the PRI political legacy that hadruled Mexico for more than 80 years. Vicente Fox, candidate of thePAN party, was polling ahead of the candidate of the incumbent PRI po-litical party, Francisco Ochoa. The PRI had retained power through a cor-rupt system of vote buying, ballot-box stufﬁng, nationalist rhetoric, andintimidation. The PRI party bosses were angered by the possibility of theircandidate’s defeat. Two weeks before the presidential election, Ochoa ex-pressed his hope that there would be no “riots” or “blood on the street” ifthe PRI lost the election.
Ochoa’s words were interpreted as a veiled threat, though he deniedany ill intent. The Mexican stock market (Bolsa) and the Mexican pesodropped 20 percent over the next week. Political violence, which hadseemed unlikely, suddenly was in the realm of possibility, even probability.Two weeks after Ochoa’s comment, the Sunday of the elections passeduneventfully, with Fox declared the victor by a 6 percent margin in the pop-ular vote. Immediately after the ofﬁcial results were announced, Fox helda press conference. In his victory speech, he expressed faith in Mexico’smarket economy and vowed to continue economic and political reforms.
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No violence came to pass. Within two days the Bolsa and the peso surgedthrough their levels of two weeks prior.
Investors in Mexico were frightened by the possibility of political vio-lence. As we’ll see in the following pages, investors’ risk probability assess-ments are distorted by their feelings—in this case, fear. Risk perceptionsare often excessively low (especially after recent gains) or too high (suchas following losses), creating opportunities for astute investors.
Risk perceptions are formed from three characteristics of a decisionsituation: (1) the perceived timeline of the outcome (prolonged outcomesappear less risky), (2) the associations the scenario induces (e.g., fearsof bankruptcy), and (3) one’s evolutionary preparedness for certain emo-tional reactions (e.g., is one constitutionally nervous or optimistic?).2 Eachof these factors can lead to distortions in probability assessment.
In this section, we look at how investors ought to assess probabilitiesof potential outcomes and how they actually do it. In particular, we’ll ex-amine how investors misjudge expected values and overreact to ambiguity.
EXPECTED VALUE AND EXPECTED UTILITY
“Every day, investors must translate investmentopportunities into probabilities—indeed, this is anessential skill. So we need to think carefully abouthow we come up with probabilities for various sit-uations and where the potential pitfalls lie.”
—Michael Mauboussin3
According to traditional economic theory, it makes no sense for some-one to buy a lottery ticket. It’s not rational. The “expected value” of a lot-tery ticket is about $0.40 for every dollar spent, meaning that the averagelottery ticket buyer is losing $0.60 on their $1.00 investment.
Yet people do play the lottery, and they go to casinos, and they day-trade stocks and currencies—even when they consistently lose. As seen inthis book, over the past 30 years behavioral economists have begun inves-tigating why people decide to pursue negative–expected-value gambles.
Most decisions in which potential outcome sizes and probabilities areknown are made according to the guidance of expected-value calculations.These calculations are functions of the brain’s analytical (not the intuitive)decision-making system. Analytical decisions consider mathematical out-come characteristics like the exact sizes, probabilities, and time delays forpotential gains and losses.
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In an expected-value calculation, each decision option is examinedseparately to determine which has the highest average return. For everychoice, the probability of each possible outcome is multiplied by its likelymagnitude. Then the various products are summed into an overall expectedreturn. Given that most investment decisions produce uncertain outcomesof unknown size, such formulas must be used cautiously.
Many people gamble and trade stocks because they like the markets,they enjoy discussing strategy with their colleagues, and they enjoy theemotional thrill. Liking something, regardless of mathematical outcomes,is called utility. Decisions made using “expected utility” rely on considera-tions of what people value qualitatively. Because the market future is fun-damentally uncertain, most investors make decisions based on expectedutility rather than expected value calculations.
Utility is a largely subjective phenomenon. Decision theorists say thata sense of utility comes from: (1) current feelings (moment utility), (2) thefeelings one expects to have after receiving an outcome (outcome utility),(3) the process of making the decision itself (decision utility), and (4) one’srecall of past similar experiences (experienced utility). The theme that runsthrough these various types of utility is feelings—utility is boiled down tohow one feels about a decision and the expected outcomes. In the end,investors often pursue the decision that they expect to make them feel thebest.
