Are Risk Premium Anomalies Caused by Ambiguity

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Are Risk Premium Anomalies Caused by Ambiguity? Author(s): Robert A. Olsen and George H. Troughton Source: Financial Analysts Journal, Vol. 56, No. 2 (Mar. - Apr., 2000), pp. 24-31Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4480230Accessed: 21-08-2014 20:31 UTC

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Are Risk Premium Anomalies Caused by Ambiguity?

Robert A. Olsen and George H. Troughton

Numerous studies have provided evidence of two equity return anomalies in recent years. The "risk-premium puizzle" is the anomaly that equity returns have been excessive relative to risk. The "small-firm effect" is the anomaly that risk premiums on small-cap stocks have been excessive relative to premiums on large-cap stocks. We present unique evidence that both of these anomalies may be caused by the presence of ambiguity. More generally, we propose that the current conceptions of risk are too limited to explain equity returns and, therefore, that the distinction between risk and uncertainty developed by Frank Knight approximately 80 years ago be revisited. As numerous other studies hzave found, risk in the traditional sense is primarily a function of the possibility of incurring a loss. Uncertainty (ambiguity) is directly related to lack of information and lack of confidence in estimatingfuture distributions of possible returns and the possibility of incurring a loss.

.............~~~~~~~~~~~~~~~~~~~~~... ......

_T wo equity return anomalies have received extensive attention in the last few years. For the first, called the "risk premium puzzle" by Siegel and Thaler (1997), the finding is

that equity returns have been excessive relative to equity risk in the last half century. For the second, called the "small-firm effect," the finding is that risk-adjusted returns on small-cap stocks have been overly large relative to those of large firms (Banz 1981). Previous studies have suggested many possible causes for these anomalies, such as myopic loss aversion, consumption patterns, extreme loss aversion, differences in asset liquidity, and risk misspecification.1

In contrast to this shotgun and, in some cases, ad hoc approach, we suggest that these two anomalies have a common, straightforward explanation. This explanation requires amending the descriptively incorrect conception of risk implicit in the subjective expected utility model underpinning modern finance. Specifically, we argue that what appear to be excessive risk premiums are, in fact, ambiguity premiums.

Almost 80 years ago, Knight (1921) drew a sharp distinction between risk and uncertainty. He hypothesized that the bearing of uncertainty (now called "ambiguity") is the primary reason for an entrepreneur's profit. In modem finance, however, risk, which is a function of an assumed known distribution of future outcomes, has taken center stage. Recent research has shown that linking risk to variability of returns is descriptively incomplete. For example, it is known that investors are loss averse and more concerned with avoiding returns below some personal target than with variability in return.2 Thus, the time appears ripe to reexamine the impact of uncertainty on security market returns. A return to the past may be necessary to make the future comprehensible.

Uncertainty/Ambiguity: A Brief History According to Knight, with risk, the distribution of possible outcomes of an economic variable is known; with uncertainty, the location and shape of the distribution is open to question. Knight believed that uncertainty was the normal state of affairs in business, and it was the primary reason for the entrepreneur's profits.

Keynes (1936) elaborated on the distinction between risk and uncertainty by suggesting that uncertainty is a function of the degree of confidence

Robert A. Olsen is professor offinanceat California State University at Chico and research associate at Decision Research. George H. Troughton, CFA, is professor of finance at California State University at Chico.

24 22000, Association for Investment Management and Research



or "weight" attached to a probability judgment. In addition, he argued that uncertainty can be reduced to risk, as has occurred in modern finance, only if the outcome-generating system operates in a deterministic fashion as in a pure game of chance, such as roulette.

Knight's approach to the distinction between risk and uncertainty was refined by Savage (1954) and Ellsberg (1961). Ellsberg appears to be respon- sible for coining the term "ambiguous probabilities." Keynes' behavioral approach to risk and uncertainty, which took into account the many faces of "unknowing," has also been the object of further investigation. For example, Shackle (1952) developed a theory of uncertainty in which probabilities were replaced by "anticipations of potential surprise." In 1957, Carter presented a model in which ranks and ranges replaced probability point estimates; this approach anticipated recent attempts to apply "fuzzy set theory" to the concept of uncertainty (Lopes 1997). Tversky and Koehler (1994) developed "support theory," in which people are shown to associate probabilities with descriptions of events rather than the events themselves. Similarly, Pennington and Hastie (1993) showed that people use stories to construct a "chain of reason" for a forecasted event. Thus, Pennington and Hastie argued that probabilities are a positive function of the consistency, completeness, and coherence of a story rather than the probability of the event itself.

