The Role of Behavioral Finance in Risk Management

CHAPTER 29

The Role of Behavioral Finance in Risk Management Hersh Shefrin Mario L. Belotti Professor of Finance Leavey School of Business Santa Clara University Santa Clara, CA 95053

I. II. HI. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII.

Introduction How Do People Perceive Risks? How Do People Perceive Probabilities? How Do People Establish Confidence Intervals? How Do Investors Perceive Equity Risk? How Do Investors Perceive the Relationship Between Risk and Return? What Factors Determine People's Attitudes Toward Risk? How Important Is Framing? What Is Regret? What Determines Evaluability? How Does Affect Cause Preference Reversal? How Do Fear and Hope Influence Risk Tolerance? How Do Fear and Hope Influence Judgments About Value? How Do Investors Measure the Risk/Return Trade-Off? How Effective are Groups at Making Decisions? Examples of Psychologically Induced Errors Is Debiasing Possible? Conclusions

RISK MANAGEMENT Copyright 9 2006, Elsevier Inc. All rights reserved.

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Abstract When it comes to the identification of risk and the choice among risky alternatives, psychology and mathematics are both key drivers. In theory, risk management is a scientific enterprise. Risks are defined using probability measures, risks are estimated using efficient statistical procedures, and risks are selected by means of an optimization program. In practice, risk management is a combination of art and science. The art of risk management reflects the psychology of risk. Psychological forces are key determinants of the way people perceive risk and control risk through the decisions they make. This chapter describes the impact of psychology on risk perception and choice, with special emphasis on risk and return in investment analysis.

Glossary Affect Magnitude of emotional reaction, positive affect being favorable and negative affect being unfavorable. Confirmation bias Overweighting evidence that confirms one's position relative to information that disconfirms one's position. Excessive optimism Overestimating probabilities of favorable events, and underestimating probabilities of unfavorable events. Framing Describing information pertinent to a decision task, including the task itself. Groupthink The tendency of people working in groups to seek consensus without adequately exploring the weaknesses o f the proposal at hand; or without exploring alternative actions. Heuristic Rule of thumb. Overconfidence Establishing confidence intervals that are too narrow. Prospect theory A behavioral theory of choice that emphasizes gains and losses as the carriers of value. Representativeness Use of stereotypic thinking, relating object or idea to class or population in which it is contained. SP/A A behavioral theory of choice that emphasizes the emotions of fear, hope, and achievement of goals.

I. INTRODUCTION Behavioral finance is the study of how psychology affects financialbehavior. This chapter describes the key elements that comprise the psychology of risk. Psychologically, risk is multidimensional. There is no single definition of risk, and therefore no simple way to measure risk in practice. Emotions, what psychologists call affect, are important and often drive decisions about how risks will be managed. People are not uniformly tolerant toward risk. The same person can display low tolerance for

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risk in some circumstances and high tolerance for risk in other circumstances. People sometimes act as if they are risk averse and sometimes act as if they are risk seeing. Different people perceive risks differently. For example, in 2003 the Financial Executives Research Foundation, insurance organization FM Global, and National Association of Corporate Treasurers conducted a joint study of risk managers and financial executives. The study found that risk managers and financial executives do not share the same view about the hazards affecting the earnings of their firms. In 2003, risk managers viewed the top risk as due to fire and explosion, whereas financial executives viewed the top risk as being related to improper management and employee practices. Risk managers favored property-related hazards over other hazards, with the corresponding weights being 70/30. In contrast, financial executives gave 50/50 (equal) weights to property-related hazards and other hazards. People are prone to biases in the ways they estimate risk. Moreover, people's perceptions of risk and risk management can be sensitive to the manner in which the risks are described. In addition, risk management decisions are often made in groups. Although decisions made by groups are sometimes superior to the decisions made by individuals, when it comes to risk management groups often accentuate psychological propensities rather than mitigate them. This effect is known as polarization. There is no single, unified psychologically based theory of risk. Unlike economists, who approach risk management with a set of unifying principles, psychologists are more piecemeal in their approach, recognizing the complex nature of human decision processes. The chapter discusses several psychologically based theories of risky choice: SP/A theory, prospect theory, regret theory, and change-of-process theory. SP/A theory focuses on the interaction between aspiration and the emotions of fear and hope. Prospect theory focuses on gains and losses. Regret theory focuses on counterfactual thinking, Change-of-process theory focuses on attractiveness and valuation. Although most of these theories focus on individuals in isolation, they also admit elements from social psychology, especially relative social standing and social status. Group processes are also social psychological in nature. The psychological aspects of risk assessment are known as heuristics and biases. Heuristics are rules of thumb. Biases are predispositions toward systematic errors. When it comes to assessing risks, humans are imperfect processors of information. The chapter describes some of the main heuristics people use and the attendant biases to which they are prone. Group processes are also an important feature of this discussion. Are there techniques that can be used to counter some of the more psychologically damaging traits? The final part of the chapter discusses this question. Among the issues addressed are the following. The history of risk management is replete with examples of risk management decisions being driven more by psychological factors than by mathematical models. Rogue traders consistently lose billions of dollars of their firms' money in vain attempts to recoup past losses. Is it possible to take preemptive action in these cases? Investors get caught up in stock market bubbles, and social forces make it difficult for the sensible to follow a contrarian course. Is it possible to provide investors with tools to help them resist

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being swept along by the herd? Can risk managers be taught how to manage the psychology of risk as well as the mathematics of risk? Answers to these questions conclude the chapter.