In a challenging decision environment such as the stock market, mostpeople make systematic errors in their outcome probability and size esti-mations. These errors are often due to the biasing inﬂuences of feelings onthe analysis of uncertain or ambiguous information. Perhaps surprisingly,even in perfect circumstances where all outcome information is known,investors still demonstrate biased decision making. This chapter will ﬁrstaddress the biases of ﬁnite expected value calculations (such as are pos-sible at casinos), with biases related to ambiguous outcome informationfollowing.
THE JACKPOT TRAP
In casinos the game with the lowest expected value is keno. In keno, play-ers select six numbers between 0 and 50. If any of their selected numbersis a match with six randomly generated numbers, then they win a jackpot.Casinos take approximately $0.29 for every $1.00 invested in keno, givingplayers the lowest expected return per dollar of any casino game. It’s thekeno jackpot, displayed in large numbers over the keno seats, that is soappealing to gamblers.
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Brain imaging studies show a disproportionate effect of outcome sizeversus probability on decision making. As the size of a potential monetarygain increases, so too does reward system activation (speciﬁcally the nu-cleus accumbens).4,5 Potential reward size is more emotionally arousingthan proportional changes in probability.6,7
When I worked in Professor Knutson’s lab at Stanford in 2003, wedesigned an experiment to measure the neural effects of changes in a re-ward’s expected value. Equivalent expected rewards caused radically dif-ferent brain responses depending on how the potential reward character-istics (size and probability) were displayed.
We designed an experiment to sort out the different effects of rewardsize (magnitude) and probability on the brain. In our preliminary results,the reward system’s response when anticipating a $5 gain was much moreintense than when anticipating a $1 gain. However, when we controlled for(eliminated) the effects of reward size from the brain’s activation map, theresults were much different.
FIGURE 13.1 The brain’s activation when playing for a $5 gain, contrastedagainst the anticipation of a $1 gain.
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FIGURE 13.2 The brain’s activation pattern when playing for an 80 percentchance of winning $5 ($4 equivalent) versus a 20 percent chance of gaining $5 ($1equivalent). These images were recorded at the same signiﬁcance threshold, andthey show the brain’s preferential activation to size.
If we looked at people’s brains while they were anticipating rewards ofdifferent expected values, with the magnitude of reward held constant at$5 but the probability of receiving it varied, the brain did not activate muchdifferently. For example, an 80 percent chance of winning $5 (expectedvalue $4) was only slightly more activating than a 20 percent chance ofwinning $5 (expected value $1). The largest absolute reward ($5) was ex-traordinarily more exciting than the absolute $1 reward. That is, subjectswere watching primarily the size of the potential reward, not the probabil-ity, even when they had equivalent expected values.
In Figures 13.1 and 13.2, equal statistical thresholds were used to gen-erate the images. That is, these activations were recorded as if with a cam-era whose shutter speed and aperture were held constant. In the top image,one can see the profound, and widely distributed, effect of gain size ($5 ver-sus $1) on brain activation. In the lower image, the highest probability ofgain (80 percent) is compared against the lowest probability (20 percent)with the reward size of $5 held constant. The greater absolute magnitudeis much more activating.
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Please understand the above results as illustrative but not watertight.This study was never published due to problems with the “high” and “low”probabilities—some subjects’ “low” probabilities were actually 50 percentdue to their better skill than others. After a redesign that ensured con-stant reward probabilities regardless of skill, a similar subsequent studywas published in the Journal of Neuroscience. However, Figures 13.1 and13.2 are derived from the ﬁrst study, and the probability confound may ac-count for some (but not all) of the dramatic activation difference betweenthe two brain images.
