teitelbaum and Hugh Son, “The Man Taking Apart AIG,” Bloomberg Markets, August 2009. 3. The CDX indexes (formerly the iBoxx indexes) are static portfolios of equally weighted credit default swaps. There are a number of such indexes, including an investment-grade index, a crossover index (sub-investment-grade names), and a high-yield index (the riskiest securities). 4. A Bayesian network is a directed graph combined with a set of conditional probability tables associated with each of its nodes. It explicitly models cause-and-effect chains of events, and systematically generates each possible outcome and the likelihood and consequences of each. 5. Bayesian methods are sometimes used in the financial community for measurement of operational risk (required by the Basel II accord), where causal relationships between, say, a failure to enforce certain administrative controls can lead to a vulnerability to fraud, as in the Barings situation (discussed in Chapter 4).
CHAPTER 10 1. George Siemens, “Connectivism: A Learning Theory for the Digital Age,” December 12, 2004; www.connectivism.ca.
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2. T. K. Landauer and S. T. Dumais, “A Solution to Plato’s Problem: The Latent Semantic Analysis Theory of Acquisition, Induction and Representation of Knowledge” (1997), lsa.colorado.edu/papers/plato/ plato.annote.html; retrieved December 10, 2004. 3. Gully APC Burns, K.M. Research Group, University of Southern California, “Neuroscientific Knowledge Engineering,” PowerPoint presentation, November 25, 2002. 4. www.IARPA.gov. 5. Although OFT was disbanded recently, its responsibilities were transferred to other areas of DoD. 6. William P. Sudnikovich, “Extensible Battle Management Language as a Transformation Enabler,” SIMULATION 80, no. 12 (2004), pp. 669–680. 7. It is estimated that U.S. defense efforts rely about 80 percent on commercial satellites. 8. Recall that, as in the Bak-Sneppen model, statistics regarding time to converge to a critical state of maximum flexibility can be gathered. CHAPTER 11 1. A conditional counterfactual can be contrasted with an indicative conditional, which indicates what is the case if its antecedent is true. 2. Patrick Suppes, A Probabilistic Theory of Causality (Amsterdam: North-Holland, 1970). 3. Technically, there is a distinction between between counterfactual and hypothetical reasoning. Counterfactual reasoning is thinking about if we had done X, then perhaps Y would have happened. while hypothetical reasoning is thinking about if we do X, then perhaps Y will happen. What connects both is causal reasoning. CHAPTER 12 1. A deterministic relationship can be viewed as a special case of a random distribution with zero uncertainty, and therefore is implicitly included in this broader definition of a belief network. 2. These examples are courtesy of Palisade and were produced using its PrecisionTree and @Risk Excel add-ins. 3. In a decision tree created with PrecisionTree, decision nodes are represented by squares, chance nodes by circles, and end nodes by triangles. The name of each node and the value of the tree at that node are shown next to each node symbol. Each branch has a label and two values, in cells above and below the branch. For a chance
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4. 5.
6. 7.
Notes
node, the two values are branch probability and branch value. For a decision node, the top cell for each branch has a TRUE or FALSE, indicating whether the branch was selected as the optimum path. The cell below the branch contains the branch value. For an end node, two values are shown: the probability that the path through the tree will occur, and the value if the path does occur. In the following discussions, the terms nodes and links will be used as being more intuitive to financial market participants. Tree structures are often used to model path-dependent valuation models. For example, in the case of an American option, which can be exercised at any time, a binomial tree (in which each parent has two children) is created to approximate changes in price over time. In a down-and-out option, the option terminates before expiration if the price of the underlying security trades below a given threshold. Delta hedging of options is a dynamic strategy in which a trader attempts to continuously immunize an options position from directional dependency by maintaining a percentage of the underlying security equal to the probability that the option will be exercised. For example, a trader might sell 50 percent of the face value of a long at-the-money call position on IBM, and sell an additional 25 percent if the price of the stock rose to a level that implied a 75 percent probability of exercise. As the price rises and falls, the trading profits (from hedging the long options position) are intended to compensate for the loss of time value in the option. Thus, net profits on the strategy are path-dependent.
CHAPTER 13 1. In a binomial (decision) tree, two price branches are assumed at each fixed step in time, and the relative probabilities of each branch are calculated. Because there are only two branches, the branches converge to a computationally tractable quantity. 2. The term risk inference network, or RIN, was originally coined by Digital Sandbox, a homeland security risk management firm in McLean, Virginia. It is used by that firm to analyze and mitigate operational risk in the national security space. CHAPTER 14 1. Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk (New York: Wiley, 1998).