II. HOW DO PEOPLE PERCEIVE RISKS? Risk is traditionally modeled as being a function of possible outcomes and their associated probabilities. However, most people do not possess precise notions of probability. Nor do they develop precise measurements of risk. Instead, people appear to develop a general sense of risk that is influenced by emotion. A study by Paul Slovic, Baruch Fischoff, and Sarah Lichtenstein titled "Rating the Risks," and published in 1979 in Environment, provides important insights into how people perceive risk. In the late 1970s, these authors conducted a study in which they asked subjects to estimate the annual fatalities and rate the risks associated with a series of 30 activities. The range of activities was wide, and included police work, firefighting, mountain climbing, nuclear power, skiing, electric power, railroads, bicycles, X-rays, motor vehicles, alcoholic beverages, and smoking. The study contrasted the risk perceptions of lay subjects with risk ratings provided by experts. The study authors found that for some activities the risk perceptions of lay subjects differed dramatically from experts. For example, lay subjects perceived nuclear power to be much riskier than did experts, but X-rays to be less risky than did experts. Notably, although experts tended to view risk in terms of expected fatalities lay subjects did not. For them, risk meant more than fatality rates. What accounts for the manner in which people form perceptions of risk? And why are they subject to systematic biases in their perceptions? Slovic and his coauthors found that two variables explain the manner in which people rate risk. The first variable is the degree to which they dread the outcome. Dread is an emotional reaction, reflecting what psychologists call negative affect. Affect describes degree of goodness, and may be positive, zero, or negative. The second variable is severity, meaning the propensity for an activity-induced injury to be fatal. The more people dread the injury from an activity, the higher they rate the risk of the activity. The more severe the outcome, the higher they rate the risk of the activity. People's perceptions of risk are also influenced by information that is readily available to them, leading to a phenomenon known as availability bias. For example, the chapter author replicated the study done by Slovic and his coauthors during the period 1998 through 2003. Notably, the perceived riskiness attached to police work and firefighting jumped after the salient events of 11 September 2001, moving from the second most risky quintile of risky activities to the most risky quintile. Availability bias might also explain the differential risk perceptions of financial executives and risk managers mentioned in the introduction. Risk managers are more familiar with insurable risks, such as property-related hazards, whereas financial executives are more familiar with hazards associated with improper management.

The Role of Behavioral Finance in Risk Management III. H O W

DO PEOPLE

657 PERCEIVE

PROBABILITIES?

Consider next the manner in which people assess probabilities. In 1980, Neil Weinstein wrote an article titled "Unrealistic Optimism About Future Life Events," published in the Journal of Personality and Social Psychology. Weinstein reported that people tend to be excessively optimistic, in that they assign probabilities that are too high for favorable events and assign probabilities that are too low for unfavorable events. The subjects in Weinstein's study were presented with a series of life events. Examples included being fired from a job, having one's work recognized with an award, living past 80, and developing cancer. Subjects were asked to identify how likely they were to experience each event relative to their peer group. Weinstein gave his subjects a list of 15 possible responses, ranging from no chance of experiencing the event (100% less) to 5 times average. Average responses for favorable events tend to be about 10% more, whereas average responses for unfavorable events tend to be about 10% less. Weinstein identifies four factors that appear to cause people to be excessively optimistic. The first is controllability. Subjects rate each life event on a 5-point scale, where 1 connotes the absence of control in affecting the probability of the event and 5 connotes perfect control. In general, controllability and optimism are positively correlated: people are inclined to be more optimistic about events in which they perceive themselves to exert greater control. The second factor causing people to be excessively optimistic is desirability. Weinstein used a 9-point scale, where 1 was extremely undesirable and 9 was extremely desirable. In general, desirability and optimism are positively correlated: people engage in wishful thinking. The third factor causing people to be excessively optimistic is experience with the event. Familiarity and understanding are similar concepts. Weinstein measured familiarity on a 5-point scale, where 1 connotes the event not happening to anyone the subject knows and 5 connotes the event having happened to the subject at least twice. The experience variable appears to be negatively correlated with optimism for unfavorable events. The fourth factor causing people to be excessively optimistic is representativeness, the overreliance on stereotypic thinking. Weinstein measured representativeness on a 3-point scale, where 1 means "no particular person with a high chance comes to mind" and 3 means "when I think about the event, a clear picture comes to mind of a particular type of person to whom the event is likely to happen." Representativeness and optimism are positively correlated. That is, people are inclined to be more optimistic about events they can picture happening to a representative individual. There are two ways that affect surfaces as an issue in respect to optimistic probabilities, First, desirability is a manifestation of affect. Desirable outcomes produce positive affect, whereas undesirable outcomes produce negative affect. Second, the degree of affect is generally influenced by imagery. Psychologists suggest that conceptual thought largely takes place through imagery, In this respect, people experience

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emotion more intensely when they can attach specific images to concepts. That might explain why representativeness appears to increase optimism bias.

IV. HOW DO PEOPLE ESTABLISH CONFIDENCE INTERVALS? One of the most robust findings by psychologists is that people are overconfident about difficult tasks. In particular, they tend to establish confidence intervals that are too narrow. In order to describe the key issue, consider the following question: What is the number of days in the gestation period of an Asian elephant? In answering this question, people are asked to provide their best guess along with a confidence interval. Each person is instructed that their confidence interval should consist of a low guess and a high guess, so that they are 90% confident that the true answer lies between their low guess and their high guess. The gestation period for an Asian elephant is 645 days. About 10% of people answering the question provide a confidence interval that includes 645 days. Instead, most people set their confidence interval too narrowly, the hallmark of overconfidence. The general point is that most people think they know more than they do. As a result, they come to be surprised more frequently than they anticipated. A wellcalibrated person who establishes 90% confidence intervals when asked to do so should expect to be surprised 10% of the time. When asked a series of 10 questions similar Iin nature to the Asian elephant question, a well-calibrated person would expect to be surprised once. In practice, people are typically surprised six times. Overconfidence is an important issue in respect to risk. As an example, consider the hedge fund Long Term Capital Management. In 1998, Long Term Capital Management made front-page headlines the world over when its losses threatened to cause a panic on global financial markets. Long Term Capital Management had calculated that on any single day its maximum loss would be $35 million. On Friday, 21 August 1998, it lost $553 million! That is, its confidence bands were too narrow by a factor of 16. Investors who are overconfident are inclined to take bigger risks than are prudent.

