1068 N.Barberis and R.Thaler Belief perseverance.There is much evidence that once people have formed an opinion,they cling to it too tightly and for too long [Lord,Ross and Lepper(1979)]. At least two effects appear to be at work.First,people are reluctant to search for evidence that contradicts their beliefs.Second,even if they find such evidence,they treat it with excessive skepticism.Some studies have found an even stronger effect, known as confirmation bias,whereby people misinterpret evidence that goes against their hypothesis as actually being in their favor.In the context of academic finance, belief perseverance predicts that if people start out believing in the Efficient Markets Hypothesis,they may continue to believe in it long after compelling evidence to the contrary has emerged. Anchoring.Kahneman and Tversky (1974)argue that when forming estimates,people often start with some initial,possibly arbitrary value,and then adjust away from it. Experimental evidence shows that the adjustment is often insufficient.Put differently, people“anchor'”too much on the initial value. In one experiment,subjects were asked to estimate the percentage of United Nations' countries that are African.More specifically,before giving a percentage,they were asked whether their guess was higher or lower than a randomly generated number between 0 and 100.Their subsequent estimates were significantly affected by the initial random number.Those who were asked to compare their estimate to 10,subsequently estimated 25%,while those who compared to 60,estimated 45%. Availability biases.When judging the probability of an event-the likelihood of getting mugged in Chicago,say-people often search their memories for relevant information.While this is a perfectly sensible procedure,it can produce biased estimates because not all memories are equally retrievable or "available",in the language of Kahneman and Tversky (1974).More recent events and more salient events-the mugging of a close friend,say-will weigh more heavily and distort the estimate. Economists are sometimes wary of this body of experimental evidence because they believe (i)that people,through repetition,will learn their way out of biases;(ii)that experts in a field,such as traders in an investment bank,will make fewer errors;and (iii)that with more powerful incentives,the effects will disappear. While all these factors can attenuate biases to some extent,there is little evidence that they wipe them out altogether.The effect of learning is often muted by errors of application:when the bias is explained,people often understand it,but then immediately proceed to violate it again in specific applications.Expertise,too,is often a hindrance rather than a help:experts,armed with their sophisticated models,have been found to exhibit more overconfidence than laymen,particularly when they receive only limited feedback about their predictions.Finally,in a review of dozens of studies on the topic,Camerer and Hogarth (1999,p.7)conclude that while incentives can
1068 N. Barberis and R. Thaler Belief perseverance. There is much evidence that once people have formed an opinion, they cling to it too tightly and for too long [Lord, Ross and Lepper (1979)]. At least two effects appear to be at work. First, people are reluctant to search for evidence that contradicts their beliefs. Second, even if they find such evidence, they treat it with excessive skepticism. Some studies have found an even stronger effect, known as confirmation bias, whereby people misinterpret evidence that goes against their hypothesis as actually being in their favor. In the context of academic finance, belief perseverance predicts that if people start out believing in the Efficient Markets Hypothesis, they may continue to believe in it long after compelling evidence to the contrary has emerged. Anchoring. Kahneman and Tversky (1974) argue that when forming estimates, people often start with some initial, possibly arbitrary value, and then adjust away from it. Experimental evidence shows that the adjustment is often insufficient. Put differently, people “anchor” too much on the initial value. In one experiment, subjects were asked to estimate the percentage of United Nations’ countries that are African. More specifically, before giving a percentage, they were asked whether their guess was higher or lower than a randomly generated number between 0 and 100. Their subsequent estimates were significantly affected by the initial random number. Those who were asked to compare their estimate to 10, subsequently estimated 25%, while those who compared to 60, estimated 45%. Availability biases. When judging the probability of an event – the likelihood of getting mugged in Chicago, say – people often search their memories for relevant information. While this is a perfectly sensible procedure, it can produce biased estimates because not all memories are equally retrievable or “available”, in the language of Kahneman and Tversky (1974). More recent events and more salient events – the mugging of a close friend, say – will weigh more heavily and distort the estimate. Economists are sometimes wary of this body of experimental evidence because they believe (i) that people, through repetition, will learn their way out of biases; (ii) that experts in a field, such as traders in an investment bank, will make fewer errors; and (iii) that with more powerful incentives, the effects will disappear. While all these factors can attenuate biases to some extent, there is little evidence that they wipe them out altogether. The effect of learning is often muted by errors of application: when the bias is explained, people often understand it, but then immediately proceed to violate it again in specific applications. Expertise, too, is often a hindrance rather than a help: experts, armed with their sophisticated models, have been found to exhibit more overconfidence than laymen, particularly when they receive only limited feedback about their predictions. Finally, in a review of dozens of studies on the topic, Camerer and Hogarth (1999, p. 7) conclude that while incentives can
