Portfolio Selection with Higher Moments

Abstract

We propose a method for optimal portfolio selection using a Bayesian decision theoretic framework that addresses two major shortcomings of the Markowitz approach: the ability to handle higher moments and estimation error. We employ the skew normal distribution which has many attractive features for modeling multivariate returns. Our results suggest that it is important to incorporate higher order moments in portfolio selection. Further, our comparison to other methods where parameter uncertainty is either ignored or accommodated in an ad hoc way, shows that our approach leads to higher expected utility than the resampling methods that are common in the practice of finance.

Keywords: Bayesian decision problem, multivariate skewness, parameter uncertainty, optimal portfolios, utility function maximization, resampling, resampled portfolios, estimation error, mean-variance portfolios, expected returns, Markowitz optimization

JEL Classification: G11, G12, G10, C11