Conditional Skewness in Asset Pricing Tests

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios. THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL ~CAPM! of Sharpe ~1964! and Lintner ~1965! has come under recent scrutiny. Tests indicate that the crossasset variation in expected returns cannot be explained by the market beta alone. For example, a growing number of studies show that “fundamental” variables such as size, book-to-market value, and price to earnings ratios account for a sizeable portion of the cross-sectional variation in expected returns ~see, e.g., Chan, Hamao, and Lakonishok ~1991! and Fama and French ~1992!!. Fama and French ~1995! document the importance of SMB ~the difference between the return on a portfolio of small size stocks and the return on a portfolio of large size stocks! and HML ~the difference between the return on a portfolio of high book-to-market value stocks and the return on a portfolio of low book-to-market value stocks!. There are a number of responses to these empirical findings. First, the single-factor CAPM is rejected when the portfolio used to proxy for the market is inefficient ~see Roll ~1977! and Ross ~1977!!. Roll and Ross ~1994! and Kandel and Stambaugh ~1995! show that even very small deviations from efficiency can produce an insignificant relation between risk and expected returns. Second, Kothari, Shanken, and Sloan ~1995! and Breen and Korajczyk ~1993! argue that there is a survivorship bias in the data used to test these new asset pricing specifications. Third, there are several specification issues. Kim ~1995! and Amihud, Christensen, and Mendelson ~1993! argue that errorsin-variables impact the empirical research. Kan and Zhang ~1997! focus on time-varying risk premia and the ability of insignificant factors to appear * The authors are from Duke University and Georgetown University respectively. We appreciate the comments of Philip Dybvig, Stephen Brown, Alon Brav, S. Viswanathan, and seminar participants at Georgetown, Indiana University, the University of Toronto, the 1996 WFA ~Oregon!, and the AFA ~New Orleans! meetings. We appreciate the helpful comments of an anonymous referee and the detailed suggestions of the editor. THE JOURNAL OF FINANCE • VOL. LV, NO. 3 • JUNE 2000