Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

Abstract

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.