Ch.18:A Survey of Behavioral Finance 1069 sometimes reduce the biases people display,"no replicated study has made rationality violations disappear purely by raising incentives". 3.2.Preferences 3.2.1.Prospect theory An essential ingredient of any model trying to understand asset prices or trading behavior is an assumption about investor preferences,or about how investors evaluate risky gambles.The vast majority of models assume that investors evaluate gambles according to the expected utility framework,EU henceforth.The theoretical motivation for this goes back to Von Neumann and Morgenstern (1944),VNM henceforth, who show that if preferences satisfy a number of plausible axioms-completeness, transitivity,continuity,and independence -then they can be represented by the expectation of a utility function. Unfortunately,experimental work in the decades after VNM has shown that people systematically violate EU theory when choosing among risky gambles.In response to this,there has been an explosion of work on so-called non-EU theories,all of them trying to do a better job of matching the experimental evidence.Some of the better known models include weighted-utility theory [Chew and MacCrimmon(1979), Chew (1983)],implicit EU [Chew (1989),Dekel (1986)],disappointment aversion [Gul (1991)],regret theory [Bell (1982),Loomes and Sugden (1982)],rank-dependent utility theories [Quiggin(1982),Segal(1987,1989),Yaari (1987)],and prospect theory [Kahneman and Tversky (1979),Tversky and Kahneman (1992)]. Should financial economists be interested in any of these alternatives to expected utility?It may be that EU theory is a good approximation to how people evaluate a risky gamble like the stock market,even if it does not explain attitudes to the kinds of gambles studied in experimental settings.On the other hand,the difficulty the EU approach has encountered in trying to explain basic facts about the stock market suggests that it may be worth taking a closer look at the experimental evidence.Indeed, recent work in behavioral finance has argued that some of the lessons we learn from violations of EU are central to understanding a number of financial phenomena. Of all the non-EU theories,prospect theory may be the most promising for financial applications,and we discuss it in detail.The reason we focus on this theory is,quite simply,that it is the most successful at capturing the experimental results.In a way, this is not surprising.Most of the other non-EU models are what might be called quasi- normative,in that they try to capture some of the anomalous experimental evidence by slightly weakening the VNM axioms.The difficulty with such models is that in trying to achieve two goals-normative and descriptive-they end up doing an unsatisfactory job at both.In contrast,prospect theory has no aspirations as a normative theory: it simply tries to capture people's attitudes to risky gambles as parsimoniously as possible.Indeed,Tversky and Kahneman (1986)argue convincingly that normative approaches are doomed to failure,because people routinely make choices that are
Ch. 18: A Survey of Behavioral Finance 1069 sometimes reduce the biases people display, “no replicated study has made rationality violations disappear purely by raising incentives”. 3.2. Preferences 3.2.1. Prospect theory An essential ingredient of any model trying to understand asset prices or trading behavior is an assumption about investor preferences, or about how investors evaluate risky gambles. The vast majority of models assume that investors evaluate gambles according to the expected utility framework, EU henceforth. The theoretical motivation for this goes back to Von Neumann and Morgenstern (1944), VNM henceforth, who show that if preferences satisfy a number of plausible axioms – completeness, transitivity, continuity, and independence – then they can be represented by the expectation of a utility function. Unfortunately, experimental work in the decades after VNM has shown that people systematically violate EU theory when choosing among risky gambles. In response to this, there has been an explosion of work on so-called non-EU theories, all of them trying to do a better job of matching the experimental evidence. Some of the better known models include weighted-utility theory [Chew and MacCrimmon (1979), Chew (1983)], implicit EU [Chew (1989), Dekel (1986)], disappointment aversion [Gul (1991)], regret theory [Bell (1982), Loomes and Sugden (1982)], rank-dependent utility theories [Quiggin (1982), Segal (1987, 1989), Yaari (1987)], and prospect theory [Kahneman and Tversky (1979), Tversky and Kahneman (1992)]. Should financial economists be interested in any of these alternatives to expected utility? It may be that EU theory is a good approximation to how people evaluate a risky gamble like the stock market, even if it does not explain attitudes to the kinds of gambles studied in experimental settings. On the other hand, the difficulty the EU approach has encountered in trying to explain basic facts about the stock market suggests that it may be worth taking a closer look at the experimental evidence. Indeed, recent work in behavioral finance has argued that some of the lessons we learn from violations of EU are