Does this increased activation to size lead to psychological effects? Infact, in previous studies subjects report more “happiness” (positive activa-tion) when awaiting larger rewards.8
In some laboratory experiments, participants trade money in simu-lated stock markets. Many times, bubbles and crashes appear in the pricesof the stocks traded during these experiments. Researchers investigatedthis phenomenon by testing for the presence of probability judgment er-rors in traders during the life cycle of an experimental market. They foundthat bubbles are correlated with traders’ preference for high-value, low-probability gains in their investments. This ﬁnding makes intuitive sense.Bubble investors are making probability errors by seeking high rewards atlow probabilities (overweighting low probabilities). They are overweight-ing the possibility of large gains.9
Professor Paul Slovic has found that emotion plays a leading role indistorting probability judgments. According to the “affect heuristic,” whenthe outcome of a gamble has a strong emotional meaning, people mentallyoverweight the size of the potential reward (or loss) versus its actual prob-ability in their decision making.10 Slovic’s ﬁnding may explain why, in myexperiment with Knutson, I saw so much reward system activation for col-lege students (presumably poor) playing a game for a series of potential $5payouts (outcomes that are very exciting for them).
PROBABILITY MISJUDGMENTS
“It is principally at games of chance that a mul-titude of illusions support hope and sustain itagainst unfavourable chances.”
—Simon Laplace, 1796
Misjudgments of probabilities are systematic and universal. Recent ex-perimental evidence shows precisely how people misestimate probabilitieswhen facing simple gambles.
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FIGURE 13.3 The probability weighting curves for most assessed risks. The dif-ferent curves represent probability functions for gambles framed as gains, losses,and other permutations. The straight line represents the actual probability.Source: Prelec, D. 1998. “The Probability Weighting Function.” Econometrica 60:497–528.
When an outcome is possible but not probable, people tend to overes-
timate its chance of occurring. This is called the possibility effect.
When an outcome is likely, people tend to underestimate its odds. This
bias has been named the certainty effect.11
Events of probability less than 40 percent are susceptible to the possi-bility effect. Outcomes with greater than 40 percent probability are in therealm of the certainty effect12 (see Figure 13.3).
For example, long shots in pari-mutuel wagering (horse and dog rac-ing) tend to be preferred bets of amateurs. Due to amateurs excessivelybetting on long shots, their expected payoffs are lower than their actualodds of winning suggest they should be (based on how tracks ﬁgure odds).The more people who bet on the long shots, the weaker their odds and thusthe lower the payout if they win.
Because bettors mentally underweight the probability of high likeli-hood winners actually winning, they avoid these bets. As a result, high-likelihood winners are often a good bet, having a better chance of winningthan predicted by most bettors.13
For the most part, there is a dissociation between intellectual judg-ments of risk and emotional feelings about risk. Emotions in uncertain or
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risky situations are more sensitive to the possibility rather than the prob-ability of strong consequences, contributing to the overweighting of verysmall probabilities.14 In general, na¨ıve investors think that very low prob-ability but emotionally loaded events (such as potential market crashes)are much more likely than they actually are.15 High-likelihood, emotionallyweighted outcomes, such as bull markets, are assumed to be less likelythan they actually are The probability weighting curve shows exaggeratedmisestimations of probability when the potential outcomes are emotionallyweighted (see Figure 13.4).
Probability assessments are biased not only by the emotions associ-ated with the event outcome, but also by one’s internal emotional state.People who are generally happy are more optimistic, judging higher prob-abilities for positive events and lower probabilities for negative events.16The inverse pattern was found for subjects in a negative emotional state.17The misjudgment of probabilities described above occurs for choicesthat are not repeated over time (except in the case of pari-mutuel wa-gering). The tendency to overweight small probabilities is true for singlechoices. This pattern does not hold true, however, for choices based on ex-perience. Investors with experience can often identify when amateurs as agroup are over or under-weighting probabilities.
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FIGURE 13.4 The probability weighting curve when emotion (aﬀect) is arousedby the potential outcomes. People further overestimate low probabilities and under-estimate high probabilities when an emotional outcome is involved.Source: Hsee, C. K., and Y. Rottenstreich. 2001. “Money, Kisses, and Electric Shocks:On the Aﬀective Psychology of Risk.” Psychological Science 12: 185–190.