V. HOW DO INVESTORS PERCEIVE EQUITY RISK? In the capital asset pricing model (CAPM), risk is measured by a single variable, beta. The beta of a stock measures the degree of non-diversifiable market risk associated with the return distribution of that stock. About 1990, financial economists began building models that feature risk factors other than the market premium, such as size, book-to-market equity, and momentum. These models were developed as a response to empirical findings that historically small capitalization stocks outperformed large capitalization stocks, value stocks outperformed growth stocks, and the stock returns to recent winners exceeded the stock returns to recent losers.

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Note that the factor model is primarily a model of returns, not risk, with theoretical reasons used to associate factors with risk. However, we need to ask whether the variables financial economists use as risk factors actually explain the manner in which investors perceive equity risk. To address this issue, consider evidence from a study by the author that asked investors, analysts, portfolio managers, and business students to rate equity risk. In the study, participants were asked to rate the riskiness of 10 stocks, after viewing current financial information about these stocks at a well-known web site. Subjects rated riskiness on a scale of 0 to 10. The financial information available at the web site displayed many variables, including market capitalization, price-to-earnings ratio, price-to-book ratio, price-to-sales, beta, past returns, financial statements, analysts' earnings forecasts, and analysts' recommendations. To what extent do these variables correlate with subjects' risk perceptions? Among professional investors and students alike, the variable that best explains perceived risk is size. For professional investors, the second most important variable is past returns, whereas for business students the second most important variable is beta. The simple correlations between perceived risk and the traditional risk factors support the traditional model, with one exception. The one exception pertains to momentum. However, in a multiple regression that controls for size, the coefficient on past sixmonth returns conforms to the traditional perspective.

VI. HOW DO INVESTORS PERCEIVE THE RELATIONSHIP

BETWEEN

RISK AND

RETURN?

As was discussed earlier, affect underlies risk perceptions associated with general activities such as smoking and nuclear power, and the probabilities attached to the occurrence of life events. Psychologists point out that people attach affect tags to mental objects in their memories, which help them quickly recognize both threats and opportunities. These mental tags are an important part of what we think of as intuition or gut instinct. One of the most important implications of the affect heuristic is that people associate high benefits to low risk, thereby treating the relationship between risk and benefits as negative. In a financial context, benefits take the form of returns. Of course, in traditional finance the relationship between risk and return is positive, not negative. However, given the role that affect plays in general risk perception might it be the case that most people act as if they believe that risk and return are negatively related? The answer to the last question is yes. A 2000 study by Yoav Ganzach "Judging Risk and Return of Financial Assets" in Organizational Behavior and Human Decision Processes first established this finding for stocks when subjects were not familiar with the securities. The study of perceived equity risk discussed in the previous section asks participants to provide their 12-month return expectations as well as their risk

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perceptions. Their risk perceptions and return expectations turn out to be negatively correlated. Even though people assess risk in a manner generally consistent with the traditional framework, they expect higher returns from safer stocks. In particular, study subjects collectively expect higher returns from low beta stocks than they do from high beta stocks. Notably, not all subjects expect higher returns from low beta stocks than from high beta stocks. Analysts and portfolio managers who cover the stocks being rated in the study questions indicate that they expect higher returns from high beta stocks than from low beta stocks. They also expect higher returns from small-cap stocks than from large-cap stocks. In 2003, this general finding was documented by Alon Brav, Reuven Lehavy, and Roni Michaely in a Duke University working paper titled "Expected Return and Asset Pricing." Why are security analysts' judgments about the stocks they cover different from most study subjects discussed previously? One reason might be that in the course of setting target prices for stocks analysts are more systematic in their approach than most investors, relying less on the affect heuristic. At the same time, security analysts erroneously expect higher returns from growth stocks than they do from value stocks. In addition, they expect higher returns from recent winners than they do from recent losers. That is, the beliefs of security analysts run counter to historical patterns when it comes to book-to-market equity and to recent returns.

VII. WHAT FACTORS DETERMINE PEOPLE'S ATTITUDES TOWARD RISK? Once people have formed their perceptions about the risk inherent in the alternatives at their disposal, how do they choose among these alternatives? What role does attitude toward risk play when it comes to choice and valuation? The answer to these questions turns out to be quite complex, in that people react to risk differently depending on context. Consider an example. Imagine that a person faces a choice between two alternatives. The first alternative is risky, and features a 25% chance that he will gain $740 and a 75% chance that he will lose $260. The second alternative is to reject the risky alternative, thereby accepting a sure incremental gain of $0. Unless someone actually enjoys facing risk, the conventional view is that most people would choose to reject the risky alternative. Why? Presumably it is because the expected payoff to the risky alternative is - $ 1 0 ( = 0.25 9 7 4 0 - 0.75 9 260), whereas the expected payoff to the risk-free alternative is $0, a higher number than -$10. Note that the numbers in this example are incremental cash flows, meaning that they indicate how the person's cash flows will change as a result of his or her choice. Notably, incremental cash flows say nothing about the context of the decision problem. For example, suppose that the person has just lost $740 and now faces the opportunity

