Robust approaches in portfolio optimization with stochastic dominance constraints

Abstract The paper deals with a modern approach of stochastic dominance in portfolio optimization. Since the distribution of returns is often just estimated from data, we look for the worst-case distribution that differs from the empirical distribution by no more than some prescribed value. First, we define in what sense the distribution is the worst one for stochastic dominance. Then, using Wasserstein distance, we derive a reformulation for robust second-order stochastic dominance and find the worst-case distribution as the optimal solution of a non-linear optimization problem. Finally, we derive programs to maximize an objective function over the weights of the portfolio with the robust stochastic dominance condition in constraints. We consider robustness in returns for second-order stochastic dominance. We apply all derived optimization programs to real-life data, specifically to returns of assets captured by the Dow Jones Industrial Average, and analyze the problems in detail using optimal solutions of optimization programs with multiple setups. The empirical analysis proceeded with an out-of-sample evaluation of portfolios formulated through the robust optimization program, employing a moving window methodology. The findings of this study indicate that for some of the values of $$\varepsilon $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ε</mml:mi> </mml:math> the robustified portfolios consistently out-of-sample outperform those derived from the non-robust optimization approach.