Recent nontraditional subjective expected utility (SEU) theories have incorporated uncertainty/ ambiguity in utility models through nonadditive probabilities or the direct placement of ambiguity in personal utility functions (Camerer and Weber 1992). However, consistent with the traditional SEU model, these newer models do not view ambiguity from a motivational or cognitive point of view; they view it as merely a reaction to the man- ner in which decision makers experience quantity (diminishing marginal utility).

In contrast to these economically based, psy- chophysical approaches, psychologists have tested theories that focus on behavioral reasons for feelings of ambiguity and ambiguity aversion. These theories identify factors, such as feelings of competence, control, and personal responsibility, and the use of heuristics, such as anchorinf and adjust- ment, as determinants of ambiguity.

In summary, support of the traditional SEU model has become unjustifiable. The model cava- lierly dismisses ambiguity through the normative ploy of arguing that ambiguity is meaningless because all probabilities must be subjectively known, if only to oneself, or through the reduction-

ist strategy of second-order probabilities (i.e., probabilities of probabilities). To the contrary, the following statements summarize the known impact of ambiguity on decision making: * Ambiguity influences selection. * In general, decision makers are ambiguity

averse. * Ambiguity causes more weight to be placed on

negative information. * Buyers pay lower prices for, and insurers

require higher premiums on, objects or hazards subject to greater difficulty in estimation of value or probability of outcome.

* Risk aversion and ambiguity aversion do not appear to be highly correlated.4

Data and Method Our data are from questionnaires distributed to professional money managers at two educa- tion-oriented professional meetings (N = 209) and a mail survey (N = 105). Approximately 68 percent of the respondents were holders of the Chartered Financial AnalystTM (CFA?) designation, and their average length of work experience was 15 years, with 90 percent having 6 or more years of experience. Some 84 percent of the respondents listed their primary duties as institutional analyst, strate- gist, or portfolio manager; 16 percent listed their occupations as investment counselor. In general, the respondents were well-trained and experienced money managers.

All questionnaires were pretested and struc- tured to avoid response bias. Respondents were allowed to remain anonymous.

The mail survey sample was obtained from a randomly selected group of CFA charterholders. The mail survey response rate was 26 percent, which is typical for this type of survey. A call to 10 percent of the questionnaire recipients (N = 40) did not suggest any significant sources of nonresponse bias.

Responses were not significantly different between the mail and the meeting respondents, so we pooled the data on tests related to the hypothe- ses.

Professional Perceptions of Risk and Ambiguity Extensive cross-disciplinary and cross-cultural studies by Slovic (1987) and others (for example, Goszczynska and Tadeusz 1991) that used the psy- chometric paradigm suggest that professional as well as novice decision makers focus on two "uncertainty related" but multifaceted dimen-

March/April 2000 25


Financial Analysts Journal

Table 1. Importance of Risk-Related Attributes (N= 169)

Attribute Mean Rating 1. The chance of incurring a large loss 2.0 2. Uncertainty about the true distribution of possible future returns 2.2 3. The chance of earning less than the target 2.8 4. Variability in the asset's return as measured numerically by standard deviation, beta, etc. 3.5 5. The chance of obtaining very large gains relative to what was expected 4.7

Note: A rating of 1 = extremely important; a rating of 5 = not important. Differences between means significant at the 1 percent level for Attributes 3, 4, and 5.

sions-downside risk (or risk of loss) and ambiguity (or unknowing/lack of knowledge). Downside risk usually refers to the risk of not meeting a target or aspiration level. Olsen's 1997 studies of investment professionals and experienced investors showed that downside risk is positively related to required returns. A large-scale study of investors commissioned by the U.S. SEC also found that downside risk is the most important risk-related attribute to mutual fund investors (Investment Company Institute 1996). Table 1 presents our findings on professional investors' feelings about downside risk and, for the first time, information about the importance of ambiguity/uncertainty in professional judgments about riskiness.

The data in Table 1 came from the responses to a question that asked respondents to rate, on a Likert-type scale from 1 (extremely important) to 5 (not at all important), the investment importance of a preselected set of risk-related attributes. The attributes were selected from risk descriptors prominent in the investment literature.