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2. In a structural credit risk model, the capital structure of a corporation is considered (e.g., its amount of senior debt, subordinate debt, and equity), and each lower class of debt or equity holders is considered to have a call option on the value above it. For example, equity holders are considered to own a call option on what is left after all bondholders have been paid. 3. When a position is given up to an exchange, the clearing corporation (consisting of various firms) guarantees performance and manages risk by establishing and collecting margin. CHAPTER 15 1. These conditions are based on a description by the great physicist Max Born. The fields of quantum mechanics and relativity, which are replete with temporal paradoxes, required reexamination of the very definition of causality. 2. In this graph, the hammer icon represents U.S. labor news (e.g., monthly unemployment statistics), the Federal Reserve Building icon represents U.S. money and banking news (e.g., changes in the fed funds rate), and the number icon represents most-read news. 3. Some events take time to work out, but those may be caused by endogenous effects such as signal amplification or other feedback loops. 4. There are a variety of data-mining tools that search the Internet for the earliest possible release of important news. For example, Connotate Technology mines corporate Web sites, on which company news is often posted before it’s released to news services. 5. There have been claims of insider trading on such events. Patterns in pre- and postnumber trading can provide important intelligence about whether such activity was present during any given event. 6. One such product is KnowledgeMiner, which uses the Group Method of Data Handling (GMDH) method of extracting knowledge from raw data. 7. In credit risk models, analysts sometimes deal with two states (e.g., normal and extreme) by overriding some statistical parameters. For example, where historical correlations between two related stocks (e.g., two auto manufacturers) might be used for normal market behavior, such correlation coefficients might be set to 100 percent (allowing perfect positive correlation and maximizing estimated risk) to generate worst-case scenarios and eliminate any risk reduction due to portfolio effects.
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8. Econometrics contains such concepts as weak exogeneity, strong exogeneity, and super exogeneity. CHAPTER 16 1. Steven M. Sears, “Odd Couple: CIA Briefs SEC,” Barron’s Online, May 21, 2007. 2. Although the term market intelligence is used to refer to other business activities, in the context of this book, it is assumed to refer only to financial markets. 3. For example, a “guerilla” is an algorithm developed by Credit Suisse that slices big orders into smaller, less conspicuous orders and “uses a variety of trading techniques to disguise its trail,” according to Credit Suisse’s Advance Execution Services Unit, which serves major hedge funds and other clients. 4. Jennifer Ablan, “Snipers, Sniffers, Guerillas: The Algo-Trading War,” www.Reuters.com, May 31, 2007. 5. Using quantitative models, the price of a credit default swap, which can be thought of as the cost of insurance on a debt issuer’s performance in making interest and principal payments, can be transformed into an implied probability of default by a given horizon date. CDS contracts and pricing information are available for single stocks, for indexes, and for sovereign debt of both developed and emerging countries. 6. In an auction of three-month T-bills by the U.S. Treasury on December 9, 2008, the low yield accepted was 0.00 percent, and that bill traded at negative yields in subsequent trading. 7. The subject of risk-adjusted preferences by investors is considered in detail in the field of behavioral economics, for which Daniel Kahneman won a Nobel Prize in Economics in 2002 (in spite of his being a psychologist rather than an economist). Kahneman often used price as the quantitative metric by which relative preference could be measured. In MARKINT, changes in price are similarly used as one metric by which changes in expectation and risk perception/aversion can be measured. 8. The difference in rates between U.S. Treasury bills and Eurodollar LIBOR rates. 9. DARPA’s stated mission is to “conceive and execute novel technology and system developments that are adaptive both in end function and in the process by which they are developed.” DARPA is responsible for much of the technological innovation that
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supports the U.S. DoD, some of which (e.g., computer networking) has had world-changing effects. 10. Joe Nocera, “Risk Management: What Led to the Financial Meltdown,” New York Times Magazine, January 4, 2009. 11. The VIX consists of a weighted average of implied volatilities for a wide range of strike prices, using either the first and second option expiration dates or the second and third if there are less than eight days to expiration. As such, it is intended to be a market estimate of future volatility in the S&P 500 Index. 12. Implied volatility is the annualized standard deviation implied by option prices. CHAPTER 17 1. The scenario deemed to be plausible yet reasonably unlikely had the following conditions: that the economy would contract by 3.3 percent in 2009 and remain nearly flat in 2010; that housing prices would fall an additional 22 percent in 2009; and that the unemployment rate would reach 8.9 percent in 2009 and 10.3 percent in 2010. Many people considered these conditions not so unlikely, and they were proved at least partially correct when the unemployment rate topped 8.9 percent by May 2009 (just four months later). 2. The Directorate of National Intelligence (DNI) commenced operations in April 2005 and is the parent of 17 intelligence agencies, including the Central Intelligence Agency (CIA), the Defense Intelligence Agency (DIA), and the National Security Agency (NSA). It is charged with oversight intended to enhance collaboration and coordination of U.S. intelligence. 3. Paul Bracken, Financial Warfare, Foreign Policy Research Institute, September 2007. 4. Walter Pincus, “Pentagon Official Warns of Risk of Cyber Attacks,” Washington Post, March 17, 2009. 5. Annual Report to Congress on Foreign Economic Collection and Industrial Espionage 2005, National Counterintelligence Executive, 2006-009, August 2006. 6. Oskar Morgenstern, “The Compressibility of Organizations and Economic Systems,” October 25, 1965. This article was based in part on work done at Rand in 1954. 7. Although recent news reports indicate that the intelligence community is currently making an effort to recruit experts in finance.
