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Asian Review of Financial Research Vol.33 No.1 pp.15-60
Ambiguity Premium and Expected Return
Yu Kyung Lee Ph.D. Student, Graduate School of Business, Seoul National University
Eun Jung Lee Professor, College of Business Administration & Economics, Hanyang University
Joon Chae Professor, Graduate School of Business, Seoul National University
Key Words : Ambiguity,Distribution uncertainty,Expected return,Kolmogorov-Smirnov statistic,Kuiper statistic


Many theories, experiments, and survey studies suggest that investors are ambiguityaverse, thereby implying the existence of a positive ambiguity premium [Please check whether this revision conveys your intended meaning. If not, please suggest a suitable alternative.]. However, some empirical studies suggest contradictory results. Baltussen, Bekkum, and Grient (2018) use the volatility of implied volatility as a proxy for ambiguity and find a negative correlation between the volatility of implied volatility and expected returns. This negative correlation is inconsistent with the theories of Epstein and Schneider (2008) and Klibanoff, Marinacci, and Mukerji (2005),which state that investors' demand for ambiguity premiums in the stock market depends on their ambiguity avoidance. That is, while most extant theoretical studies on ambiguity suggest a positive correlation between ambiguity and expected returns on stocks, most empirical studies rarely prove this relationship. This study analyzes whether there is a significant correlation between ambiguity and expected stock returns in the Korean stock market and also empirically analyzes whether there exists a positive ambiguity premium. In the financial sector, asset-pricing models such as a capital asset -pricing model (CAPM) are based on various assumptions about the distribution of stock returns. For example, a CAPM assumes that stock returns follow a multivariate normal distribution. Many empirical studies, however, question the type of probability distributions of stock returns (Fama, 1965; Rosenberg, 1974; Tsay, 2010); they suggest that the probability distribution of stock returns does not follow a normal distribution, and are even skeptical about whether such a distribution exists. In particular, Knight (1921) argues that ambiguity is defined as the uncertainty about the location and shape of a probability distribution. Ellsberg (1961) and Camerer and Weber (1992) also note that Knightian uncertainty or ambiguity is generally defined as uncertainty about distribution. Thus, the degree of uncertainty in a distribution is directly related to Knight's (1921) ambiguity definition. If the recent distribution of stock returns unexpectedly differ from those in the past, the investor must pay a higher cost to better understand the difference between the recent and the past probability distribution of returns. Therefore, he/she will require higher premiums to hold these stocks. The main goal of this study is to empirically analyze whether there is a premium for the ambiguity of stock returns at the individual firm-level. To estimate investors' difficulties in understanding distributions of stock returns, this study presents the Kolmogorov-Smirnov (KS) and Kuiper (K) statistics, which measure the difference between the probability distribution of recent stock returns and those of past returns as a proxy for the ambiguity of stock returns. The results show that high-ambiguity stocks in the probability distribution of returns earn, on average, higher returns. An investor who is averse to high-ambiguity stocks demands a premium for that stock, thereby increasing his/her expected returns of the stock. This study examines whether such an ambiguity premium exists in the Korean stock market, and demonstrates that high-ambiguity stocks in return distributions lead to, on average, higher returns. We also find that the difference between the returns for portfolios with the highest and lowest distribution uncertainty is significantly positive. The bottom decile portfolio (S) by KS shows expected average monthly returns of 0.11%, and the top decile, 3.26%. When forming decile portfolios by K, stocks (S) with the least distribution uncertainty provide 0.07% of the expected average monthly average returns, and the stocks (B) with the most distribution uncertainty, 3.22%. In terms of value-weighted average returns, the V-W average returns for portfolios with the most distribution uncertainty are substantially higher. Using Fama and French's (2015) five-factor model, we show that our measures for distribution uncertainty are highly correlated with alphas estimated from five-factor specifications. The magnitude of the alphas is positively related to the level of distribution uncertainty, implying that high distribution uncertainty portfolios earn more positive abnormal returns. The alphas of the B-S spread are significantly positive. As a result, the Kolmogorov-Smirnov (KS) statistic and the Kuiper (K) statistic are correlated with future stock returns. To determine the robustness of the empirical results, we extensively investigate whether the effect of distribution uncertainty persists after controlling for firm characteristics such as beta, size, book-to-market ratio, momentum, short-term reversal, and illiquidity. Overall, the results from these robustness tests using alternative measures of distribution uncertainty still support our hypothesis. Moreover, the results remain significant even after controlling for the characteristics of the distribution of returns, such as intrinsic volatility, skewness, kurtosis, and maximum returns. Next, we examine the cross-sectional relationship between distribution uncertainty and expected stock returns at the firm level using Fama-MacBeth (1973) regressions. The results show a significant correlation between the degree of distribution uncertainty and expected returns even after controlling for a variety of other firm-level variables. Our findings demonstrate the existence of ambiguity premiums in the Korean stock market.
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