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to accept the risk. Accepting the risk means that he faces a 25% chance of breaking even and a 75% chance that his loss will grow from $740 to $1,000. In their 1979 article "Prospect Theory," published in Econometrica, psychologists Daniel Kahneman and Amos Tversky found that the majority of people who perceived themselves to be in the domain of losses would choose the risky alternative, despite the lower expected payoff. However, if the context for the choice task did not involve a loss almost everyone rejected the risky alternative. Kahneman and Tversky concluded that for the decision task described here people are prone to be risk seeking when they perceive themselves to be in the domain of losses, and are prone to be risk averse when they perceive themselves to be in the domain of gains. In other words, context is key insofar as attitude toward risk is concerned. Keep in mind that attitude toward risk is complex. Are people always prone to be risk averse in the domain of gains? The answer to this question turns out to be no. To explain why this is the case, consider a choice between two alternatives that feature either a non-zero gain or a zero gain. The first alternative offers a possible incremental gain of $2,000 and the second alternative offers a possible incremental gain of $4,000. Suppose that the probabilities of winning a non-zero amount are 90% for the first alternative and 45% for the second alternative. The majority of people choose the first alternative. Note that both alternatives feature the same expected payoff, $1,800. However, the first alternative is less risky. Next, suppose that the probabilities of winning a non-zero amount are 0.2% for the first alternative and 0.1% for the second alternative. The expected payoff for both alternatives is $4. However, in this situation the vast majority of people choose the risky alternative. Kahneman and Tversky concluded that magnitudes of probability make a difference. Although people appear to be risk averse when the probability of a non-zero gain is moderate to large, they act as if they are risk seeking when the probabilities of a non-zero gain are small. Kahneman and Tversky suggested that this behavior pattern emerges because people tend to overweight small probabilities. Notably, the same feature leads people to act as if they are risk averse when they perceive themselves to be in the domain of losses. They suggest that overweighting of small probabilities might explain why people choose to purchase lottery tickets, a risky alternative in the domain of gains, but choose to purchase insurance against small losses (risk averse in the domain of losses, in that paying the insurance premium constitutes a loss). Attitude toward risk is complex. Do people always overweight small probabilities? The answer to this question turns out to be no. In a 1977 article rifled "Preferences for Insuring Against Probable Losses: Insurance Implications," which appeared in The Journal of Risk and Insurance, Paul Slovic, Baruch Fischoff, Sarah Licthenstein, Bernard Corrigan, and Barbara Combs reported that when the probabilities of nonzero payoffs fall below a critical level people tend to code these probabilities as zero, thereby treating the associated events as being impossible. Kahneman and Tversky suggest that attitude toward risk is driven more by considerations of loss aversion than by risk aversion. Their framework, called prospect theory, postulates that people experience losses more intensely than gains of the same

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Prospect Theory Value Function

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FIGURE 29.1 The graph of the value function in prospect theory, which is a utility function defined over the domain of gains and losses relative to a specified reference point.

magnitude. Experimental evidence suggests that on average people experience a loss roughly 2.5 times as intensely as they experience a comparable gain. Prospect theory features an S-shaped value function to measure the experience of gains and losses. This function is concave in the domain of gains and convex in the domain of losses, reflecting the tendency of people to be risk averse in the domain of gains but risk seeking in the domain of losses. Prospect theory also features a nonlinear weighting function for probabilities that lead people to weight small probabilities differently than they do moderate to large probabilities. Figures 29.1 and 29.2 portray these two functions. Again, attitude toward risk is complex. Are people always prone to behave in a risk averse fashion in the domain of gains when the probability of a non-zero payoff is moderate to large? The answer to this question turns out to be no. Suppose a person has just won $1,500 and faces the opportunity to choose a 50/50 (incremental) gamble in which he or she will either win $450 or lose $450. Richard Thaler and Eric Johnson wrote an article titled "Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice," which appears in Richard Thaler's (editor) 1991 volume Quasi-Rational Economics. Thaler and Johnson found that the prior gain of $1,500 leads the majority of people to accept the risky alternative. They call this phenomenon the "house money effect."

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Prospect Theory Weighting Function 1.2

0.8

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0 0.05 0.09 0.14 0.18 0.23 0.27 0.32 0.36 0.41 0.45 0.5 0.54 0.59 0.63 0.68 0.72 0.77 0.81 0.86 0.9 0.95 0.99

Probability F I G U R E 29.2 The graph of the prospect theory weighting function, which is defined over the cumulative probabilities associated with gains (or loses). The steep slope at the origin signifies that small probabilities associated with extreme outcomes are overweighted relative to the probabilities of other events.

Johnson and Thaler suggest that people experience successive gains of $1,500 and $450 separately, but integrate the loss of $450 into the prior gain of $1,500. That is, the experience of successive gains of $1,500 and $450 is superior to the experience of a one-time gain of $1,950, whereas the experience of a one-time gain of $1,050 is superior to a loss of $450 and prior gain of $1,500 experienced separately. The house money effect postulates that the prior gain of $1,500 serves as a cushion for subsequent losses (up to $1,500).

VIII. HOW IMPORTANT IS FRAMING? Kahneman and Tversky used the term framing to connote the way a decision task is described. Consider a decision task framed as follows. Imagine that a decision maker is asked to make two choices. The first choice involves either (A) accepting a sure $240 or (B) facing a gamble that pays $1,000 with probability 0.25 or $0 with probability 0.75. The second choice involves either (C) accepting a sure $750 loss or (D) facing a gamble that results in either a loss of $1,000 with probability 0.75 or $0 with probability 0.25. Assume that the gambles selected are played out concurrently.

