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

Abstract

Recent studies in the empirical Þnance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The Þrst is skewness in the distribution of individual stock returns, while 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 signiÞcance 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, using monthly data. We use models that can capture time-varying means and variances of stock returns, and also the presence of time-varying skewness and kurtosis. Further, we use copula theory to construct models of the time-varying dependence structure that allow for greater 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 sexible distribution model. For a variety of performance measures and levels of risk aversion our results suggest that capturing skewness and asymmetric dependence leads to gains that are economically signiÞcant, and statistically signiÞcant in some cases.