In congruence with previous studies, we found that these professional investors rated downside risk, as represented by the chance of incurring a large loss or failure to meet a target, as a dominant dimension of risk. Consistent with the developing ambiguity literature, we also found, however, that these professional investors rated uncertainty

about the true distribution of possible future returns as a close second in importance. Variability of return, as measured by standard deviation or beta, received ratings of only slightly to moderately important. The chance of earning a large gain was considered to be unimportant. The low weight given to variability of return and upside potential as risk factors is consistent with the results of previous studies by Olsen.

Table 2 presents the results of our attempt to identify the separate effects of risk and ambiguity by asking respondents to rank, on a seven-point Likert scale, 20 actual stocks as to level of perceived risk. Some participants ranked the stocks without knowing the company names; a second group ranked them with the company names provided. Participants were to use the values we provided of the stocks' standard deviations of returns, betas, Value Line safety ranks,5 and an Index of Analyst Disagreement (IAD), which we computed. With the exception of the IAD data, we took the stock values provided by Value Line. The IAD was computed by ranking stocks on a scale of 1 to 5 by their coefficient of variation of forecasted earnings based on data from I/B/E/S International. The number 1 indicated the least disagreement among the analysts; 5 indicated the most disagreement. Respon- dents were told that the IAD should be seen as a

Table 2. Relationship between Risk Attributes and Perceived Risk: Partial Correlation Coefficients

No Company Names With Company Names Risk Attribute (N = 210) (N = 230) Safety rating 0.32 0.36 Index of Analyst Disagreement 0.29 0.31 Beta 0.24 0.27 Standard deviation 0.05 0.23

R2 (all attributes) 0.54 0.70 Note: All coefficents significant at the 1 percent level except the 0.05 coefficient for standard deviation in the first column.

26 ?2000, Association for Investment Management and Research



Exhibit 1. Attitudes toward Information for Decision Making (N= 209)

Question 1 I would treat two securities with equivalent quantitative risk measures as equally risky.

Agree: 33% Disagree: 67%

Question 2 The ability to construct a coherent and complete "story" with the facts of a situation is one of the most important factors when making projections or recommendations.


proxy for the degree to which analysts disagree among themselves about the future behavior of the stock. Because of this disagreement among information sources, the IAD is a measure of ambiguity or uncertainty.

The magnitude of the partial correlation coefficients in Column 1 in Table 2, which provides responses when the company names were not given, shows that downside risk, as measured by the safety rank, was the most important dimension of perceived risk.6 The IAD was a close second in importance. Standard deviation was seen as insig- nificant. As will be discussed, the insignificance of standard deviation is probably a result of respondents' difficulty in evaluating this measure of risk when a frame of reference, such as a company name or industry, was not present.

Column 2 of Table 2 presents partial correlation coefficients for risk attributes for the same companies as Column 1, but in this case, respondents were told the names of the companies. Note that the relative rankings of the attribute coefficients stayed about the same but all of them increased in absolute value, as did the R2 for the equation as a whole. With the exception of the ambiguity variable that we added to our study, the results are similar to those reported by Farrelly and Reichenstein (1984). Using named real companies and professional portfolio managers, they found downside risk, as measured by the Value Line safety rank, to be the dominant measure of perceived risk. The authors included I/B/E/S earnings predictability indexes in their model. If one makes the not unrealistic assumption that measures of earnings predictability can be seen as ambiguity measures, Farrelly and Reichenstein's results confirm those of Table 2. That is, Farrelly and Reichenstein found earnings predictability indexes to be second, and sometimes first, in importance as an attribute of perceived risk.

The most notable change from Column 1 to Column 2 in Table 2 is the large increase in the partial correlation coefficient for standard deviation. A likely reason for the increased correlations when the names were given is that identification of the company helped the respondents "frame" the

information and interpret the meaning of the quantitative risk and ambiguity measures.

Two pieces of evidence support this hypothesis. First, the partial correlation coefficients for beta, the safety index, and the IAD increased much less when company names were revealed than did the coefficient for standard deviation, as would be expected because the former measures are already relative measures of risk and, therefore, already framed to some degree. The second piece of evidence is provided in Exhibit 1, which reports the responses to two questions relevant to the hypothesis. Exhibit 1 shows that 67 percent of the respondents would not treat stocks with equivalent quantitative risk measures as equally risky. In addition, 88 percent of the respondents said that it is important to be able to construct a complete story to make projections and recommendations. These responses indicate that analysts define risk and ambiguity much more broadly than the numbers alone do.