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In an experimental setting, the majority of subjects choose the sure gain A in the first choice. In the second choice, the majority of subjects choose to face the risky alternative D. These subjects could have instead chosen to face the gamble B in gains, and accepted the sure loss C. However, for reasons described earlier most people behave as if they are risk averse in the domain of gains and risk seeking in the domain of losses, given the opportunity to break even. Consider a second decision task. A person is told that she must face a gamble in which she will lose either $1,000 with probability 0.75 or $0 with probability 0.25. In addition, she faces a choice of (E) to accept an incremental $100 irrespective of how the gamble turns out or (F) to reject the $100. Almost everyone accepts the $100. There is a connection between these two decision tasks. Refusing the $100 in the second decision task provides the same gambles as in the first decision task when the person chooses the sure gain A and accepts the risky loss B. Accepting the $100 in the second decision task provides the same gambles as in the first decision task when the person chooses the risky gain and accepts the sure loss. The framing of the first decision task induces people to make choices that are stochastically dominated. The first decision task (A versus B, C versus D) is framed opaquely. People do not willingly choose to face stochastically dominated gambles, if they can avoid doing so. The second decision task (E versus F) is framed transparently. As a result, almost everyone rejects the stochastically dominated alternative. One thing these examples make clear is that people are not adept at reframing their decision tasks. In this respect, people tend to make decisions sequentially, in piecemeal fashion. For example, most people mentally separate the two choices in the first decision task, first choosing between the sure gain and the risky gain and then moving on to choose between the sure loss and the risky loss. That is, people tend to place each choice into its own mental account and then make choices mental account by mental account. What most people fail to do is combine payoffs across mental accounts.

IX. W H A T IS R E G R E T ? Regret is an emotion generated by counterfactual thinking that stems from secondguessing one's own past decision with the benefit of hindsight. Consider an example. Imagine a random drawing from a jar with 36 numbers, numbered 1 through 36. Consider a choice between two gambles. The first gamble pays $2 if the number drawn is between 1 and 29, and $0 if the number drawn is between 30 and 36. The second gamble pays $9 if the number drawn is between 30 and 36, and $0 if the number drawn is between 1 and 29. Think about a person who chooses the second gamble and then watches as the number 23 is drawn from the jar. What emotions does this person experience? The first emotion stems from having won $0. However, the person might also experience a second emotion, if after the fact he or she finds it easy to imagine having made the more conservative choice and thereby winning $2 instead of $0. Regret is the ex post disutility associated with counterfactual thinking of this sort. The magnitude of the regret is a function of the differential payment, $2 versus $0. If regret is a strong

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emotion, a person might choose between the two alternatives described by seeking to minimize expected regret.

X. WHAT DETERMINES EVALUABILITY? The example discussed in the previous section illustrating the concept of regret focuses on the comparison of $2 relative to $0, and $9 compared to $0. Consider whether the extent of regret would be meaningfully impacted if the $0 payoff were to be replaced by a 5-cent loss (-$0.05). That is, consider whether the anticipation of $2 or $9 is experienced differently if contrasted with a 5-cent loss instead of $0. In a 2002 article titled "The Affect Heuristic" that appeared as a chapter in the collection Heuristics and Biases: The Psychology of Intuitive Judgment (edited by Tom Gilovich, Dale Griffin, and Daniel Kahneman), Paul Slovic, Melissa Finucane, Ellen Peters, and Donald MacGregor reported that the answer to the previous propositions is affirmative. Their work suggests that the anticipation of a $9 gain is experienced more intensely when contrasted with a 5-cent loss than when contrasted with $0. That is, the $9 gain is more evaluable when set against -$0.05 than when set against $0. Slovic et al. suggest that this is because people tend to evaluate gambles using payoff ratios, such as 9/0.05, but that the affective processing in our brains does not meaningfully interpret 9/0 even though it is theoretically infinite. As evidence of this point, the authors conducted an experiment asking subjects to rate the attractiveness of gambles such as those described previously, featuring gains of $2 and $9, and either losses of $0 or losses of $0.05. Consider three groups of subjects. The first group was asked to rate only the gamble "win $9, lose $0." The second group was asked to rate only "win $9, lose $0.05." The third group was asked to rate both "win $9, lose $0" and "win $9, lose $0.05." The key finding of the experiment is that the second group of subjects ranked the gamble "win $9, lose $0.05" as more attractive than the first group ranked "win $9, lose $0." However, the third group (which ranked both gambles) ranked the gamble "win $9, lose $0.05" as less attractive than "win $9, lose $0." This finding suggests that a strong contextual background is necessary for people to experience the appropriate affective response when anticipating the prospect of winning $9. Such a background is provided by the prospect of a small loss of $0.05, either as part of the same gamble or as part of a comparison gamble. Specifically, people respond favorably to a win/loss ratio equal to 9/0.05, viewing such a ratio as highly attractive. However, their response to winning $9 without a stronger context results in a lower anticipatory affect level.

XI. HOW DOES AFFECT CAUSE PREFERENCE REVERSAL? Rating attractiveness, choosing among alternatives, and making judgments about value are not equivalent psychological processes. Indeed, people often assign valuations to

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alternatives that are opposite to their judgments about attractiveness and choice, a feature known as preference reversal. They appear to use a different process when engaging in valuation than they do when making a choice, a feature known as change

of process. To illustrate preference reversal, consider two alternatives discussed previously: (1) win $2 with probability 29/36 and (2) win $9 with probability 7/36. Typically, people rate the first alternative as more attractive than the second. However, when asked how much they would be willing to pay (WTP) in order to face these alternatives most people place a higher value on the second alternative. One explanation for preference reversal involves the manner in which probabilities and amounts are treated in forming judgments about attractiveness and risk. The hypothesis states that probabilities loom large in judgments about attractiveness, because probabilities stipulate the likelihood of winning. In contrast, amounts loom large in judgments about value, in that value is measured in the same units as amount; namely, dollars. In this regard, winning $2 with probability 29/36 is judged to be more attractive than winning $9 with probability 7/36 because the probability of winning $2 is considerably higher than the probability of winning $9. By the same token, winning $9 with probability 7/36 is judged to be more valuable than winning $2 with probability 29/36 because $9 is relatively much greater than $2. An intriguing finding is that when a small loss such as $0.05 replaces winning $0 the attractiveness of winning $9 increases, to the point where preference reversal disappears. The explanation for why this happens inwolves the affect associated with the prospect of winning $9. Adding a small loss serves to increase the affect attached to winning $9, even for judgments about attractiveness. Therefore, amount as well as probability enters the process for judging attractiveness.

