EXTREME RISK MANAGEMENT

REVOLUTIONARY APPROACHES TO EVALUATING AND MEASURING RISK

By CHRISTINA RAY

The McGraw-Hill Companies, Inc.

Copyright © 2010 The McGraw-Hill Companies, Inc.
All rights reserved.
ISBN: 978-0-07-170059-7

Contents

PrefaceChapter 1 Plausibility versus Probability: Two WorldviewsChapter 2 The Evolution of Modern AnalyticsChapter 3 Natural Selection on Wall StreetChapter 4 A Review: Risk Management Metrics, Models, and Best PracticeChapter 5 Systemic Risk and Systems ThinkingChapter 6 Belief Systems and the Inadvertent Conspiracy: The Global
Capital Markets as SystemChapter 7 Analytic Tradecraft and Model RiskChapter 8 The Future as Forecast: Probability, Likelihood, and
UncertaintyChapter 9 An Alternative Path to Actionable IntelligenceChapter 10 Solutions: Moving toward a Connectivist ApproachChapter 11 An Introduction to Causality: Theory, Models, and InferenceChapter 12 Bayesian Inference Networks: Estimating Vulnerability,
Consequences, and LikelihoodChapter 13 Securities Valuation, Risk Measurement, and Risk Inference
NetworksChapter 14 Risk Fusion and Supermodels: A Framework for Enterprise Risk
ManagementChapter 15 Inferring Causality from Historical Market BehaviorChapter 16 Sensemaking for Warnings: Reverse-Engineering Market
IntelligenceChapter 17 The United States as Enterprise: Implications for National
Policy and SecurityNotesIndex

Excerpt

CHAPTER 1

Plausibility versus Probability: Two Worldviews

Over the last three decades or so, sophisticated financial modeling has beenalmost exclusively statistical in nature. The ready availability of massiveamounts of historical market data has fueled the creation of valuation and riskmeasurement models built on concepts such as association, correlation, andlikelihood.

All these models create implicit forecasts, that is, estimates of expected andpossible future scenarios for a security or a portfolio of securities. Mostoften, these forecasts are based on the assumption that the future marketbehavior is well represented by the past.

However, this stochastic approach implies a worldview that ignorescausality in favor of correlation. In this world, it doesn’tmatter whether gold prices increased because interest rates decreased or viceversa. It also doesn’t matter whether the prices of a utility stock and anairline stock are directly related in some fashion or whether, instead, they areboth driven by a common dependence on fuel prices. This world is a supremelyefficient world as well: all prices reflect new information immediately, andthat information is transmitted instantaneously around the globe.

However, intuition belies these notions. Traders and portfolio managers knowthat events drive prices. Catalysts such as the release of an economic indicatoror an earnings report drive prices, and chain reactions precipitated by animportant event can take a finite amount of time to propagate.

Such statistical models were often sufficient in the past, when the volume andcomplexity of derivative instruments were far lower than they are today. Butnow, the value and risk of popular instruments such as options on creditderivatives and complex asset-backed securities increasingly depend on themodeling of low-probability, high-consequence events. If the models used are notadequate for the task of anticipating such high-consequence events, massivelosses and market disruptions can occur. Certainly the financial disruptionsthat began in 2007–2008 are abundant evidence of such failures.

But as the old saying goes, “Correlation is not causation.” The alternative to astatistical model is a causal model that explicitly creates an alternativeworldview, one in which cause and effect are modeled in logical or temporalorder.

This alternative world is one in which plausibility rather thanprobability is modeled. The consequences and likelihood of events thathave never before occurred but that can be reasonably anticipated (as aconsequence of other events) are included in the quantitative models. Suchmodeling is the forte of the intelligence community and those responsible fornational security, who must create metrics and construct solutions for threatsthat have never before occurred.

Plausibility can be determined from a mixture of expert opinion, hard facts, andhistorical experience. Although the structure of any causal model may be guidedby 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 tovalidate and inform the model. A causal model is not necessarily deterministic;it can allow for uncertainty. Ideally, causal inference facilitates theintegration of substantive knowledge with statistical data to refine the formerand interpret the latter.

Such causal models are used in other disciplines, most notably epidemiology anddecision science. They are little used in finance, with the notable exception ofthe measurement of operational risk (i.e., the risk of loss due to human error).Causal models are nearly absent from quantitative modeling for purposes ofinstrument valuation or market and credit risk measurement.

The preference that quantitative analysts have for “frequentist” orprobabilistic models over causal models over the last three decades isunderstandable for a number of reasons.

First, such models are relatively easy to create and implement, using financialtheories (such as modern portfolio theory) that are already well accepted and inthe public domain.

Also, until recently, neither the mathematical language nor the technical toolsthat might facilitate the creation of causal models existed. Although thefinancial community commenced serious quantitative modeling in the 1970s, itwasn’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 ofcausality that might have facilitated such model building did not exist at thetime the financial community was choosing its path. Perhaps more important, evenif such models had been created, the data required to inform them were usuallyinsufficiently granular, synchronized, and properly organized for use in acausal 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 technologicalinnovations have made causal inference practical in the financial arena.

