A closed-form mean–variance–skewness portfolio strategy

Abstract

This paper analyzes portfolio selection problems with multivariate normal-gamma distributed risky returns. We obtain a partial elliptic cone-shaped mean–variance–skewness (MVS) frontier and a closed-form MVS portfolio strategy for investors with a cubic utility function. We show that the utility improvement and Sharpe ratio loss of our MVS strategy relative to the traditional mean–variance strategy depend on the investor’s prudence and risk-aversion levels, and the mean and variance of a max-skewness portfolio. Moreover, we obtain a three-moment capital asset pricing model, and propose a max-skewness factor in addition to the market factor.