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Ambiguity Aversion Bias

The practical justification for the study of general economics is a belief in the possibility of improving the quality of human life through changes in the form of organization of want-satisfying activity.

—Frank K. Knight, economist, University of Chicago (1921)

BIAS DESCRIPTION

Bias Name:Ambiguity Aversion Bias Type:Cognitive

General Description. People do not like to gamble when probability dis- tributions seem uncertain. In general, people hesitate in situations of ambiguity, a tendency referred to as ambiguity aversion. Frank H. Knight, of the University of Chicago, was one of the twentieth century’s most eclectic, thoughtful economists and one of the first to write on ambiguity aversion. Knight’s 1921 dissertation, entitled “Risk, Uncertainty, and Profit,” defined a riskas a gamble with a precise probability distribution.

“Uncertainty,” according to Knight, materializes when the distribution of possible outcomes resulting from a gamble cannot be known. Knight’s groundbreaking treatise concluded that people dislike uncertainty (ambiguity) more than they dislike risk.

Ambiguity aversion appears in a wide variety of contexts. For in- stance, a researcher might ask a subject to estimate the probability that a

CHAPTER 12

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certain team will win its upcoming college soccer game; the subject might estimate a 50 percent likelihood of success. The researcher might then ask the subject to consider an electronic slot machine, which is guaran- teed to display either a “1” or a “0,” each with a probability of 50 percent. Would the subject prefer to bet on the football game (an ambiguous bet) or on the slot machine (a bet that offers no ambiguity of the risks involved)? In general, most subjects in such a study would probably choose the slot machine, demonstrating the ambiguity aversion bias.

Technical Description. Leonard J. Savage, author of the classic 1954 book The Foundations of Statistics,¹ developed “Subjective Expected Utility Theory” (SEUT) as a counterpart to the expected utility concept in economics. This theory states that, under certain conditions, an individual’s expectation of utility is weighted by that individual’s subjective probability assessment.

Using SEUT, Daniel Ellsberg²performed a classic ambiguity aversion experiment that examined, technically, ambiguity aversion. His experiment went as follows:

Suppose that subjects are presented with two boxes, referred to here as Box 1 and Box 2. The subjects are advised that Box 2 contains a total of 100 balls, exactly half of which are white, and half of which are black.

Box 1 likewise contains 100 balls, again a mix of white and black, but the proportion of white to black balls in Box 1 is kept secret. Subjects are asked to choose one of the following two options, each of which offers a possible payoff of $100, depending on the color of the ball drawn at ran- dom from the relevant box.

1A. A ball is drawn from Box 1. The subject receives $100 if the ball is white, $0 if the ball is black.

1B. A ball is drawn from Box 2. The subject receives $100 if the ball is white, $0 if the ball is black.

A similar follow-up scenario is then posed, and subjects choose again between two options.

2A. A ball is drawn from Box 1. The subject receives $0 if the ball is white, $100 if the ball is black.

2B. A ball is drawn from Box 2. The subject receives $0 if the ball is white, $100 if the ball is black.

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Ellsberg found that 1B was typically preferred to 1A, and that 2B was likewise preferred to 2A. These choices are inconsistent with SEUT:

the choice of 1B implies a subjective probability that fewer than 50 percent of the balls in Box 1 are white, while the choice of 2B implies the op- posite. The experiment suggests that people do not like situations where they are uncertain about the probability distribution of a gamble. SEUT does not account for an agent’s degree of confidence in a probability distribution, and it fails to accurately predict the outcome of Ellsberg’s experiment because it cannot capture ambiguity aversion.

PRACTICAL APPLICATION

When it comes to financial markets, people often make decisions based on subjective probabilities. For example, on learning that the Federal Reserve System (the Fed) is going to increase interest rates by 50 basis points, an investor must determine the probability that, say, Citigroup’s stock will fall as a result. Does ambiguity aversion factor into the ensuing subjective probability evaluation? A study by Chip Heath and Amos Tversky³concluded that this depends on the investor’s subjective competence level.

When people feel skillful or knowledgeable, they prefer to stake claims on ambiguous events, whose outcomes they believe they can predict based on their own judgment, rather than on equiprobable chance events (known probability events). By contrast, when people do not feel skillful or knowledgeable, they prefer to wager on chance events. This is known as the competence effect, and it is a facet of ambiguity aversion extremely relevant to investors that is explored in more depth later.

John R. Graham, Campbell R. Harvey, and Hai Huang of Duke University illustrated the competence effect with an experiment.⁴

Participants first report their subjective knowledge level about the game of football. Next, they are asked to predict the winner of a football game and also report their subjective probabilities of the predictions being correct. Then they are asked to choose between two bets, either to bet on their own judgment, or a lottery that provides an equal chance of winning. In this example, subjective competence is captured in two dimensions: the self-rated knowledge level, and the subjective probability of the football prediction

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being correct. The results of this experiment are shown in [Figure 12.1] (adapted from Heath and Tversky 1991, Figure 4). The percentage of participants choosing to bet on their own judgments in- creases with both measures of subjective competence. When subjects feel that they are highly competent in predicting the results of football games, they prefer to bet on their own judgment.

