Mean/Variance Relation and the Conditional Distribution

Abstract

This paper examines the relation between the expected return and the conditional variance using three conditional error distributions 1) the conditional normal error distribution, 2) the Generalized Error Distribution, and 3) the skewed student's t-distribution. Using a GARCH-M model modified by allowing skewness in mean, we find support for a significant and positive mean/variance relation when the skewed student's t-distribution is used. Our results show that the time variations in conditional skewness influence the dynamics of the conditional mean and conditional variance, as reflected by the reduced volatility persistence and a significant mean/variance relationship. This further stresses the point that there is an intimate relation between return, volatility and skewness; within the GARCH-M framework, conditional skewness plays a role analogous to heteroskedasticity by smoothing out the conditional mean and conditional variance process.