These findings are consistent with a recent SEC study of mutual fund investors (Investment Com- pany Institute), which found that only 26 percent of recent mutual fund purchasers used any quantitative risk measures at all and that approximately 52 percent of long-term investors preferred narra- tive-based information to quantitative measures of risk.

In a third exercise, respondents were asked to rate asset classes by level of perceived risk (see Appendix A for the exact wording of the questions and the asset classes). The risk and ambiguity attributes they were to use can be summarized as follows: "large loss" and "below target return" as measures of risk; "ability to predict risk" and "familiarity with the investment" as measures of ambiguity. These measures of ambiguity were intended to reflect the completeness of information about each asset class. Table 3 presents the results.

All of the partial correlation coefficients in Table 3 are significant, as is the relatively large R2. Consistent with the results in Table 1 and empirical evidence from a prior study of professional investors (Olsen 1997a, 1997b), we found risk to be most

March/April 2000 27



Table 3. Relationship between Risk Attributes and Perceived Risk of Asset Types (N = 610)

Attribute Partial Correlation Very large loss 0.58 Ability to estimate risk 0.46 Familiarity 0.23 Below-target returns 0.20

R2 (all attributes) 0.73 Note: All coefficients significant at the 1 percent level.

strongly related to the possibility of realizing a large loss. Consistent with Knight's conception of uncertainty, ambiguity was highly associated with the inability to estimate risk (that is, identify with confidence the distributions of possible future returns).

Ambiguity and the Small-Firm Effect The small-firm effect is the finding that observed risk-adjusted returns on small-cap stocks have been overly large relative to those of larger and more well-known companies. Current financial models judge risk-adjusted returns by reference to a measure of risk based on an assumed known prospec- tive distribution of returns. However, as Chan and Chen (1991) noted, small firms are characterized by more marginal efficiency and weaker competitive positions than large firms, which makes a quantitative estimate of their future distribution of returns very difficult. Also, the confidence with which one can estimate those returns is much lower. Empirical studies by Foster, Olsen, and Shevlin (1984), Bernard and Thomas (1990), and Bernard (1993) presented evidence that abnormal returns after earnings announcements are signifi-

cantly greater for small firms than for large firms. Therefore, a reasonable supposition is that ambiguity about future return distributions, and thus ambiguity premiums, might account, in part, for the anomalously large observed risk premiums on small-firm stock. Exhibit 2 presents evidence sup- porting this hypothesis.

Responses to the first and second questions reproduced in Exhibit 2 indicate that professional investors find estimating stock return distributions for small firms more difficult than for large firms and generally feel less confident about their predic- tions when investing in small-cap stocks. Responses to the third and fourth questions shown suggest that, in general, when predictability declines and ambiguity rises, reliance on formal quantitative metrics declines. In particular, 64 percent said that judgment, as opposed to quantitative analysis, becomes more important as complexity increases, and 89 percent of respondents agreed that quantitative analysis is of little use in evaluating volatile companies. Thus, in the case of small, little-known companies, traditional quantitative measures of risk, such as standard deviation and beta, may be incomplete predictors of risk-adjusted returns and may need to be augmented by measures of ambiguity.

Conclusions and Implications Our findings suggest that, like other professional decision makers, professional investors are ambiguity averse. Thus, observed market returns should reflect ambiguity premiums as well as risk premiums. Current equilibrium models, such as the capital asset pricing model, tend to underestimate required returns because they do not contain any

Exhibit 2. Ambiguity, Confidence, and Company Size (N= 209)

Question 1 Estimates of future stock return distributions are more unreliable for small than large firms. Agree: 84% Disagree: 16%

Question 2 Greater ambiguity (uncertainty about probability estimates) tends to make me less confident when investing in small versus large firm stocks.


Question 3 As a forecasting/recommendation task becomes more complex and difficult, I tend to rely more on judgment and less on formal, quantitative analysis.