In fact, even when presented with a lottery with a greater chance of winning, they would still prefer to bet on their football predictions. In other words, they are willing to pay a premium to bet on their own judgments. When people do not feel competent, however, the matching chance lottery is preferred.

Implications for Investors. Private-client behavior often demonstrates ambiguity aversion. The most obvious and directly applicable situation

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High Knowledge

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FIGURE 12.1 Percentage of Participants Who Chose Their Own Judgments over Matched Chance Lotteries

Source: Graham, Harvey, and Huang, 2003.

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is investor uncertainty regarding the distribution of a security’s return. As a prerequisite for investing, uncertain people are likely to demand a higher expected rate of return than they would demand if they felt certain about the risk/return trade-off of the security in question. Pascal Maenhout⁵showed that if investors are concerned about the uncertainty of a model of a stock’s returns, they will demand a higher “equity premium” as compensation for the ambiguity in the probability distribution that they intuit. (Barring unreasonably high anxieties about uncertainty, Maenhout did point out that ambiguity aversion only partially solves the equity premium puzzle.)

Ambiguity aversion also sheds light on the problem of insufficient diversification. For example, investors may feel that local stock indexes are more familiar—less ambiguous—than foreign stock indexes. They may also consider firms that are situated close to them geographically to be less ambiguous than those located far away. Other investors may give in- creased preference to their own employers’ stocks, which seem less ambiguous than the stocks of unfamiliar firms. Since less ambiguous assets are attractive, people invest heavily in those and invest little or nothing at all in ambiguous assets. Their portfolios therefore become underdi- versified, relative to what modern portfolio theory would recommend.

Another important aspect of ambiguity aversion that is important for investors is the competence effect. Here, investors who believe that they are more skillful or knowledgeable in making financial decisions (i.e., those who do not perceive as much ambiguity in investment situations) are more willing to act on their judgments. For example, investors who feel more competent may trade more frequently than investors who feel less competent. Along these lines, investors are more willing to shift assets overseas when they feel that they understand foreign markets. The Research Review in this chapter further investigates the competence effect as it relates to investor behavior.

Box 12.1 contains a review of investment mistakes that stem from ambiguity aversion.

RESEARCH REVIEW

In their insightful paper “Investor Competence, Trading Frequency, and Home Bias,” Graham, Harvey, and Huang⁶argued that investors who perceive themselves as financially savvy are, in accordance with the

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competence effect, more willing to act on their judgments. Furthermore, they show that investors who feel more competent tend to trade more frequently than investors who feel less competent. The competence effect also contributes to home bias, or the tendency to keep assets geographically nearby. In contrast, when investors feel less competent, they are more likely to avoid investing in foreign assets.

BOX 12.1 Ambiguity Aversion Bias: Behaviors That Can Cause Investment Mistakes

1. Ambiguity aversion may cause investors to demand higher compensation for the perceived risks of investing in certain assets. Thus, the investors may hold only conservative investments, which can cause the potential to outlive an asset base, purchasing power erosion, and other consequences.

2. Ambiguity aversion may restrict investors to their own national indexes (e.g., Standard & Poor’s 500) because these indexes are more familiar than foreign ones. This is particularly important in light of the boom in exchange traded funds (ETFs), which offer Americans the ability to invest in often unfamiliar locales, such as China and South America. Similarly, ambiguity aversion may cause investors to favor companiesthat are geographically close to them and to ignore investments that seem to be located distantly. Remaining confined to specific national indexes or companies limits options for diversification and pre- vents investors from exploiting profit opportunities abroad.

3. Ambiguity aversion can cause investors to believe that their employers’ stocks are safer investments than other companies’

stocks because investments in other companies are ambiguous.

Enron, WorldCom, and other crises demonstrate the obvious perils of investing too heavily in a single company’s stock.

4. A unique aspect of ambiguity aversion is the competence effect.

Here, investors presented with an uncertain probability distribution might be expected to display caution due to ambiguity aversion. However, judging themselves competent in some per- tinent realm (e.g., foreign stocks, small company stocks, etc.), these investors actually accept morerisks than they should.

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The following is excerpted from the “Introduction” of Graham, Harvey, and Huang’s paper.

When people feel skillful or knowledgeable in an area, they would rather bet on their own judgment (even though it is ambiguous) than on an equiprobable chance event (e.g., drawing balls from an urn with known contents), even though the outcome of the chance event has an unambiguous probability distribution. However, when participants do not feel competent, they prefer to bet on the unambiguous chance event. Therefore, the effects of ambiguity aversion are conditional on the subjective competence level of participants.

When people feel less knowledgeable, however, they tend to choose the matched-chance lottery. The competence effect is particularly relevant to understand investor behavior. In financial markets, investors are constantly required to make decisions based on ambiguous, subjective probabilities. It is likely that their educational background and other demographic character- istics make some investors feel more competent than others in understanding the array of financial information and opportunities available to them.

