into their decision. Of subjects participating in both random and skill-based versions of the game, 77 percent had higher profit per round in the random-rank game. On average, participants earned $1.31 more when playing the random-rank game. In fact, only 52 of 111 participants achieved a positive profit when playing the skill-based game. Thus, it appears participants were likely to overestimate the probability that their skill would exceed that of other participants.

Risk Aversion and Production

Under the rational—expected utility—model, someone facing a decision of whether to engage in a venture or not will decide to continue with the venture if the expected utility of engaging in the venture is greater than the utility of other options, or if

where π is the random profit potentially generated by the new venture and π is the certain income generated by the opportunities forgone if the venture is started. To see the competing impacts of risk aversion and overconfidence on entry, consider the Taylor series expansion of the utility function about the mean of profits, μπ . This approximation is given by

where RA is the coefficient of absolute risk aversion, usually thought to be greater than zero. Thus, the greater the variance of the profit resulting from the new venture, the less likely the person is to start up the new venture. Alternatively, the higher the mean profit,

the more likely it is that the person will start the venture. If people misperceive the variance or the mean of the distribution of profits from the new venture, this can cause them to decide to engage in the venture when in fact they should abstain.

Overconfidence

Overconfidence can fall into one of two categories. Thus far we have talked about overconfidence as a general inflation of the probability that the person holds the correct view. This is the type of overconfidence most often referred to in the psychology literature, and it is the type that generally results from a pattern of confirmation bias. This type of overconfidence necessarily results in believing that the person faces less uncertainty (e.g., a lower variance of profit) than is truly the case. For clarity, we refer to this as overconfidence of one’s own knowledge. Alternatively, many use the term overconfi- dence to refer to a bias of beliefs in favor of whatever outcomes may be more favorable for the person. Thus, for example, entrepreneurs might not only fail to perceive the potential variance of the distribution of profits for their new venture, they might believe the profits that would be realized on average are much higher than truth would dictate. We refer to a biasing of beliefs in favor of one’s own welfare as optimistic overconfidence.

Interestingly, it can be very difficult to disentangle these two types of overconfidence in many situations. Entrepreneurship creates an interesting example. In this case, overestimating the profits one will achieve has the same impact on entry as underestimating the amount of risk one faces. Camerer and Lovallo’s experiment is clearly designed to examine how people evaluate their own abilities—primarily a function of optimistic overconfidence. People face risk in both treatment arms of the experiment, and they could potentially display overconfidence of one’s own knowledge in both treatments. Only the skill-based treatment directly inserts an assessment of one’s own ability. Unfortunately, nearly all direct tests of overconfidence muddle these two types of overconfidence. For example, Busenitz and Barney conducted tests of whether probabilistic judgments are well calibrated, ostensibly seeking to find overconfidence of one’s own knowledge. Unfortunately, the probabilities were elicited by asking participants to assess their ability to make a correct guess to a series of questions. Thus, the probability judgments would also be affected by optimistic overconfidence. Similarly, when asked to guess confidence interval values, one might not widen the confidence interval enough because one overestimates one’s own ability to guess the correct answer.

In general, overconfidence (of either type) leads to decisions that might seem rash or ill informed to an objective observer. Potential entrepreneurs start a business failing to recognize the risks involved or overestimating the probability of profits. Stock traders might not diversify as much as they should, believing that there is much less risk in the particular investments they have chosen than will actually be realized. As a rule, people tend to be overconfident. However, they become more overconfident when they face a more difficult question. Thus, questions about which they have little information will inspire overconfidence, and questions that they know with certainty might actually induce underconfidence. On average, when people say that something will occur with certainty, it occurs about 80 percent of the time—thus the impossible happens about one fifth of the time!

EXAMPLE 8.7 Gender Differences and Trading

Rational models of stock trading suggest people should seldom trade stocks. Intuitively, if everyone has access to the same information, then everyone must have identical expectations about the future value of a stock. Thus, if all are rational and none have private information, trading stock in any company is unnecessary unless the person selling is seeking to cash out, say, to provide income in retirement. In reality, however, a majority of stocks in the New York Stock Exchange change hands every year (for example, 76 percent of stock shares changed hands in 1998). This seems to entirely defy the rational model of trading. A risk-averse person should be willing to buy a share of a stock if Ept + 1− RA2σ2 > pt, where pt + 1 is the future value of the stock and pt is the current trading price, RA is the level of absolute risk aversion, and σ2 is the perceived variance of the future value of the stock. The term RA2σ2 can be called the risk premium, or the penalty for the level of risk involved in investing in the stock. Further, anyone holding the stock would be willing to sell only if Ept + 1 − RA2σ2 < pt. If everyone has the same beliefs regarding the future value of the stock, and if all have the same aversion to risk, then no seller would sell below and no buyer would buy above pt = Ept + 1− RA2σ2. Thus, this would determine the market price and no one would have any particular motivation to sell or buy.

