Investor sentiment and the crash risk of anomalies

We find that the return skewness of major stock market anomalies varies with investor sentiment. Following periods of low sentiment, these strategies exhibit significantly more negative skewness and greater crash risk, as evidenced by a more negative Conditional Value-at-Risk (CVaR). In contrast, these strategies display positive skewness following high investor sentiment. These findings contribute to the debate of whether it is risk or mispricing that explains anomaly returns. Our results suggest that left-tail risks cannot account for the higher returns earned by anomalies in high-sentiment states—taking tail risks into account in fact makes it more challenging to explain the state dependence of anomaly returns from a risk-based perspective. In contrast, our results are consistent with the mispricing perspective. If the extent of overpricing of the short side to an anomaly portfolio is indeed greater than the long side following high sentiment (as suggested by Stambaugh et al. 2012) and that crash risks are higher when investor sentiment and the degree of overpricing is high (as suggested by Baker and Wurgler 2006, 2007), the crash risk of the short side would also be greater than that of the long side—reducing the crash risks of the long-short portfolio during these times. Although diversification across anomalies enhances their Sharpe ratios, it fails to reduce their crash risks.