Higher moments matter! Cross‐sectional (higher) moments and the predictability of stock returns

Abstract

In this paper we investigate the predictive power of cross-sectional volatility, skewness and kurtosis for future stock returns. Adding to the work of Maio (2015), who finds cross-sectional volatility to forecast a decline in the equity premium with high predictive power in-sample as well as out-of-sample, we highlight the additional role of cross-sectional skewness and cross-sectional kurtosis. We find cross-sectional skewness to deliver a significant contribution to the performance of cross-sectional volatility in the short run (less than 12 months forecasts), while cross-sectional skewness and cross-sectional kurtosis contribute significantly to the performance of cross-sectional volatility at horizons greater than 12 months. Furthermore, we document a clear benefit of including higher moments when disaggregating excess market returns along the value and size dimension. In this case, both cross-sectional skewness and cross-sectional kurtosis span the predictive quality towards large-cap and growth stocks. Overall, the addition of higher order cross-sectional moments significantly improves the predictive performance of cross-sectional volatility, a variable that is already regarded as having high predictive power with respect to the equity premium.