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VIVIDNESS, IMAGINATION, AND DESIRE
“Our probability assessments shift based on howothers present information to us.”
—Michael Mauboussin18
Emotionally, investors have stronger reactions if possible outcomesare more vivid or imaginable. Before the Mexican elections, anticipation ofrioting in Mexico City brought to mind images of violence, chaos, destruc-tion, and bloodshed. Likewise, a vividly imagined possibility of bankruptcy,personal poverty, job loss, or market panic will generate the desire to sellany assets that carry such risks. The possibility of wealth and material suc-cess in an impulsive and inexperienced investor will lead to a strong driveto buy securities that appear promising.
Feelings of fear or worry in the face of decisions under risk or un-certainty have an all-or-none characteristic: they are more sensitive to thepossibility rather than the probability of negative consequences. For ex-ample, the thought of receiving a painful electric shock is enough to sparkintense fear in experimental subjects. Changes in the precise likelihood ofbeing shocked have little impact on the degree of fearfulness. The increas-ing vividness of a potential reward or catastrophe exaggerates the possibil-ity effect.19
People who have more control over their imaginative faculties aremore physiologically responsive to images. For example, researchersfound that these people salivate more when thinking of their favorite food,become more sexually aroused in fantasy exercises, and have a greaterability to increase their heart rate using visual imagery. In all likelihood,the possibility and certainty effects are exaggerated in these individuals.It’s tempting to speculate that imaginative people are thus more motivatedby fantasies of imminent ﬁnancial wealth or ruin.
AMBIGUITY AND UNCERTAINTY
“The fundamental law of investing is the uncer-tainty of the future.”
—Peter L. Bernstein
Most people are averse to uncertainty and ambiguity. A classic exper-iment into ambiguity aversion studied subjects’ choices between two urnsof red and black balls. Participants were asked if they would rather bet onthe drawing of a black ball from the urn in which the proportion of red
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and black balls was unspeciﬁed, or one in which the ratio was 50:50. Mostsubjects avoided ambiguity, preferring to bet on the urn with the knownratio of red to black balls.20
People shy away from decisions about which they have insufﬁcient in-formation, especially when an alternative decision with more informationis available or the decision maker has less information about a choice thanothers. People prefer to make decisions where they know the odds and thepossible outcomes, and they avoid investing where the odds are unknown.With experience, they learn to infer the approximate odds in a situation.
AMBIGUITY IN THE MARKETS
“The future is never clear, and you pay a very highprice in the stock market for a cheery consensus.Uncertainty is the friend of the buyer of long-termvalues.”
—Warren Buffett
Ambiguity aversion is reﬂected in the returns of stocks of companieswith ambiguous information on their balance sheets (e.g., research and de-velopment spending) that cannot traditionally be correlated with futurevaluations. Stocks with poorer earnings quality (having more ambiguousinformation) have greater long-term returns than those with better (moretransparent) accounting.21 As a result of aversion to ambiguous items onaccounting statements, investors mistakenly avoid such stocks and missout on greater long-term returns.
The effect of accounting ambiguity may be to bias how investors feelabout the stock in question. Investors with limited information about astock are more likely to rely on their feelings when judging whether tobuy or sell shares. In the case of poor earnings quality, those feelings arelikely to be excessively negative. However, there are some interesting ex-ceptions.
Typically, investors prefer to avoid stocks with ambiguous accounting,but when optimism is high, investors may project an unfounded positivespin onto the uncertain data. In the late 1990s, initial public offerings (IPOs)of Internet companies with negative cash ﬂows had relatively higher initialtrading prices. According to researchers, “The role of earnings in valuationof these ﬁrms . . . completely disappeared in 1999.”22 Presumably, investorsconsidered negative cash ﬂows to be an investment in the future. The lackof concrete earnings information led to an exaggerated projection of in-vestors’ optimism. In such cases of “irrational exuberance,” investors are
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ambiguity loving. In summary, investors are usually ambiguity averse, es-pecially when they are pessimistic, but during periods of optimism, theybecome ambiguity loving.