Consider one of the key questions in causal inference: How can one distinguishbetween mere correlation and cause and effect? When the sun rises and the cockcrows, was one of these two events the catalyst for the other, or were they boththe consequence of a third event?

One of the best methods of validating causal relationships is viaexperimentation. We can wake up the cock at 3 a.m. and see if this causes thesun to rise. Or an experiment can be designed to eliminate all variables butone: for example, in medical trials, the effect of the drug on a patient. Toproduce valid results, such an experiment would probably contain key featuresused in causal modeling, such as randomization (e.g., patients are randomlyselected to receive an experimental drug or a placebo) and elimination ofexogenous factors (e.g., variations in age or sex).

Fortunately, in finance, the capital markets are a laboratory that continuouslyprovides us with natural experiments. Thus, rather than using historical marketprices in statistical analyses, we can use them in causal inference models.Every day, traders receive information about catalytic events that move marketsand are able to observe the synchronous or subsequent effects of thosecatalysts.

Technological advances now make the observation of these natural experimentsboth possible and practical. Formerly, end-of-day data were relatively uselessfor determining causation because so many important events occur during thecourse of a trading day. Just as in a medical trial, when there are multiplevariables, reliable causal inferences are exceedingly difficult to make.

Only in the last few years has commercial software become available that iscapable of capturing event data and synchronizing those data with real-timemarket data of the highest granularity. This synchronized information gives usthe means to learn from one controlled experiment at a time, even if theexperiments last just seconds.

Although many events occur in the course of a trading day, few of them occursimultaneously, where simultaneous is defined as occurring within thesame very small window of time. For example, we might capture the earliestmoment at which an earnings report became public or a report on crude oilinventory was released. If we then examine the real-time behavior of stock oroil prices in the seconds to minutes after the release, we can form opinionsabout how such an event drives prices.

Besides potentially providing better estimates of value and risk, causal modelsmay be more intuitive and understandable by risk managers and portfolio managersthan statistical models are. For example, the language of causality is a naturallanguage for risk management. Examples of causal concepts are influence,ignorability, disturbance, effect, confounding, intervention, and explanation.

The graphic representations that substitute for mathematical equations lendthemselves well to financial applications. As Pearl points out, there is noanalog in algebra or statistics to the causal operator “given that I do,” thatis, the effect of a deliberate action on the outcome of the analysis. However,these representations lend themselves well to programming. Computer codedoes allow such operators; the statement A = B is a substitution ratherthan a statement about an inviolate relationship between A and B.

Similarly, hedge positions can be considered “interventions” that can blockcertain paths: those that lead to undesirable outcomes, such as very largelosses. Such a hedge might be a security that is already in a portfolio or,alternatively, an exogenous variable that drives changes in one or moresecurities in the portfolio.

Further, the identification of hierarchically organized causes lends itself verynaturally to the identification of systematic and specific risks as required bythe Basel II accord. Such methods may provide results that are far superior tothose provided by statistical methodologies such as principal componentanalysis, the results of which can be degraded by spurious correlations withoutexpert intervention.

Causal models also provide a natural framework for the estimation of two keyrisk measures for which no industry-standard methods yet exist: economic capital(the amount of capital required to ensure the continued existence of theenterprise to a very high degree of confidence) and enterprise risk (the risk toan enterprise from all sources of risk). In such models, expert opinion can beintegrated with historical behavior to systematically generate all plausiblefuture scenarios, estimate their likelihood, and measure their consequences.

All else being equal, a causal approach is preferable to a statistical approachfor several reasons.

First, a causal approach allows a more general solution. A statistical solutioncan be simulated, albeit inefficiently, using a causal network that includes anerror component. However, the reverse is not true.

Second, causal networks do not require extensive historical data for all thesecurities and instruments in a portfolio. Causal models can be used even whenhistory is not a reliable indicator of the future—for example, when ashift in risk regime has occurred or when new risk factors such as changingregulatory policy are expected to have a significant impact.

Causal networks can also be allowed to have a specific order in which eventsoccur or a temporal component suitable for high-frequency trading and real-timerisk management. Forecasts of consequential behavior produced in sufficient timeto execute a trade can be used in automated, algorithmic trading. Further,observed market behavior that is time dependent (e.g., volatility clusters andjump diffusion processes) might be more easily explained in terms of causalmodels than it is by statistical models. Also, instead of relying on solutionssuch as GARCH methods or stochastic volatility models to calibrate observationsto history, such observations might be explained in terms of the observable,noninstantaneous effects of traders’ and portfolio managers’ behavior.