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8. Currently, President Rafael Correa of Ecuador (who has a Ph.D. in economics from the University of Illinois) is using the findings of a debt audit commission as the legal basis for the country’s defaulting on its foreign debt obligations. Ecuadorian debt currently trades at a yield of about 67 percent. 9. Prices are as of end of day November 25, 2009. This is about the same as Japan and France, and somewhat higher (reflecting greater risk) than Germany.
INDEX
A Abu Dhabi, 109–112 Acyclic graphs, 181 Actionable intelligence, 144–152 defined, 144 financial community, 144–145, 150–152 human inability to model complexity, 147–148 intelligence community, 144–146, 150–152 market intelligence as, 242 scenario generation, 146–147, 148–150 Adaptation, 163 Against the Gods (Bernstein), 8, 206 Agent-based approaches, 162 AIG Financial Products, 28, 147–148 Al Qaeda, 249–250 All-source intelligence, 95, 155–156, 167–168 Alpha, 45 American-style options, 105, 189 Analytic Space (A-Space), 97, 262 Analytic tradecraft, 94–96 (See also Intelligence community [IC]) Analytical value at risk, 35, 36, 42 Analytics, evolution of modern, 8–22 Bachelier and Brownian motion, 12–13 Bernoulli’s theory of risk measurement, 8–12 Fama and efficient market hypothesis, 14–15 Markowitz and modern portfolio theory, 16–19 Samuelson and economic meta–theories, 15–16 Sharpe’s systematic and specific risk, 19–22 Anchoring bias, 100 Arcs, 181 A-Space (Analytic Space), 97, 262 Asset liquidity risk, 44 Assets, risk-weighted, 50, 51 Availability bias, 100
B Bachelier, Louis, 12–13, 15–16 Backtest reports, 54, 55 Bak, Per, 71, 74 Bak-Sneppen evolution model, 71–73, 74 Banality, 64 Barings Bank, 44 Basel Committee on Banking Supervision, 50, 51, 57–58, 60 Basel I accord, 50, 59 Basel II accord, 50–52, 57–58, 59 Battle Management Language, 157 Bayesian approach forecasting, 118–129 frequentist approach, fusion with, 122–124, 125 frequentist approach vs., 118–121 threat assessment framework using, 150 (See also Bayesian inference networks [BINs]; Belief networks) Bayesian filtering, 185 Bayesian inference networks (BINs), 175–205 belief networks, 178–179, 182–183 creating, 191–192 defined, 180 efficiency and, 183–186 extreme scenario generation and, 187–188 financial applications, benefits of, 189–192 financial applications, computational tractability in, 195–196 graphical representations of decision networks, 179–182 hypothesis testing and, 121–122 risk example, 192, 194–195 stochastic modeling problems vs., 186–187 valuation example, 192, 193–194 (See also Risk inference networks [RINs]) Bear Stearns, 78, 227, 255
279
280 Behavioral finance, 20–22 Belief networks, 176–183 about, 176–177 components, 178–179 defined, 176, 180 solving, 183 specifying, 182–183 Belief systems, 81 Bernoulli, Daniel, 8–12, 16, 17–18, 253 Bernstein, Peter L., 8, 206 Best practice in risk management, 52–58 evolution of models, 56–58 risk control mechanisms, 52–56 risk limit/usage reports, 52–53 stress testing, 57–58 tactical vs. strategic approaches, 52 Beta, 45 Biases, 20–22, 90, 98–100, 147–148 Bin Laden, Osama, 249, 250 Binomial decision trees, 189 Black Monday scenario, 46–47 Black swan events, 65, 67 Black-Scholes partial differential equation, 13 Bond-equivalent positions, 32 Bracken, Paul, 249, 253 Brownian motion, 12–13 C C2 (command and control), 52, 156 CANTV (Compania Anonima Nacional Telefono de Venezuela), 221–222 Capital asset pricing model (CAPM), 19 Capital markets, global (See Global capital markets) Carlson, Jean, 76, 258–259 Cassano, Joseph, 148 Causal capacity, 89, 170–171, 174, 228 Causal inference, 168–169, 177 (See also Bayesian inference networks [BINs]) Causal models, 4–7 Causal networks, 176 Causality, 165–174, 216–229 conditions for, 217 correlation vs., 1–2, 25–26 data-driven approach to, 226–227 defined, 165, 169 in econometric models, 223–224 explicit, 223–224 historical views of, 165–166 implicit, 223 inferring from historical market behavior, 216–229 mining financial data for, 217–222 predictability and, 216