Investors’ sentiment inﬂuences both their purchasing behavior andstock price performance. To investigate how market sentiment affectsthe returns of stocks with ambiguous or subjective information on theirbalance sheets, researchers compared a composite measure of investorsentiment with their subsequent performance. Highly subjective stockswere considered to be small stocks, young stocks, high volatility stocks,unproﬁtable stocks, non-dividend-paying stocks, extreme growth stocks,and distressed stocks. The researchers discovered that when investors areoptimistic, stocks with ambiguous, uncertain and generally subjective in-formation underperform over the subsequent period (one year). When in-vestors are pessimistic, the opposite occurs. A contrarian approach to sen-timent improves returns in more ambiguous and uncertain stocks.23
Emotion also plays a role in how investors feel about the “idea” or storybehind a stock. Researchers found that emotion and imagery, aroused bythe concept of a stock, bias predictions of stock performance. Accordingto researchers, emotion and imagery may be the only judgmental baseson which individuals are able to rely when information about a ﬁnancialoffering is vague.24 Stocks with exciting stories cause people to forecasthigher stock returns.
Interestingly, during times of greater uncertainty in the markets, whenprices are volatile and trading volume high, investors tilt their portfoliostoward familiar local stocks.25 Investors prefer the familiar and the knownwhen market price action indicates potential danger. Perhaps this prefer-ence is driven by a need for certainty and comfort, which are more likelyto be found closer to home.
Additionally, investors’ behavioral biases are increased by uncertainty.When stocks are more difﬁcult to value using objective accounting data, in-vestors exhibit a stronger disposition effect. Overconﬁdence is increasedby market-wide uncertainty.26 Even among executives, ambiguity in cor-porate accounting heralds the presence of behavioral biases such as lossaversion and overconﬁdence among management.
An interesting reversal of ambiguity aversion occurs when people feelthe need to make more money than that offered in a certain outcome. Inone gambling experiment, when participants’ ﬁnancial need was greaterthan the known option’s expected average payout, subjects preferred theambiguous (high volatility) option.27 People are more willing to take achance when other options won’t give them the payoff they want. Dur-ing the Internet bubble, as investors and portfolio managers scrambled tocatch up with their perceptions of others’ wealth, they may have felt a moreacute need to take a chance for proﬁt.
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This need-based pursuit of ambiguity supports loss aversion and thedisposition effect. When investors are painfully losing in an investment,they would rather take an unknown chance for a comeback in the stockthan sell it for a guaranteed loss.
In other scenarios, psychologists have found that people tend to be-lieve they can have what they want, regardless of evidence to the contrary.The intensity of one’s desire for an outcome increases one’s estimation ofthe likelihood he or she will actually get it.28 Their wanting creates over-conﬁdence in their skills, which translates into an expectation of success.In another study, participants told to expect an outcome that conﬂictedwith their desires gave no weight to the evidence. They remembered infor-mation that supported their ability to get what they wanted, rather than theexplicit information telling them to expect otherwise.29 If investors wantto believe that a money-losing Internet stock is more valuable than onewith earnings, then they will value it higher, regardless of the evidence.These studies demonstrate the “conﬁrmation bias,” in which informationsupporting one’s desires is accepted, but evidence contradicting them isignored.
NEUROSCIENCE OF AMBIGUITY, RISK,AND REWARD
“Markets are constantly in a state of uncertaintyand ﬂux and money is made by discounting the ob-vious and betting on the unexpected.”
—George Soros
Caltech researchers designed a monetary experiment to identify thedifferent brain regions directing risky decision making (where probabili-ties are known) and uncertain decision making (where information aboutprobabilities and outcomes is absent). As seen above, in prior experimentson risky decision making, participants were more likely to take risk whenthe probabilities were known versus when the odds were ambiguous.30
The researchers, including economist Colin Camerer, found that higherlevels of ambiguity led to increasing activation in the amygdala (fear andmemory) and orbitofrontal cortex (emotion and reason integration) anddecreasing activation in the nucleus accumbens (reward). That is, partic-ipants appeared to ﬁnd ambiguity fearsome, and tried to integrate theirconsideration of unknown risks with their prior experiences in such sit-uations. Ambiguity caused decreased activity in the nucleus accumbens,
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thus implying that ambiguity arouses disappointment. However, higher-expected-value decisions (without ambiguity), led to increasing activationin the nucleus accumbens.