central to understanding a number of financial phenomena. Of all the non-EU theories, prospect theory may be the most promising for financial applications, and we discuss it in detail. The reason we focus on this theory is, quite simply, that it is the most successful at capturing the experimental results. In a way, this is not surprising. Most of the other non-EU models are what might be called quasinormative, in that they try to capture some of the anomalous experimental evidence by slightly weakening the VNM axioms. The difficulty with such models is that in trying to achieve two goals – normative and descriptive – they end up doing an unsatisfactory job at both. In contrast, prospect theory has no aspirations as a normative theory: it simply tries to capture people’s attitudes to risky gambles as parsimoniously as possible. Indeed, Tversky and Kahneman (1986) argue convincingly that normative approaches are doomed to failure, because people routinely make choices that are
1070 N.Barberis and R.Thaler simply impossible to justify on normative grounds,in that they violate dominance or invariance. Kahneman and Tversky (1979),KT henceforth,lay out the original version of prospect theory,designed for gambles with at most two non-zero outcomes.They propose that when offered a gamble (x,p;y,q), to be read as"get outcome x with probability p,outcome y with probability g",where x≤0≤yory≤0≤x,people assign it a value of π(p)v(x)+π(q)u(y), (1) where o and t are shown in Figure 2.When choosing between different gambles,they pick the one with the highest value. VALUE LOSSES GAINS 0 10 STATED PROBABILITY:P Fig.2.Kahneman and Tversky's(1979)proposed value function o and probability weighting function This formulation has a number of important features.First,utility is defined over gains and losses rather than over final wealth positions,an idea first proposed by Markowitz (1952).This fits naturally with the way gambles are often presented and discussed in everyday life.More generally,it is consistent with the way people perceive attributes such as brightness,loudness,or temperature relative to earlier levels,rather than in absolute terms.Kahneman and Tversky (1979)also offer the following violation of EU as evidence that people focus on gains and losses.Subjects are asked 12. 12 All the experiments in Kahneman and Tversky (1979)are conducted in terms of Israeli currency.The authors note that at the time of their research,the median monthly family income was about 3000 Israeli lira
1070 N. Barberis and R. Thaler simply impossible to justify on normative grounds, in that they violate dominance or invariance. Kahneman and Tversky (1979), KT henceforth, lay out the original version of prospect theory, designed for gambles with at most two non-zero outcomes. They propose that when offered a gamble (x, p; y, q) , to be read as “get outcome x with probability p, outcome y with probability q”, where x 0 y or y 0 x, people assign it a value of p( p) v(x) + p( q) v( y), (1) where v and p are shown in Figure 2. When choosing between different gambles, they pick the one with the highest value. Fig. 2. Kahneman and Tversky’s (1979) proposed value function v and probability weighting function p. This formulation has a number of important features. First, utility is defined over gains and losses rather than over final wealth positions, an idea first proposed by Markowitz (1952). This fits naturally with the way gambles are often presented and discussed in everyday life. More generally, it is consistent with the way people perceive attributes such as brightness, loudness, or temperature relative to earlier levels, rather than in absolute terms. Kahneman and Tversky (1979) also offer the following violation of EU as evidence that people focus on gains and losses. Subjects are asked 12: 12 All the experiments in Kahneman and Tversky (1979) are conducted in terms of Israeli currency. The authors note that at the time of their research, the median monthly family income was about 3000 Israeli lira
Ch.18:A Survey of Behavioral Finance 1071 In addition to whatever you own,you have been given 1000.Now choose between A=(1000,0.5) B=(500,1) B was the more popular choice.The same subjects were then asked: In addition to whatever you own,you have been given 2000.Now choose between C=(-1000,0.5) D=(-500,1). This time,C was more popular. Note that the two problems are identical in terms of their final wealth positions and yet people choose differently.The subjects are apparently focusing only on gains and losses.Indeed,when they are not given any information about prior winnings,they choose B over A and C over D. The second important feature is the shape of the value function o,namely its concavity in the domain of gains and convexity in the domain of losses.Put simply, people are risk averse over gains,and risk-seeking over losses.Simple evidence for this comes from the fact just mentioned,namely that in the absence of any information about prior winnings3 B A,C D. The o function also has a kink at the origin,indicating a greater sensitivity to losses than to gains,a feature known as loss aversion.Loss aversion is introduced to capture aversion to bets of the form: E=(110,;-100,) It may seem surprising that we need to depart from the expected utility framework in order to understand attitudes to gambles as simple as E,but it is nonetheless true.In a remarkable paper,Rabin(2000)shows that if an expected utility maximizer rejects gamble E at all wealth levels,then he will also reject (20000000,;-1000,), an utterly implausible prediction.The intuition is simple:if a smooth,increasing,and concave utility function defined over final wealth has sufficient local curvature to reject 13 In this section GG2 should be read as"a statistically significant fraction of Kahneman and Tversky's subjects preferred G to G2
