Orateur
Description
We extend portfolio selection models with classical stochastic dominance constraints by allowing a controlled violation of these constraints. This relaxation permits the returns of feasible portfolios to differ from those that stochastically dominate the benchmark within a tolerance measured by the Wasserstein distance. We formulate an optimization problem that incorporates the stochastic non-dominance constraints, assuming discrete distributions of returns. Additionally, we examine the relationship between this approach and portfolio models based on almost stochastic dominance. To assess the proposed method, we apply the second-order stochastic non-dominance constraints to the portfolio selection problem using a dataset of daily returns from 49 U.S. industry representative portfolios. A moving-window analysis over 96 years demonstrates that allowing small levels of stochastic non-dominance, particularly when measured by the Wasserstein distance of order two, can increase out-of-sample returns while maintaining a similar level of risk compared to the classical second-order stochastic dominance approach.