Index in stochastic models, 223 theory-driven approach to, 226 utility of, 166–167 CDOs (collateralized debt obligations), 6, 27, 147 CDS (See Credit default swap [CDS]) Cebrowski, Arthur, 156–157 Central Intelligence Agency (CIA), 246 Chain rule of probability theory, 184–185 Chains, 182 Chaotic systems, 68, 79–80 Charts and charting, 90–91 Chavez, Hugo, 221, 239, 246 Chertoff, Michael, 145–146 Chicago Board of Exchange Volatility Index (See Volatility Index [VIX]) Chief risk officers (CROs), 52 Chilton, Kevin, 250 China, 158–159, 234 CIA (Central Intelligence Agency), 246 Closed-form value at risk, 35, 36, 42 Clustering, 72–73, 138 Cobweb model, 172–173 Cognitive biases, 20–22, 98–100, 147–148 Cohesiveness, 98 Collateralized debt obligations (CDOs), 6, 27, 147 Collectivist dynamics, 163 Command and control (C2), 52, 156 Commodity risk, 43 Communication, and global capital markets, 86–87 Compania Anonima Nacional Telefono de Venezuela (CANTV), 221–222 Complex adaptive systems, 68–69 Complex systems, 65–67, 76–77, 84, 87–92, 258–259 Complexity, 147–148, 162–164 Conceptual models defined, 101 Dubai example, 108–112 in financial community, 114–115 in intelligence community, 101, 105–108 Conditional probability, 107, 121–122 Conditional value at risk, 39 Confirmation bias, 21, 99, 147–148 Confounders, 181 Connectivism, 153–164 agent-based approaches, 162 in finance, 162 global capital markets and, 86 knowledge landscape, 154 learning and, 153–154 modeling, 159–160
Index network-centric operations and modern warfare, 156–159 red-team exercises, 160, 161–162 sensemaking, 154–156 war games, 160–161 Conspiracy bias, 99, 100 Control, 92, 163 Corn prices, 87–88 Correlation, 1–2, 25–26 Correlation risk, 210, 212–213 Counterfactual condition, 166, 179 Cox, Christopher, 230 Credible intervals, 117 Credit crisis (2007–2008), 89–90, 245 Credit default risk, 44 Credit default swap (CDS) clearing corporation, 259 correlation risk, 210, 212–213 credit risk and, 44 Dubai, 108–112 indexes, 210, 212–213 market intelligence and, 234 spreads, 30, 256 Credit risk, 32, 43–44, 50–51 Credit risk models, 209 Credit spread risk, 44 Credit spreads, 209–210, 211 Critical thinking, 96–98, 114 Crop prices, 172–173 CROs (chief risk officers), 52 Cross-sectional data, 224 Cumulative causation, 196 Currency risk, 43 Cyber attacks, 250–252 D DAGs (directed acyclic graphs), 179, 180, 181–182, 189, 227 DARPA (Defense Advanced Research Projects Agency), 236–237 Data cross-sectional, 224 end-of-day, 25 event, 3–4 mining, 178 panel, 224 real-time market, 3–4 synchronization of, 3–4, 25 Daula, Tom, 82 Decentralized control, 163 Decision analysis, 176 Decision networks, 176, 177–178, 179–182 (See also Belief networks) Decision support, 9, 207–208
281 Decision trees binomial, 189 in hypothesis testing, 104–105 influence diagrams vs., 179–180 Decision variables, 177 Defense Advanced Research Projects Agency (DARPA), 236–237 Delta hedging of options, 182 Department of Defense (DoD), 156–159, 236–237 Department of Homeland Security (DHS), 145–146 Determinism, 61, 68, 217 DHS (Department of Homeland Security), 145–146 Directed acyclic graphs (DAGs), 179, 180, 181–182, 189, 227 Directed graphs, 181 Directed links, 181 Directorate of National Intelligence (DNI), 96, 247–248, 254, 255 Discounting, hyperbolic, 21 Distributions fat-tailed, 20 Lévy, 20, 21 normal/Gaussian, 12, 20, 124, 126–129 posterior, 128 prior, 128 skewed, 20 DNI (Directorate of National Intelligence), 96, 247–248, 254, 255 DoD (Department of Defense), 156–159, 236–237 Dow Jones CDX indexes, 148, 149 Dow Jones Industrial Average, 18 Down-and-out options, 37, 182 Doyle, John, 76, 258–259 Drivers and trends, 66–67, 247–248, 254–258 Dubai World, 108–112 Dumais, S. T., 153 Dynamic Bayesian networks, 177 Dynamic systems, 67–68, 76–77, 172–173 Dynamic value at risk, 56–57, 76–77, 213 Dynamical systems, 67, 68 E Econometric models, explicit causality in, 223–224 Economic capital, 45 Economic systems, feedback in, 203–204 Economic warfare, 248–249 Ecuador, debt, 255 Edges, 181 Efficiency, 16–18, 183–186