Ch. 18: A Survey of Behavioral Finance 1071 In addition to whatever you own, you have been given 1000. Now choose between A = (1000, 0.5) B = (500, 1). B was the more popular choice. The same subjects were then asked: In addition to whatever you own, you have been given 2000. Now choose between C = (−1000, 0.5) D = (−500, 1). This time, C was more popular. Note that the two problems are identical in terms of their final wealth positions and yet people choose differently. The subjects are apparently focusing only on gains and losses. Indeed, when they are not given any information about prior winnings, they choose B over A and C over D. The second important feature is the shape of the value function v, namely its concavity in the domain of gains and convexity in the domain of losses. Put simply, people are risk averse over gains, and risk-seeking over losses. Simple evidence for this comes from the fact just mentioned, namely that in the absence of any information about prior winnings 13 B A, C D. The v function also has a kink at the origin, indicating a greater sensitivity to losses than to gains, a feature known as loss aversion. Loss aversion is introduced to capture aversion to bets of the form: E = 110, 1 2 ; −100, 1 2 . It may seem surprising that we need to depart from the expected utility framework in order to understand attitudes to gambles as simple as E, but it is nonetheless true. In a remarkable paper, Rabin (2000) shows that if an expected utility maximizer rejects gamble E at all wealth levels, then he will also reject 20000000, 1 2 ; −1000, 1 2 , an utterly implausible prediction. The intuition is simple: if a smooth, increasing, and concave utility function defined over final wealth has sufficient local curvature to reject 13 In this section G1 G2 should be read as “a statistically significant fraction of Kahneman and Tversky’s subjects preferred G1 to G2.”
1072 N.Barberis and R.Thaler E over a wide range of wealth levels,it must be an extraordinarily concave function, making the investor extremely risk averse over large stakes gambles. The final piece of prospect theory is the nonlinear probability transformation.Small probabilities are overweighted,so that (p)>p.This is deduced from KT's finding that (5000,0.001)>(5,1), and (-5,1)>(-5000,0.001), together with the earlier assumption that o is concave (convex)in the domain of gains (losses).Moreover,people are more sensitive to differences in probabilities at higher probability levels.For example,the following pair of choices, (3000,1)>(4000,0.8;0,0.2), and (4000,0.2;0,0.8)>(3000,0.25), which violate EU theory,imply π(0.25) π(1) π(0.2) π(0.8) The intuition is that the 20%jump in probability from 0.8 to 1 is more striking to people than the 20%jump from 0.2 to 0.25.In particular,people place much more weight on outcomes that are certain relative to outcomes that are merely probable,a feature sometimes known as the "certainty effect". Along with capturing experimental evidence,prospect theory also simultaneously explains preferences for insurance and for buying lottery tickets.Although the concavity of o in the region of gains generally produces risk aversion,for lotteries which offer a small chance of a large gain,the overweighting of small probabilities in Figure 2 dominates,leading to risk-seeking.Along the same lines,while the convexity of o in the region of losses typically leads to risk-seeking,the same overweighting of small probabilities induces risk aversion over gambles which have a small chance of a large loss. Based on additional evidence,Tversky and Kahneman(1992)propose a gener- alization of prospect theory which can be applied to gambles with more than two
1072 N. Barberis and R. Thaler E over a wide range of wealth levels, it must be an extraordinarily concave function, making the investor extremely risk averse over large stakes gambles. The final piece of prospect theory is the nonlinear probability transformation. Small probabilities are overweighted, so that p( p) > p. This is deduced from KT’s finding that (5000, 0.001) (5, 1), and (−5, 1) (−5000, 0.001), together with the earlier assumption that v is concave (convex) in the domain of gains (losses). Moreover, people are more sensitive to differences in probabilities at higher probability levels. For example, the following pair of choices, (3000, 1) (4000, 0.8; 0, 0.2), and (4000, 0.2; 0, 0.8) (3000, 0.25), which violate EU theory, imply p(0.25) p(0.2) < p(1) p(0.8). The intuition is that the 20% jump in probability from 0.8 to 1 is more striking to people than the 20% jump from 0.2 to 0.25. In particular, people place much more weight on outcomes that are certain relative to outcomes that are merely probable, a feature sometimes known as the “certainty effect”. Along with capturing experimental evidence, prospect theory also simultaneously explains preferences for insurance and for buying lottery tickets. Although the concavity of v in the region of gains generally produces risk aversion, for lotteries which offer a small chance of a large gain, the overweighting of small probabilities in Figure 2 dominates, leading to risk-seeking. Along the same lines, while the convexity of v in the region of losses typically leads to risk-seeking, the same overweighting of small probabilities induces risk aversion over gambles which have a small chance of a large loss. Based on additional evidence, Tversky and Kahneman (1992) propose a generalization of prospect theory which can be applied to gambles with more than two