Robust reward-risk performance measures with weakly second-order stochastic dominance constraints

In this paper, we propose a framework for robustifying reward-risk-based portfolio optimization equipped with weak type second-order stochastic dominance constraints that substantially improves upon their conventional versions. In particular, relying on stable sub-Gaussian and Student's t distributions, we extend a robust optimization technique that is very popular among conventional robust statistical estimation methods and consider a new notion of weak second-order stochastic dominance. Furthermore, we study the effects of the distributional assumptions on optimal portfolios while addressing the estimation errors directly in the portfolio optimization process. The empirical analyses show that the robustified formulations improve the performance measures upon their classic versions for out-of-sample portfolios.(c) 2022 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.

Automated summary

In this paper, a framework is proposed for robustifying reward-risk-based portfolio optimization with weak type second-order stochastic dominance constraints, significantly improving upon conventional versions. By utilizing stable sub-Gaussian and Student's t distributions, a popular robust optimization technique in conventional statistical estimation methods is extended, and a new notion of weak second-order stochastic dominance is considered. The effects of distributional assumptions on optimal portfolios are studied, and estimation errors are directly addressed in the portfolio optimization process. Empirical analyses demonstrate that the robustified formulations improve performance measures for out-of-sample portfolios.