Given this model, people should normally take the current price as a signal of the future value of the stock. Thus, those who learn rationally will modify their beliefs to fit in with the market view. Alternatively, those who are overconfident might fail to take the market price as a signal of the true value of the stock. Rather, they might see any difference between their own beliefs and the market price as an opportunity. For example, suppose a trader believes that value of a stock is above the market price. If she were rational she might learn from the price that she overvalues the item and revise her beliefs downward. Alternatively, if she is overconfident, she believes the probability she is right is higher than it is in truth. Thus, she will fail to revise her beliefs downward enough and will decide to buy more of the stock. In this way, overconfidence leads to the execution of more trades than truthful perceptions about the market. Moreover, if she buys the stock and her perceptions about future value are wrong, she will be surprised by earning a smaller amount on average than if she had not purchased the stock. A similar story would lead to selling and earning less than expected if the initial beliefs were that the stock was worth less than the market price.

Brad Barber and Terrance Odean argue that although both men and women are overconfident, men tend to be more overconfident than women. Further, men are particularly overconfident in their ability to engage in “masculine” tasks. They asserted that stock trading is perceived generally as a masculine task and set out to find the fingerprints of gender-based overconfidence on trading patterns. They examined investment data from nearly 40,000 households over the years 1991 through 1996. Single women bought or sold an average of about 4 percent of their stock portfolio each month, and single men bought or sold about 7 percent of their portfolio each month. Thus the turnover for men is much higher. However, both men and women display a relatively high rate of turnover compared to the near 0 percent predicted by rational theory. Further, these trades reduce the returns of the portfolio. The average single man

earns 0.24 percent less per month than he would have without trading, about 3 percent less per year. The average single woman earns about 0.12 percent less per month than she would without trading, about 1.5 percent per year.

Men and women also have different attitudes toward risk generally. Men are usually less risk averse than women and should thus be willing to pay more for risky stocks. Being less risk averse than the rest of the market can also lead to excess trading. People who are less risk averse than the market average will be willing to pay more for the stock because they do not care about the risk and face a lower-than-average risk premium. As an extreme case, consider someone who is risk neutral, RA = 0. The risk-neutral person is willing to purchase any stock at a price at or below expected future value. Thus any stock with a risk premium built into the current market price should be purchased by the riskneutral investor. At the same time, the risk-neutral investor behaves so as to maximize the expected value of the investment, finding the maximum average return. Thus, if differences in trading were driven solely on differences in risk aversion, those who trade more (less averse to risk) should display a higher return on average. Differences in risk aversion cannot explain the trading patterns of men because the men earn lower average returns owing to the trades. This must be due to misperception of risk rather than differing attitudes toward the risk faced.

EXAMPLE 8.8 Amateurs and Professionals

It is to be expected that professional experience will help to hone one’s skills in whatever task is common in a profession. Stuart Oskamp sought to examine how amateur and professional psychologists differ in their ability to recognize or predict behavioral patterns in a clinical setting. Thus, Oskamp wanted to simulate the way information would unravel or develop in a series of meetings with a psychologist. Participants were presented a series of background stories and information about a client. The information consisted of four stages in all, each covering a different chronological piece of the client’s life. After each stage of the information was presented, each participant was asked the same series of 25 multiple-choice questions about the client’s behavior that was related to, but not directly addressed by, the information that had been presented. For example, one question asks how the client acted in social situations in college (e.g., “stayed aloof and withdrawn,” or “acted the clown”). Further, participants were to rate their degree of confidence in their answer by assessing the probability that their answer is correct. Participants consisted of professional psychologists, graduate students in psychology, and undergraduate students in psychology.

Table 8.3 presents the average accuracy and confidence of all participants by stage in Oskamp’s experiment. The accuracy of the predicted behaviors does increase slightly as a participant obtains more information about the client (from 26 percent to about 28 percent). However, the improvement in true accuracy is minuscule compared to the increase in confidence (from 33 percent to 53 percent). Not only are the participants overconfident in every stage, their level of overconfidence increases as they obtain more information. This is a pattern that is highly consistent with confirmation bias, whereby people increasingly believe in their conclusion as they receive any information. Although