A causal approach can use all available information to inform the model,not just historical pricing data. In the terminology of the intelligencecommunity, this is the use of “all source intelligence.” For example, additionalfundamental information might be used to inform (or override) certain causalrelationships. The sensitivity of an airline to the price of fuel might beindependently modeled by a fundamental equity analyst and then compared to therelationship inferred by the causal model. Or if a publicly traded home builderhas never before hedged its interest-rate exposure but has just started such aprogram, the past dependence of the company’s stock price on interest ratesmight be overridden.

A causal approach is far more dynamic than a statistical approach because itallows the introduction of prior knowledge. A forecast of one-day riskis substantially different one second after the release of the monthlyunemployment statistics from what it was one second before that release,based on knowledge of both market expectations and the actual news. In thelanguage of causal modeling, these are the prior and posteriordistributions.

Most important of all, a causal structure provides far more transparency than dostatistical parameters. The graphical language of causal modeling reveals thefundamental relationships assumed by experts and inferred from data and lendsitself to the use of visualization tools that enhance clarity and aid humancognition.

The process of building such a model also removes some of the intellectualbarriers between the front office and the middle office and between technicalanalysis and fundamental analysis. Causal relationships that can be understoodand vetted by human experts with multiple areas of expertise are far more likelyto be repeated in the future.

Clearly, causal models are somewhat more difficult to implement and to informthan are statistical models. However, when they are used for certain purposes,such as valuing complex derivative instruments, estimating extreme or real-timeportfolio risk, or designing an optimal hedging strategy, they are well worththe effort.

For example, one of their major advantages is the ability to perform discrete-timeand discrete-outcome modeling. Although common statistical methodologiessuch as copula approaches are mathematically elegant, they often implicitlyeliminate the granularity, asymmetry, and noncontinuous behavior that areinteresting features (and opportunities for profit) of real markets. By doingso, they may substantially over- or underestimate value or risk, particularlyfor instruments with a narrow payoff window, such as nth-to-default tranches incollateralized debt obligations, or in strategies such as calendar or pricespreads in options.

What a causal approach lacks in computational elegance it may make up for inaccuracy. Consider a situation in which Treasury bond traders are split 50/50 onwhether the Treasury will announce an auction of 30-year bonds. This is a binaryevent: it will occur, or it will not; the yield curve will flatten or steepen. Arealistic forecast of changes in 30-year bond yields just after the announcementis likely to be bimodal because there is no neutral event.

The benefit of a causal model is its ability to generate many plausiblescenarios in a systematic fashion. The likelihood of some of these scenarios maybe higher than in a random-walk world; that of others may be lower. Markets mayhave “hot spots” and “cold spots”: scenarios in which a convergence of certainchain 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 possibleoutcomes can be granular, be asymmetrical, and have extreme outcomes, hasprofound implications for financial engineering, portfolio management, riskmanagement, and even decision science. Clearly, a set of possible futurescenarios substantially different from those created using continuous, normallydistributed variables, suggests radically different results for all kinds ofestimates.

Specifically, valuation models, particularly those for securities or complexderivative instruments, will produce results that are substantially differentfrom the results of standard models that assume normality, symmetry, andoutcomes that are in line with historical experience. Portfolio optimization andperformance attribution models are similarly affected. The interactions betweenthe securities in the portfolio may be poorly described by statistical measuressuch as correlation, and an ideal portfolio (i.e., one with an optimum risk-returnprofile) constructed using such scenarios might look quite different fromone constructed using more traditional methods.

Most important, risk measurement models based on causal methods may estimaterisk to have a magnitude that is either far greater or far less—as well asless continuous—than that estimated using traditional stochastic models.Certain outcomes that were formerly assumed to be virtually impossible must nowbe considered, whereas others are now less likely than before. At the heart ofall risk measurement (and in fact all financial engineering) is the ability togenerate all plausible alternative scenarios and estimate their likelihood. Thesensitivity of a portfolio, an enterprise, or even the global capital marketsthemselves to the most extreme of these scenarios provides a systematic methodfor generating stress tests (i.e., measures of the consequences of aparticular scenario) and ensuring the continued existence of the system as weknow it.

The use of causal methods also provides solutions; they can be used to mitigateas well as measure risk. They provide a method for inserting circuit breakersinto 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 oncrude oil to hedge the risk of large declines in the price of airline andhospitality stocks, or a regulator might modify capital requirements orposition-limit rules.

The ultimate goal of enterprise risk management is as a quantitativedecision-making tool. Ultimately, the use of causal methods facilitates thehighest-level goal of risk management: decision making by senior management. Anunderstanding of the possible future paths that might trigger tipping points andlead to catastrophic outcomes can assist C-suite executives in optimizing theirbusiness strategies on a risk-adjusted basis.

SUMMARY

In this chapter, we contrasted frequentist and causal approaches to riskmanagement and their utility in measuring and mitigating extreme risk andoptimizing decision making.

WHAT’S NEXT

In the next chapter, we will relate key milestones in the evolution of riskmanagement philosophy and describe the most recent and revolutionary innovationsin quantitative decision making.

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