Question 4 Quantitative valuation models are less useful in analyzing securities of new or more volatile companies. Agree: 89% Disagree:11%




provision for ambiguity. Moreover, understatement of returns may be especially pronounced for assets whose return potentials are most ambiguous and difficult to quantify. We have offered some tentative survey evidence for this hypothesis as it relates to small-cap stocks.

The presence and pricing of ambiguity may account, in part, for two other risk-related phenom- ena. First, most initial public offerings (IPOs) are sold at relatively large discounts. Studies by Beatty and Ruthen (1986), Muscarella and Vetsuypens (1989), and Clarkson and Merkley (1994) showed that ex ante uncertainty is positively related to the size of IPO discounts. Thus, the large discounts may be partly caused by the high degree of ambiguity surrounding the future performance of new stocks. Second, Poterba and Summers (1995) and Miller (1978) noted that required returns on large, nonroutine, capital-budgeting expenditures tend to be set high relative to costs of capital based on existing financial models. They suggested that the excess required return may be a result of the fact that managers tend not to evaluate projects in a portfolio context. Another possibility, however, is that the excess required return is a result of the

ambiguity associated with forecasting the future of large, nonroutine capital projects.

Appendix A. Asset-Class Questions Survey respondents were asked to rate 10 asset classes on a seven-point scale along the following dimensions: * Overall, how risky is each of the following

investments? * How likely is it that this asset could generate a

very large loss? * How likely is it that each of the following

investments will earn a return below what you expect (your target)?

* How familiar are you with the risks and returns of each of the following investments?

* To what extent do you feel it is possible to accurately estimate the future risk (distribution of returns) for each of the following investments?

The 10 asset classes were insured savings accounts, long-term U.S. T-bonds, long-term high-grade cor- porate bonds, junk bonds, blue chip stocks, OTC stocks, shares in real estate investment trusts, stock options, residential real estate, and gold bullion.

Notes 1. For examples, see Fama and French (1993, 1996); Gneezy

(1997); Berk (1997); Bemartzi and Thaler (1995); Jensen and Johnson (1997, 1998); Schwert (1983); Lakonishok and Sha- piro (1986); Barber and Lyon (1998).

2. See Shapira (1995); Tversky and Kahneman (1992); Harlow and Rao (1989); Olsen (1997a, 1997b); Laughhunn and Payne (1980); Lopes (1997).

3. Einhom and Hogarth (1985, 1986); Heath and Tversky (1991); Jungerman (1997); Huber (1995); Sarin and Weber (1992); Tversky (1997).

4. See Weber and Millimon (1997); Smidts (1997); Dyer and Sarin (1982); Wakker and Fennema (1996); Ghosh and Ray (1997); Sarin and Weber (1992); Muthukrishnan (1995); Kunreuther, Meszaros, Hogarth, and Spranca (1995).

5. Value Line (1999) describes its safety rank as "a measure- ment of potential risk associated with individual common stocks. The safety rank is computed by averaging two other Value Line indexes-the Price Stability Index and the Financial Strength Rating."

6. Multicollinearity is not likely to be a major source of difficulty when interpreting the correlation coefficients in Table 2 because the actual correlations between the risk variables were very low and stepwise regression did not reveal significant instability in the variable coefficients. In addition, a test with an artificially constructed set of securities, where (by design) values of risk variables were made orthogonal, gave virtually identical results to those shown in Table 2.

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Issue Table of ContentsFinancial Analysts Journal, Vol. 56, No. 2 (Mar. - Apr., 2000), pp. 1-120Front Matter [pp. 1-15]Author Digests [pp. 6+8-10+12-14]Behavioral FinanceInvestor Sentiment and Stock Returns [pp. 16-23]

Market AnomoliesAre Risk Premium Anomalies Caused by Ambiguity? [pp. 24-31]

Market StructureAn Empirical Study of Bond Market Transactions [pp. 32-46]

Risk ManagementValue at Risk [pp. 47-67]

ValuationFranchise Labor [pp. 68-76]Finding Firm Value without a Pro Forma Analysis [pp. 77-84]Symmetrical Information and Credit Rationing: Graphical Demonstrations [pp. 85-95]Stocks versus Bonds: Explaining the Equity Risk Premium [pp. 96-113]

Book ReviewsReview: untitled [p. 114]Review: untitled [pp. 115-116]Review: untitled [pp. 116-117]

Back Matter [pp. 118-120]

Are Risk Premium Anomalies Caused by Ambiguity

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