When patients with lesions in the orbitofrontal cortex (the excessiverisk takers famously identiﬁed by Damasio) were tested in the Caltechtask, they were found to be insensitive to the level of risk and ambiguityin choices. That is, they made the same decisions regardless of whetherthe outcome probabilities were known or not. Thus, it appears that theorbitofrontal cortex governs the integration of emotion and reason—weighing information about actual probabilities and payoffs against one’sfeelings about risk. Impairment of the orbitofrontal cortex leads to difﬁ-culty integrating ambiguity aversion (fear) into decision making.31
THE POSSIBILITY THAT YOUARE OVERWEIGHT
Investors are uniquely susceptible to distortions in probability assessment,especially when events are novel or rare. The market future is uncertain,and information is too often ambiguous. Emotions play a large role in bi-asing low probability assessments. The following is a list of conditions inwhich investors are vulnerable to overweighting low probabilities and be-coming biased by the possibility effect:
Ĺ Vivid or easily imagined results.Ĺ Minimal awareness about the event’s likely outcomes.Ĺ Minimal investor conditioning or experience with such events.Ĺ Event is represented as a relatively novel/unique phenomenon.Ĺ Desiring, wanting, or needing the outcome to occur.Ĺ Feeling a personal or emotional stake in the outcome.Ĺ Feeling excited or fearful about the event happening.Ĺ Ambiguous information about the event.
While investors can try to be aware of the above conditions during their de-cision making, it is extremely difﬁcult to do so. The list is long and complex,and some of the effects are subconscious and quite subtle. Nonetheless, Ihope that this list will provoke some thought about how your own oddsassessments might be impacted. The next sections address the problemof trust. What role does trust play in investors’ interpretations of marketinformation or interactions with clients?
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THE TRUSTING BRAIN
When people hear ambiguous or uncertain information and must make arapid decision, how do they assess if it is truthful? If they trust the source,then they are likely to take the information at face value.
A Securities and Exchange Commission (SEC) ﬁling from a respectedcorporation is one of the most trustworthy types of corporate information,in part because a fraudulent SEC ﬁling leads to prison time for executives.Both a history of honesty from the source and harsh consequences for mis-information are crucial support for the veracity of provided information.
Among the least believable sources of stock information are anony-mous faxes, e-mails, cold calls, and Internet message boards. A promo-tional fax about a small gold-mining stock in Alberta is untrustworthy forobvious reasons. There are no consequences for misinformation, and onehas no history of experience with the promoter.
Investment information is always somewhat suspect. Yet most in-vestors believe dubious information if it appears under the banner of atrusted news source. Researchers in Muenster, Germany, found that sub-jects were more likely to believe an ambiguous headline if it was in thebanner of a trusted brand-name magazine. Their trust activated the medialprefrontal cortex (MPFC).32 The MPFC is activated by emotionally satisfy-ing events and learning about rewards. It appears that trust feels good, andpeople trust a news source when it agrees with their underlying politicalbeliefs and biases.
NEUROSCIENCE OF THE ULTIMATUM GAME
One of the simplest ways to elicit trusting (or distrustful) behavior in eco-nomic experiments is to use a paradigm called the ultimatum game. In eachround of the ultimatum game, participants have the opportunity to sendmoney provided by an experimenter to another participant. This money istripled, and the receiving player can return all, some, or none of this moneyback to the player who sent the money to him. The “proposer” is given asum of money, for example, $10. Then the proposer offers some percent-age of that $10 to a “responder,” say $5. The amount of money transferredto the responder is tripled by the experimenters, so it is now $15. The re-sponder then has an opportunity to reciprocate the transfer by sendingsome of the $15 back to the proposer. Obviously, some proposers and re-sponders never send money, some transfer a little, and some transfer themajority. There are tremendous individual differences in money transfers.
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