Portfolio optimization based on stochastic dominance and empirical likelihood

Abstract

This study develops a portfolio optimization method based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption framework which allows for dynamic and non-Gaussian multivariate return distributions. The SD/EL method can be implemented using a two-stage procedure which first elicits the implied probabilities using Convex Optimization and subsequently constructs the optimal portfolio using Linear Programming. The solution asymptotically dominates the benchmark and optimizes the goal function in probability, for a class of weakly dependent processes. A Monte Carlo simulation experiment illustrates the improvement in estimation precision using a set of conservative moment conditions about common factors in small samples. In an application to equity industry momentum strategies, SD/EL yields important out-of-sample performance improvements relative to heuristic diversification, Mean-Variance optimization, and a simple 'plug-in' approach.