On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear to be more highly correlated during market downturns than during market upturns. In this paper we examine the economic and statistical significance of these asymmetries for asset allocation decisions in an out-of-sample setting. We consider the problem of a CRRA investor allocating wealth between the risk-free asset, a small-cap and a large-cap portfolio. We use models that can capture time-varying moments up to the fourth order, and we use copula theory to construct models of the time-varying dependence structure that allow for different dependence during bear markets than bull markets. The importance of these two asymmetries for asset allocation is assessed by comparing the performance of a portfolio based on a normal distribution model with a portfolio based on a more flexible distribution model. For investors with no short sales constraints we find that knowledge of higher moments and asymmetric dependence leads to gains that are economically significant, and statistically significant in some cases. For short sales constrained investors the gains are limited