Portfolio Optimization with Higher-Order Stochastic Dominance Constraints

Abstract

A framework is developed for portfolio optimization with higher-order Stochastic Dominance constraints. A finite system of restrictions on the lower partial moments can be used for evaluating the efficiency of a given benchmark and for constructing enhanced portfolios which dominate the benchmark for the relevant class of risk averters. The system can be linearlized for discrete distributions, allowing for implementation using Linear Programming. Imposing higher-order restrictions expands the set of improvement possibilities and mitigates the risk of suboptimality due to estimation error. A simulation study exemplifies these benefits, for a simple hypothetical investment problem. In an empirical application to equity industry rotation, accounting for kurtosis aversion and Decreasing Absolute Prudence improves out-of-sample performance beyond levels achieved using more permissive assumptions.

Keywords: Portfolio Choice, Higher-Order Risk, Stochastic Dominance, Linear Programming, Enhanced Indexing, Industry Rotation

JEL Classification: C61, D81, G11