Are Risk Premium Anomalies Caused by Ambiguity?

Numerous studies have provided evidence of two equity return anomalies in recent years. The “risk-premium puzzle” 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 have 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 estimating future distributions of possible returns and the possibility of incurring a loss. In recent years, numerous studies have noted that actual risk premiums on common stocks are larger than would be expected if investors were perceiving risk as only a function of variability of return. Studies have also indicated that the risk premium for small-cap stocks is greater than it theoretically should be. Previous theoretical and empirical research on risk perception conducted in noninvestment domains suggests that risk premiums are not only a function of beliefs about future outcomes but also a function of the degree of confidence decision makers have about their beliefs. More specifically, in situations where decision makers' beliefs are subject to greater ambiguity (lack of knowing), risk premiums appear to be greater. One purpose of this study was to see whether risk premiums on common stocks are also a direct function of ambiguity of belief about possible future distributions of returns. The data in the study came from the responses of 314 professional money managers (68 percent of whom were holders of the Chartered Financial Analyst™ designation) surveyed at a conference or by mail. All materials were pretested and structured to avoid response bias. Also, we presented survey respondents with diverse exercises in order to confirm the generality of response patterns. In the first exercise, respondents were asked to rate a number of potential risk attributes by the degree of their importance to risk assessment. Consistent with results of such exercises conducted in other decision domains, we found that measures of downside risk, such as the size of possible loss, received the highest ratings, but measures of ambiguity about such downside outcomes were rated a close second. Measures of variability of return were rated less highly. A second exercise had respondents rate actual common stocks as to perceived risk level (measured by conventional risk measures), a downside risk measure, and a measure of ambiguity based on disagreement among experts about future prospects. We found that downside risk and ambiguity were considered to be the most significant explanatory factors. Statistical testing ruled out multicollinearity between explanatory variables. A third exercise asked respondents to rate asset classes instead of individual stocks. The results were similar to those for individual stocks, with downside risk and ambiguity having significant explanatory power. Finally, respondents were asked about their risk perceptions in various investment decision environments. Their responses indicated that they felt less confident when making forecasts for small companies. They also believed that quantitative models are of little use in making decisions for new companies. When ambiguity was great, they tended to rely less on analytical techniques and quantitative information than on narrative information about the companies. This study implies that risk premiums are influenced by ambiguity about future outcomes. Current valuation models underestimate required risk premiums that vary directly with uncertainty of belief or ambiguity. We thus propose that the distinction between risk and uncertainty developed by Frank Knight some 80 years ago be revisited. As this study and numerous others have found, risk in the traditional sense is more a function of the possibility of incurring a loss than of variability of return. Uncertainty (ambiguity) is directly related to lack of information and lack of confidence in estimating that possibility for the future.