282 Efficient market hypothesis (EMH), 12, 14–15, 20–22, 87, 232 Eisenhower, Dwight D., 249 Electricity prices, 37, 38, 39 Emergent properties, 70 EMH (efficient market hypothesis), 12, 14–15, 20–22, 87, 232 End-of-day data, 25 Energy prices, 87–88 Enterprise risk, 49 Enterprise risk management (ERM), 9, 49, 206–207 (See also Risk inference networks [RINs]) Equity risk, 43 ES (expected shortfall), 39 Estimation theory, 225 Estimators, 185 ETL (expected tail loss), 39 European-style options, 13 Event data, 3–4 Everyday risk, 48 Evolution forces and mechanisms in systems, 69–73 of modern analytics (See Analytics, evolution of modern) of trading industry (See Trading industry, evolution of) EVT (extreme value theory), 37–39, 40, 42 EWMA (exponentially weighted moving average), 40 Expected shortfall (ES), 39 Expected tail loss (ETL), 39 Experimentation, 3–4, 169, 223–225 Expert knowledge, 171–173, 196–197 Expert systems, 197 Exponentially weighted moving average (EWMA), 40 Exposition of a New Theory on the Measurement of Risk (Bernoulli), 8–12 Extreme value at risk, 37–39, 40, 42 Extreme value theory (EVT), 37–39, 40, 42 Extreme waves, 61 F Fama, Eugene, 12, 14–15 Fat-tailed distribution, 20 Fed action, implied probabilities of, 220, 221 Feedback, 90, 172–173, 196, 203–204 Feldstein, Andrew, 212 Financial community actionable intelligence, 144–145, 150–152 complexity concepts, 162–164 conceptual models, 114–115
Index decision support and, 207–208 intelligence community vs., 144–146, 150–152, 162–164 risk inference networks, 201, 203 risk methodologies, 150–152 scenario generation, 146 Financial drivers and trends, 254–258 Financial warfare, 248–253 Flight to quality scenario, 46, 47 Ford, 210 Forecasting, 117–143 Bayesian approach, 118–129 frequentist approach, 2–3, 118–129 parameter risk, 117–118 regime change, 139–142 volatility, 134–139 Forensic risk review reports, 54 4:15 report, 33 Fragility, in complex systems, 91–92, 258–259 Framing bias, 100 Frequentist approach, 2–3, 118–129 Funding liquidity risk, 44 FutureMAP (Futures Markets Applied to Prediction), 236–237 G GARCH (generalized autoregressive conditional heteroskedasticity), 5, 26, 138 Gaussian distribution, 12, 20, 124, 126–129 Geithner, Timothy, 245 General Motors (GM), 210 Generalized autoregressive conditional heteroskedasticity (GARCH), 5, 26, 138 Gibbs sampling, 186 Global capital markets, 81–93 belief systems and worldviews, 81 characteristics, 79–80, 84–86 as complex system, 84, 87–92 connectivity and contagion, 86–87 human decision making in, 82–83 knowledge in, 209–210 as self-organizing system, 77–80, 84, 85–87 as system, 82, 83 systemic risk, 81–82 Global Industry Classification Standard (GICS), 209 Global Information Grid, 250 GM (General Motors), 210 Gold, 78–79, 123–124, 125, 218 Goldman Sachs, 240–241 Granger, Clive, 225 Granger causality, 225 Guerrillas, 231
Index
283
H Hedge fund industry, 23, 89 Hendry, David, 169, 208 Higher order uncertainty, 117 Highly optimized tolerance (HOT), 76, 91–92, 203, 258–259 High-water-mark rules, 89 Historical value at risk, 36, 40, 42, 48 HOT (highly optimized tolerance), 76, 91–92, 203, 258–259 Hsia, Tim, 231–232 Human intelligence (HUMINT), 95, 155, 254 Hume, David, 165–166 Hyperbolic discounting, 21 Hypotheses defined, 103 generating competing, 103–104 testing, 101, 102–105, 121–122 Hypothesis trees (See Decision trees) Hysteresis, 65, 88–89
knowledge discovery in, 155 market intelligence and, 231–232, 234, 236–239, 242–243 model risk, 94–95 models and methods, 97 network-centric operations and modern warfare, 156–159 red-team exercises, 160, 161–162 risk inference networks, 196–197, 199–201, 202 risk methodologies, 151–152 scenario generation, 146–147 sensemaking, 154–156, 157–158 war games, 147, 160–161 (See also National security) Intelligence Preparation of the Battlefield (IPB), 161 Interest-rate risk, 43
I IARPA (Intelligence Advanced Research Projects Activity), 155 IC (See Intelligence community [IC]) Idiosyncratic risk, 19, 44–45, 201, 203 India, insider trading by adversaries, 230 Indicators, 199, 201, 202, 234–235 Inductive inference, 167 Inductive reasoning, 167–168, 226 INEW (Integrated Network-Electronic Warfare), 159 Information new, 119–120 structuring, 102–103, 107 Insider trading, 230–231, 233–234 Integrated Network-Electronic Warfare (INEW), 159 Intelligence Advanced Research Projects Activity (IARPA), 155 Intelligence community (IC) actionable intelligence, 144–146, 150–152 agent-based approaches, 162 all-source intelligence, 155–156 analytic tradecraft, 95–96 complexity concepts, 162–164 conceptual model creation, 101, 105–108 critical thinking in, 96–98 financial community vs., 144–146, 150–152, 162–164 hypothesis testing by, 101, 102–105
