Optimal Portfolio Choice with Fat Tails and Parameter Uncertainty

Abstract

Existing portfolio combination rules that optimize the out-of-sample performance under estimation risk are calibrated assuming multivariate normally distributed returns. In this paper, we show that this assumption is not innocuous because fat tails in returns increase the out-of-sample mean and variance of estimated portfolios relative to normality. Consequently, portfolio combination rules should allocate less weights to the sample mean-variance portfolio and the sample global minimum-variance portfolio, and more weight to the risk-free asset, than the normality assumption prescribes. Empirically, accounting for the impact of fat tails in the construction of optimal portfolio combination rules significantly improves their out-of-sample performance.

Keywords: portfolio combination, elliptical distribution, estimation risk

JEL Classification: C58, G11, G12