XII. HOW DO FEAR AND HOPE INFLUENCE RISK TOLERANCE? Researchers working in the emerging field of neuro-economics are studying how attitude toward risk is determined by brain function. This line of research analyzes the emotion of fear as a neurological mechanism. Notably, fear appears to be the central emotion that underliesthe reluctance to accept risk. In a 1987 article tiffed "Between Hope and Fear: The Psychology of Risk," which appeared in Advances in Experimental Social Psychology, Lola Lopes proposed a psychologically based model of risk-taking based on two emotions. The first emotion is fear and the second emotion is hope. Lopes suggested that both emotions influence choice, and in turn are moderated by a third variable, the desire to achieve an aspiration outcome (or goal). She called her theory SP/A theory, where the S stands for the need for security, the P stands for the need for upside potential, and the A stands for aspiration. In her theory, fear underlies security and hope underlies potential. Formally, the SP/A choice model is a constrained maximization, with the objective function having the form of an expected payoff and the constraint being a floor for the

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probability that the payoff meets or exceeds the aspiration level. The expectation in the SP/A objective function does not generally use the actual probability distribution, but a distribution modified by the emotions of fear and hope. Fear tends to operate on the probabilities attached to low-payoff states, magnifying their relative importance. Hope tends to operate on the probabilities attached to highpayoff states, magnifying their relative importance. A person for whom fear is the dominant emotion will act as if he or she is excessively pessimistic. A person for whom hope is the dominant emotion will act as if he or she is excessively optimistic. Someone who is cautiously optimistic will act as if he or she is excessively pessimistic about the prospect of very low payoffs, and excessively optimistic about the prospect of very high payoffs. In order to study the manner in which fear and hope exert their influence on choice among risky alternatives, Lopes presented subjects with six payoff distributions. These appear in Figures 29.3 through 29.8. Particularly important are the shapes of the underlying density functions, with the following labels selected to capture these shapes: risk floor, short shot, uniform, peaked, bimodal, and long shot. The risk floor

FIGURE 29.3 The probability density function for the payoffs associated with the altemative known as the risk floor.

F I G U R E 29.4 The probability density function for the payoffs associated with the alternative known as the short shot.

F I G U R E 29.5 as peaked.

The probability density function for the payoffs associated with the alternative known

FIGURE 29.6 The probability density function for the payoffs associated with the alternative known as uniform.

F I G U R E 29.7 as bimodal.

The probability density function for the payoffs associated with the alternative known

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FIGURE 29.8 The probability density function for the payoffs associated with the altemative known as the long shot.

shape features a non-zero minimum payoff. The short shot offers a high probability of a modest payoff, and small probability of a somewhat larger payoff. The peaked distribution is unimodal. The uniform distribution is flat. The bimodal distribution offers the prospect of either a very low payoff or a very high payoff. Finally, the long shot offers the small probability of a very high payoff, and a high probability of a low payoff. The expected payoff of each of the six distributions is the same number, $110. Notably, Lopes did not directly provide her subjects with this information. Lopes recorded the comments of her subjects as they talked themselves through the choice process. She hypothesized that her subjects would base their choices among these six alternatives by focusing attention on both very low payoffs and on very high payoffs. Avoiding low payoffs reflects the need for security. Achieving high payoffs reflects the need for both potential and aspiration. Lopes found that as a group her undergraduate subjects favored the risk floor. In this respect, consider how the risk floor compares to the other alternatives. Relative to the short shot, the risk floor offers a higher floor ($77 is better than $0), and a higher maximum possible payoff ($220 exceeds $143). The risk floor is superior

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to the peaked distribution for low payoffs, and similar at high payoffs. A similar statement holds when comparing the risk floor to the uniform distribution. The risk floor is superior to the bimodal distribution in respect to avoiding low payoffs, but is not superior in respect to the probability of high payoffs. The same statement applies to the long shot. Moreover, the long shot offers the possibility of an exceptionally high payoff, $483, much higher than any of the other alternatives. People for whom hope is the dominant emotion, and those who have very high aspiration points, will be inclined to favor the long shot.

XIII. HOW DO FEAR AND HOPE INFLUENCE JUDGMENTS ABOUT VALUE? The chapter author conducted a study to investigate valuation in the Lopes framework. The study used as subjects undergraduate business students, MBA students, and investment professionals. Subjects were asked to rank order the alternatives by attractiveness, indicate the maximum amount they would be willing to pay (WTP) in order to face each of the six alternatives, indicate the least amount they would be willing to accept (WTA) to sell their fight to face each alternative, and finally to construct a portfolio mix of the six alternatives, if they had $100 to spend and each alternative was equally priced. In this study, the two top-ranked alternatives in terms of attractiveness were the risk floor and the short shot. However, in contrast to Lopes' original finding subjects consistently ranked the short shot as being more attractive than the risk floor. Apparently, the high probability of a modest gain is strong enough to override the clear superiority of the risk floor in respect to very low payoffs. There is evidence of preference reversal in respect to some alternatives, with the effect strongest among undergraduate subjects. Professional investors exhibit the lowest incidence of preference reversal. All groups of subjects provided WTA valuations that were larger than their WTP valuations. This tendency reflects a general phenomenon that has been well studied in the behavioral decision literature. Richard Thaler calls this phenomenon the endowment effect, because once an object enters a person's endowment through ownership the person places a higher value on that object. The ratio WTA/WTP measures the strength of the endowment effect. Notably, the endowment effect increases in strength across the six alternatives. It is lowest for the risk floor and short shot, and highest for the long shot. People are very reluctant to sell their long shots. Portfolio mix is interesting. Although portfolio allocation and attractiveness rank are highly correlated, this correlation does not extend to the long shot. On average, people allocate about 10% of their portfolio to the long shot, with the remainder spread out across the other alternatives, but mainly concentrated in the short shot and risk floor. Lopes emphasized that people like to combine very safe and very risky alternatives.