K Kahneman, Daniel, 21 Keynes, John Maynard, 90 Knowledge engineering, 154 expert, 171–173, 196–197 framework in causal inference models, 168 in global capital markets, 209–210 mining, 222 models, 154 prior, 5 transforming data to, 154–156 Knowledge landscape, 154
J J.P. Morgan, 33, 41
L Landauer, T. K., 153 Leeson, Nick, 44 Legal risk, 44, 49 Lehman Brothers, 29, 30, 78, 227, 255 Lehner, Paul, 75 Leptokurtosis, 88 Lévy distribution, 20, 21 LGD (loss given default), 44, 51 Likelihood, 128–130 Links, 181 Liquidity risk, 44, 49 Location arbitrage, 86 Long-Term Capital Management (LTCM), 28–29, 160, 210 Loss given default (LGD), 44, 51
284 M Macro shocks, 62–63, 87 Malkiel, Burton, 89–90 Mandelbrot, Benoît, 21 Marginal utility function, 10 Marginal value at risk, 39 Margining rules, 88 Market intelligence (MARKINT) advantages, 243 bottom-up approach to, 235–236 as collaborative environment, 232 conceptual framework, 235–236 defined, 231 Department of Defense and prediction markets, 236–237 financial drivers and trends, 254–258 generating indications and warnings, 234–235 global markets as prediction markets, 236 Goldman Sachs example, 239–241 insider trading by adversaries, 230–231 intelligence community use of, 231–232, 234, 236–239, 242–243 making actionable, 242 mission-based focus, 254 risk regimes and warning systems, 241–242 theoretical foundations, 232–234 top-down approach to, 235–236 tradecraft and, 231–232 Venezuela sovereign debt yields example, 237–239 Market risk, 43, 49, 51 Markov process, 12, 15–16 Markowitz, Harry, 16–19 Maximum likelihood, 128 McAdie, Robert, 210 Mean, 130–134 Micro shocks, 62–63, 87 Mindsets, 98 Model risk, 28, 94–95, 112–115, 191 Models (See specific models) Modern portfolio theory (MPT), 16–19, 36 Moffat, James, 73, 157, 241 Monte Carlo simulation, 185–186 Monte Carlo value at risk, 36–37, 42, 48 Morgenstern, Oskar, 253 Mortgage prepayment rates, 27 Mortgage-backed securities, 27 MPT (modern portfolio theory), 16–19, 36 Multiperiod value at risk, 192, 194–195 N Nakheel PJSC, 108–109 Napoleon III, 66
Index Narayanan, M.K., 230 Nash, John, 69 National chief risk officer (NCRO), 246, 261 National security, 245–262 approaches to systemic risk, 245–247 cyber attacks and financial warfare, 250–252 economic and financial warfare, 248–250 financial drivers and trends, 254–258 HOT systems, robustness, and fragility, 258–260 market intelligence and mission-based focus, 254 net-centric approach to financial warfare, 252–253 Office of the Director of National Intelligence, 96, 247–248, 254, 255 unrestricted warfare, 248, 249–250 (See also Intelligence community [IC]; Warnings, making sense of) Nature nodes, 183 NCIX (Office of the National Counterintelligence Executive), 250, 251 NCRO (national chief risk officer), 246, 261 Negative feedback, 196 Network-centric operations (NCO), 73, 156–159, 252–253 Network-centric warfare (NCW), 156–159 Network-enabled capability (NEC), 158 Neural nets, 178 Nocera, Joe, 240 Nodes, 181, 183 Non-equilibrium order, 163 Nonlinear interaction, 163 Non-Obvious Relationship Awareness (NORA), 103 Normal distribution, 12, 20, 124, 126–129 O Office of the Director of National Intelligence (O/DNI), 96, 247–248, 254, 255 Office of the National Counterintelligence Executive (NCIX), 250, 251 Open-source intelligence (OSINT), 95 Operation Iraqi Freedom, 158 Operational risk, 44, 51 Options American-style, 105, 189 delta hedging of, 182 down-and-out, 37, 182 European-style, 13 pricing with uncertain mean, 192, 193–194 short positions in, 68 Options Clearing Corporation, 20 OSINT (open-source intelligence), 95
Index P Panel data, 224 Parameter identification problem, 224 Parameter risk, 117–118 Parametric value at risk, 35, 36, 42 Paris, layout of, 66 Patel, Navroz, 210, 212, 213 Paths, 182 PCA (principal component analysis), 4, 190 Pearl, Judea, 3, 4, 176, 180, 217, 226, 227 Performance attribution reports, 53–54 Plausibility vs. probability, views of, 1–7, 61 Political risk, 44 Portfolio volatility, 19 Positive feedback, 196 Posterior distribution, 128 Power laws, 72–73 Predictability, 64, 216 Predictive failure, 170–171 Prices corn, 87–88 crop, 172–173 electricity, 37, 38, 39 energy, 87–88 gold, 123–124, 125, 218 mortgage-backed securities, 27 option, 192, 193–194 patterns in, 14 returns and, 25 Principal component analysis (PCA), 4, 190 Prior distribution, 128 Probabilistic causation, 217 Probability chain rule theory, 184–185 conditional, 107, 121–122 frequentist vs. Bayesian approach to, 118–119 plausibility vs., views of, 1–7 Q Qiao, Liang, 248, 249, 250 Quantitative decision support, 9 Quantitative trading strategies, ascent of, 23–28 Questionable cause, 169 R Random bias, 99, 100 RAROC (risk-adjusted return on capital), 45, 52 Real-time market data, 3–4 Recovery rate, 27, 44 Red-team exercises, 160, 161–162 Regime change, 64–65, 139–142, 191, 203–204, 241–242 Regulatory capital, 45 Regulatory rules, testing, 213–214