We study two types of investor behavior, namely trading frequency and home bias. Although there exists extensive literatures on both trading frequency and home bias, these two have always been treated separately. In this paper, we argue that these two as- pects of behavior are driven (at least in part) by the same under- lying psychological bias, namely, the competence effect. With regard to trading frequency, we hypothesize that investors who feel more competent tend to trade more frequently than investors who feel less competent. This occurs because investors who feel more knowledgeable in making financial decisions should be more willing to act on their judgments. . . . Our empirical results are consistent with this hypothesis. We argue that the competence effect also contributes to home bias. Home bias refers to the tendency to overweight domestic equities and underweight international equities in investment portfolios. . . . When an investor feels that he fully understands the benefits and risks involved in investing in foreign assets, he is more willing to invest in foreign securi- ties. In contrast, when an investor feels less competent, he is more

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likely to avoid foreign assets. Consistent with these predictions, our results suggest that investors with more competence are more likely to invest in international assets.⁷

So, the research that Graham, Harvey, and Huang conducted suggests two important practical applications for ambiguity aversion bias with respect to individual investors: (1) The competence effect holds, and people who feel less competent regarding some key aspect of some financial decision are less likely to heed their judgments than people who feel more competent; (2) ambiguity aversion bias helps to explain home bias.

Practitioners need to be keenly aware of these investor tendencies.

DIAGNOSTIC TESTING

This section contains two questions. People who may be subject to ambiguity aversion bias answer both questions.

Ambiguity Aversion Bias Test

Question 1: Suppose you are a big fan of your local AAA baseball team, the Smallville Cougars. You are sitting in the stands just prior to the start of a game, and someone you don’t know approaches you and offers you a gamble. First, he asks you what the odds are that the Cougars will win tonight’s game. You estimate that the odds are 1 to 1 (50 percent), because the Cougars are playing the Bigville Titans, who linger midpack in the standings but overall have a decent team.

The man then asks you if you would be willing to bet money on the game, based on those odds. You feel confident in your assessment, and you agree. You’re surprised, however, when the man then produces a handheld, electronic slot machine and suggests that perhaps you would rather wager on the slot machine than on the baseball game. The machine pays off every time three cherries appear, an outcome that occurs 50 percent of the time. Assuming that the amount of money at stake is equal in each case, which bet do you accept?

Question 2:The scenario is the same as in Question 1, but there are some differences: Suppose that you are not only a big fan of your local AAA baseball team, the Smallville Cougars, but that you helped to put the team together and know all of the competitors in the league

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very well. This time, when the stranger approaches you, assume that you estimate 1 to 2 (67 percent) odds in favor of the Cougars. Since you know a significant amount about the team, you are again confident enough to answer in the affirmative when the man asks, given these odds, if you are willing to bet on the game. Assume that, as be- fore, the man produces a slot machine and says you’ll win just as much money if the slot machine produces three cherries as if the Cougars beat the Titans. This time the slot machine pays off—that is, produces three cherries—70 percent of the time. Which gamble do you choose?

Test Results Analysis

Question 1: People who elect the slot machine are more likely to be subject to ambiguity aversion than people who would stick with the baseball bet. The slot machine is a much less ambiguous bet, although to the subject the odds are the same.

Question 2: People who choose to bet on the game may be subject to the competence effect; feelings of expertise or skillfulness may lead these people to accept less optimal odds than they otherwise would. In this case, the outcome of the game has a lower probability than that of the slot machine, and the game was picked anyway as a result of competence effect.

ADVICE

There are two primary topics on which people exhibiting ambiguity aversion might benefit from some advice: We’ll look at managing ambiguity aversion, and then we’ll look at tactics for addressing the competence effect.

Ambiguity Aversion

As noted earlier, there are several key areas of which investors need to be aware with regard to ambiguity aversion. People who are ambiguity averse may not be investing in certain equity asset classes because they demand too high an equity premium; they may invest only in local or national stock indexes or only in companies located in geographically

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familiar places. Furthermore, they may unduly favor their own corpora- tions’ stocks over stocks of other firms.

When people demand too high a premium for investing in certain equity asset classes (such as small cap, international, etc.) and don’t understand the distribution of potential outcomes, education is critical in reforming such potentially unprofitable behavior. Investors need to be educated on how the relevant asset classes perform and how adding these asset classes to a diversified portfolio can be a beneficial action. Clients who only invest in certain familiar indexes because they do not feel they can predict the probable payoffs of investing elsewhere may likewise benefit from more information about the benefits of other options. In short, education is the key to overcoming ambiguity aversion.

Competence Effect

When investors demonstrate the competence effect, it is very important that they be counseled on potential investor mistakes such as trading too frequently, which can be “hazardous to one’s wealth.” The competence effect also contributes to home bias, or the tendency to keep assets geographically nearby. Graham, Harvey, and Huang demonstrated that the investors most willing to shift a portion of their assets into foreign secu- rities are those who feel most competent about investing in foreign assets.

The key advice that can be offered is to not let competence in a certain area prevent investments in other areas as well. For example, if you have an investor who is an expert in real estate, does that mean that he or she should be 100 percent invested in real estate? The obvious answer is no.

Stick to the fundamentals of a balanced, well-diversified portfolio.