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RISK/RETURN

MEASURE

THE

TRADE-OFF?

The Sharpe ratio measures risk premium per unit standard deviation. Along with the Sharpe ratio, professional investors use the Sortino ratio to measure the relationship between risk and return. Whereas the denominator of the Sharpe ratio is return standard deviation, the denominator of the Sortino ratio is return semi-standard deviation. Semi-standard deviation is the square root of semi-variance, the probability-weighted integral of squared deviations for realized values below some threshold t. If the threshold t is zero, the semi-standard deviation only reflects volatility associated with losses, but not gains. Hedge funds employ both Sharpe ratios and Sortino ratios, arguing that both ratios are important components of risk. Since 2000, Frank Sortino has been critical of the use of the Sortino ratio he introduced, suggesting that it does not accord sufficient emphasis to upside potential. The experimental evidence pertaining to WTP valuations for the Lopes risk distributions provides some interesting insights into this issue. As was mentioned earlier, all six Lopes distributions feature the same expected payoff, but different payoff standard deviations. The only exception occurs for the risk floor and short shot, in that they do have the same standard deviation. Consider the subjective risk premium computed as the difference between the expected payoff and WTP. This is the premium that would apply if the investor actually paid his WTP. The ratio of this risk premium to a corresponds to a Sharpe ratio. Notably, this ratio is monotonically declining across the six alternatives. That is, when the Lopes alternatives are priced according to WTP the risk premium per unit standard deviation is highest for the risk floor and short shot, and lowest for the long shot. In this respect, the long shot is priced expensively relative to the other alternatives. Its pricing reflects the value attached to the opportunity for upside potential.

XV. H O W E F F E C T I V E MAKING

A R E G R O U P S AT

DECISIONS?

In discussing the effectiveness of group process, it is important to distinguish between two types of decision tasks. The first type of task is known as an intellectual task, so called because it refers to a problem having a correct answer. An example of an intellectual task would be calculating the raw rate of return on an investment. The second type of task is known as a judgmental task. An example of a judgmental task involves deciding whether or not to terminate a project that has been losing money. This task is judgmental because decision makers might have to form judgments about the associated risks, and because their attitudes toward those risks might be subjective.

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The most important feature of group decision making is that groups typically improve on individual decision making when the tasks are intellectual but amplify psychological biases when the tasks are judgmental. The improvement for intellectual tasks occurs when people are able to offer independent ideas and information about a task. British scientist Francis Galton appears to have been the first person to document this phenomenon. In 1906 he watched a group of contestants attempting to guess the weight of an ox at a county fair. Galton was astonished to find that the mean guess of the contestants was very close to the actual weight of the ox. When it comes to judgmental tasks, the impact of group process is typically detrimental rather than beneficial. For example, groups tend to polarize opinions. If, individually, members of a group are mildly inclined to be risk seeking in the domain of losses, group process will tend to induce the group to be strongly inclined toward risk seeking behavior. Polarization tends to occur because people are inclined to seek consensus when participating in groups. They tend to offer evidence and support for proposals that have been advanced during the group process. As a result, a mild tendency to be risk seeking on the part of one individual will tend to be reinforced by others, thereby strengthening the propensity to be risk seeking within the group. Groups also tend to be poor at sharing information. In a 1985 article titled "Pooling of Unshared Information in Group Decision Making: Biased Information Sampling During Discussion," which appeared in The Journal of Personality and Social Psychology, Garold Stasser and William Titus identified a key reason for the occurrence of this phenomenon. Stasser and Titus conducted an experiment involving the selection of a job candidate. Two types of decision groups were asked to make the selection. All individuals in the first group received complete information about every candidate, and that information clearly identified a best candidate, say A. In contrast, no individual in the second group received complete information about every candidate. However, the second group collectively did receive complete information about every candidate, and the issue at hand was whether they would find a way to pool the information at their disposal. In the Stasser-Titus experiment, the members of the second group did not adequately share information, and in consequence did not choose the best candidate. Rather, they focused on the candidate, say B, that their individual information inaccurately suggested was best, and the group dynamic resulted in a search for evidence to support candidate B. In order to identify the candidate who was truly superior, the members of the group would have had to share information that was favorable to candidates other than B, and to share information that was detrimental to candidate B. The drive for group consensus tends to result in a phenomenon Irving Janus called groupthink, in his 1982 book Groupthink. Groups tend to suffer from what psychologists call confirmation bias, the tendency to overweight information that confirms views that are held, and to discount or ignore information that disconfirms views held. Because the drive for consensus leads people to offer information to support the group action, group members suffer from confirmation bias, and come to have unwarranted confidence in the ultimate decision taken by the group.