285 Reports backtest, 54, 55 forensic risk review, 54 4:15, 33 performance attribution, 53–54 risk limit/usage, 52–53 Reputational risk, 44, 49 Returns, 21, 25 RINs (See Risk inference networks [RINs]) Risk aversion, 234 Risk categories, 43–45 (See also specific types of risk) Risk inference networks (RINs), 196–215 about, 196–197 building, 197–199 decision support and, 207–208 defined, 196 for dynamic value at risk, 213 as enterprise risk management (ERM) framework, 206–215 feedback mechanisms in, 203–204 in financial community, 201, 203 indicators and warnings, 199, 201, 202 in intelligence community, 196–197, 199–201, 202 market network representation, 204–205 modeling specific risk in, 201, 203 modeling systemic risk in, 201, 203, 204–205 notation, 197–199 (See also Bayesian inference networks [BINs]) Risk limit/usage reports, 52–53 Risk management, 32–60 best practice, 52–56, 52–58 causal models for, 167–168 enterprise risk, 49 international standards, Basel Committee, 50–52 value at risk (VaR), 32–49, 59–60 (See also specific topics) Risk model selection, 48–49 Risk premium, 9 Risk-adjusted return on capital (RAROC), 45, 52 RiskMetrics Group, 40, 41 Risk-weighted assets, 50, 51 Robustness, in complex systems, 91–92, 258–259 Rogue waves, 61 Roots, 182 Roubini, Nouriel, 79–80 Roy, A. D., 17–18 Russia, credit default swap spreads, 256 S Samuelson, Paul, 13, 15–16, 253 S&P 500 Index (SPX), 134, 140
286 Scenario analysis, 45–48, 58 Scenario generation, 146–147, 148–150, 187–188 Scheduled events, 219 Schiller, Robert, 90–91 Self-fulfilling prophecies, 89–90 Self-organization, 163, 214–215 Self-organized criticality (SOC), 73, 76 Self-organizing systems, 69–70, 73–74, 76, 77–79, 84, 85–87 Sensemaking, 154–158 (See also Market intelligence [MARKINT]; Warnings, making sense of) September 11, 2001 terrorist attacks, 230, 249–250 Sequential Bayesian filtering, 185 Serial correlation, 78–79 Sharpe, William, 19–22 Sharpe ratio, 19 Short positions in options, 68 Siemens, George, 153 Signals intelligence (SIGINT), 95, 155, 242 Simulations, 75–76, 185–186 Skepticism, 167–168 Skewed distributions, 20 Smith, Adam, 85 Sneppen, Kim, 71, 74 SOC (self-organized criticality), 73, 76 Sovereign debt, 30, 237–239, 256 Sowa, John, 217 Specific risk, 19, 44–45, 201, 203 St. Petersburg Paradox, 9–10 Stable systems, 79–80 Standard and Poor’s 500 Index (SPX), 134, 140 Standard deviation, 130–134 Static value at risk, 56–57 Statistical bias, 100 Statistical/stochastic models advantages of causal models over, 4–7 Bayesian inference networks vs., 186–187 correlation in, 1–2 implicit causality in, 223 volatility models, 5 Stewart, Ian, 153 Stiglitz, Joseph, 80 Strategic risk, 44 Stress tests about, 46–48 Bayesian inference networks in, 190 defined, 7 U.S. banks, 245 value at risk vs., 57–58, 59–60 (See also Scenario analysis) Stressed value at risk, 51, 57–58 Strong-form efficiency, 14
Index Structural credit risk models, 209 Structured analysis, 101 Subsymbolic reasoning, 178 Suez Canal, 249 Suppes, Patrick, 169–170 Symmetry breaking, 76 System models, 74–75 Systematic risk, 19, 44–45 Systemic risk approaches to, 245–247 contagion process, 62–63 defined, 81–82 magnitude of, 92 risk inference network modeling, 201, 203, 204–205 Systems about, 63–64 belief, 81 chaotic, 68, 79–80 complex, 65–67, 76–77, 84, 87–92, 258–259 complex adaptive, 68–69 defined, 63 drivers of behavior, 64–65 dynamic, 67–68, 76–77, 172–173 dynamical, 67, 68 economic, 203–204 expert, 197 self-organizing, 69–70, 77–79, 84, 85–87 stable, 79–80 toy, 75–76 warning, 241–242 Systems thinking, 61–80 black swan events, 65, 67 complex systems, 65–69, 76–77 defined, 63–64 evolution forces and mechanisms, 69–73 global capital markets, 77–80 highly optimized tolerance (HOT), 76 models and simulations, 74–76 plausible vs. probable, 61 regime change, 64–65 “rogue waves”and chance, 61 self-organizing, 73–74, 76, 77–79 systemic risk and contagion, 62–63 T Tail risk, 37, 38, 39 TARP (Troubled Assets Relief Program), 29 Technology improvements, 23–24 TED (Treasury-Eurodollar) spread, 234 Theory of Speculation, The (Bachelier), 12–13 Thinking, critical, 96–98, 114 Threat assessment framework, 149–150 Tilman, Leo, 70, 259
Index Tipping points, 67, 76, 170–171 Toy systems, 75–76 Tradecraft, 95–96, 231–232 Trading industry, evolution of, 22–31 Treasury bills, 234 Troubled Assets Relief Program (TARP), 29 Tversky, Amos, 21 Two and twenty rule, 89 U Uncertainty, 117, 120–121 Undirected links, 181 Unemployment statistics, 219, 221 United States bank stress tests, 245 credit default swap spreads, 256 sovereign debt, 237–239, 256 (See also National security) Unrestricted Warfare (Qiao and Wang), 248, 249, 250 Unscheduled events, 219 Utility, 9, 10 Utility functions, 9, 10 Utility variables, 177 V Value at risk (VaR) about, 33, 34 applications using, 33–34 best practice in risk management and, 52, 54 computation methods, classical, 35–39 conditional, 39 confidence level, 33 criticisms and responses, 59–60 defined, 11 dynamic, 56–57, 76–77, 213 extreme value, 37–39, 40, 42 forensic risk review reports and, 54 Goldman Sachs, 240–241 historical, 36, 40, 42, 48 marginal, 39 methodologies, comparison of, 39–40, 41, 42 model design, 41–42 Monte Carlo, 36–37, 42, 48 multiperiod, 192, 194–195 parameter estimation, 41–42 parameter generation, 40–41 static, 56–57 stressed, 51, 57–58 variance-covariance, 35, 36, 42 Value-based biases, 98 VaR (See Value at risk [VaR]) Variance-covariance value at risk, 35, 36, 42
287 Venezuela inflation rate, 246 nationalization of companies, 221–222 sovereign debt yields, 237–239 Vertices, 181, 183 Viniar, David, 240 Vision 2015 statement, 247–248, 254, 255 Visualization tools, 102–103 VIX (See Volatility Index [VIX]) Volatility contour plots of, 141, 142 forecasting, 134–139 portfolio, 19 stochastic models, 5 theoretical explanations and models, 137–139 of volatility, 134–137 Volatility Index (VIX) historical distribution, 137 regime change and, 139–142, 241–242 volatility of volatility, 134–137 Von Neumann, Johnny, 253 W Wall Street, trading industry evolution, 22–31 Wang, Xiangsui, 248, 249, 250 War games, 147, 160–161 Ware, Bryan, 149–150 Warfare economic, 248–249 financial, 248–253 network-centric operations and, 156–159 unrestricted, 248, 249–250 Warnings, 199, 201, 202, 234–235, 241–242 (See also Market intelligence [MARKINT]) Warnings, making sense of, 230–244 DARPA, 236–237 insider trading, 230–234 market intelligence (MARKINT), 231–239, 242–243 September 11, 2001 terrorist attacks, 230, 249–250 (See also National security) Wason, Peter, 21 Waves, rogue, 61 Weak-form efficiency, 14 Wealth of Nations, The (Smith), 85 Weatherstone, Dennis, 33 Weaver, Warren, 66 Wiener process, 12–13 Worldviews, 81 Z Zhu, Min, 254
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ABOUT THE AUTHOR
Christina I. Ray is senior managing director for market intelligence at Omnis and cohead of the firm’s practice in threat finance and market intelligence. She is an experienced trader, a hedge fund manager, a risk manager, and the author of The Bond Market—Trading and Risk Management (McGraw Hill, November 1992), which is used as a textbook in the finance departments of graduate schools and in the training programs of certain primary dealers. Prior to Omnis, Ms. Ray held a number of senior positions at Drexel Burnham, Daiwa Securities, and A. G. Becker Paribas, where she was involved at various times as an options trader, a risk manager, and a trading manager. She devotes her applied mathematics and program development skills to the creation of algorithms for both the public and private sector designed to provide early warning of tactical and strategic threats. Ms. Ray’s specialized interest and the focus of her activities involves the fusion of risk measurement methods used by the intelligence community and the financial community in areas that involve low-probability, high-consequence events. She can be contacted at
[email protected].