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XVI. EXAMPLES OF PSYCHOLOGICALLY INDUCED ERRORS There are many examples that illustrate the psychological phenomena discussed previously. Take the case of risk seeking in the domain of losses, In 1995, Daiwa Bank trader Toshihide Iguchi lost Daiwa $1.1 billion. In the same year, Barings Bank trader Nicholas Leeson lost Barings $1.4 billion. In 2002, John Rusnak, a trader at Allied Irish Banks PLC, lost the bank $519.1 million. In all three cases, these traders lost money by taking aggressive bets trying to break even. A dramatic non-financial example of how psychology affects group process effectiveness involves the loss of the space shuttle Columbia on 1 February 2003. The Columbia had burned up upon reentry into the Earth's atmosphere, a result of it being struck by a piece of insulating foam during its launch. The report issued by NASA's Columbia Accident Investigation Board identified a series of problems with the internal decision process used to assess the risk of a disaster. The key decision group during the Columbia mission was the Mission Management Team (MMT). As the Columbia was in orbit, the MMT was briefed by many subgroups, including members of NASA's Debris Assessment Team (DAT). Members of the DAT were very concerned that the foam strike during launch could lead to a disaster upon reentry. They communicated their concerns to the MMT. In particular, they requested photographs of the Columbia in orbit, taken by the Department of Defense, in order to assess the potential damage. The leadership of the MMT took the position that if the Columbia was damaged during the launch, then nothing could be done about it. This led them to dismiss concerns that the potential damage would affect "safety of flight," the NASA term for a fatal risk. As a result, the MMT would not approve the request by the DAT for in-orbit photographic evidence that would enable them to assess potential damage. In dismissing the need for additional information to assess the risk of a disaster upon reentry, the MMT exhibited confirmation bias. More generally, the MMT did not probe DAT members for evidence that would disconfirm their own position that the potential damage caused by the foam would not affect safety of flight. That is the key point. For its part, the DAT did not frame its concerns particularly well. As was discussed in Section VIII, framing effects can be incredibly important, The Columbia Accident Investigation Board faulted the DAT for a poor PowerPoint presentation. The report stated that it was easy to understand how the members of the MMT might read the DAT's densely packed PowerPoint slides and fail to realize that the situation was life threatening. The issues described previously remain valid, even if the Columbia were to have landed safely. These issues pertain to what makes for effective group process. The processes in place at NASA for assessing risk resulted in its managers exhibiting confirmation bias and engaging in poor information sharing.

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XVII. IS DEBIASING POSSIBLE? When psychologists use the termdebias, they mean the reduction or elimination of the psychological biases discussed in earlier sections. A 1977 article titled "Debiasing"-reprinted in the 1982 collection Judgment Under Uncertainty: Heuristics and Biases (edited by Daniel Kahneman, Paul Slovic, and Amos Tversky)mby Baruch Fischhoff concluded that psychological biases are hardwired and are resistant to efforts aimed at mitigation. Think about John Rusnak, the trader at Allied Irish Bank who lost $519 million seeking to break even. Surel3/he was aware of the fate of Nicholas Leeson, whose situation he shared. Leeson made front-page headlines all over the world, and served a prison term for his actions. Yet, Rusnak did not learn the lesson and indeed repeated the mistake himself. As for groups, remember the loss of an earlier space shuttle (Challenger) in 1986. The same criticisms that were leveled at NASA decision processes in 1986 for the loss of the Challenger were leveled in 2003 in respect to the loss of the Columbia. NASA did not debias, or at least it did not debias sufficiently, to overcome deep psychological biases. At the same time, there are real-world examples of group process improvement. Jack Stack is the chief executive officer of the firm Springfield Remanufacturing Corporation (SR~). In his book The Great Game of Business, Stack described the processes in place at his firm. SRC's processes encourage group members to share information effectively in a format called "the huddle," and to challenge one another's positions in an atmosphere of mutual~ respect. These processes serve to mitigate the tendency toward groupthink.

XVIII. CONCLUSIONS Psychological elements play important roles in determining the way people perceive risk, evaluate risk, and choose among risky alternatives. Among the key factors affecting risk perception are affect, familiarity, representativeness, and control. Notably, people are predisposed to being overconfident and excessively optimistic. Among the key factors affecting choice among risky alternatives are the emotions of fear and hope. Notably, people are predisposed to being averse to risk in the domain of gains but risk seeking in the domain of losses. When people work in groups, and the decision tasks are judgmental rather than intellectual, group dynamics tend to exacerbate psychological propensities rather than mitigate them. Although possible, debiasing is extremely challenging and requires a sustained, disciplined approach with direction from the top.

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References and Further Reading Camerer, C., Loewenstein, G, and Prelec, D. (2005). Neuroeconomics: How neuroscience can inform economics. Journal of Economic Literature, 43:5-60. Celati, L. (2004). The Dark Side of Risk Management: How People Frame Decisions in Financial Markets. London: Prentice-Hall/Financial Times. Ganzach, Y. (2000). Judging risk and return of financial assets. Organizational Behavior and Human Decision Processes 83:353-370. Payne, J. (2005). It is whether you win or lose: The importance of the overall probabilities of winning or losing in risky choice. Journal of Risk and Uncertainty, 30(1):5-19. Shefrin, H., and Statman, M. (2000). Behavioral portfolio theory. Journal of Financial and Quantitative Analysis 35(2): 127-151. Shefrin, H., and CaldweU, D. (2001). Determinants of the magnitude of willingness to accept relative to willingness to pay. Journal of Behavioral Decision Making 14(2):87-106. Slovic, P., Finucane, M., Peters, E., and MacGregor, D. (2002). The affect heuristic. In T. Gilovich, D. Griffen, and D. Kahneman (eds.). Heuristics and Biases: The Psychology of Intuitive Judgment. New York: Cambridge University Press. Surowiecki, J. (2004). The Wisdom of Crowds. New York: Doubleday.