Portfolio Optimization Based on Almost Second-Degree Stochastic Dominance

In portfolio optimization, the computational complexity of implementing almost stochastic dominance has limited its practical applications. In this study, we introduce an optimization framework aimed at identifying the optimal portfolio that outperforms a specified benchmark under almost second-degree stochastic dominance (ASSD). Our approach involves discretizing the return range and establishing both sufficient and necessary conditions for ASSD. We then propose a three-step iterative procedure: first, identifying a candidate portfolio; second, assessing its optimality; and third, refining the discretization scheme. Theoretical analysis guarantees that the portfolio identified through this iterative process improves with each iteration, ultimately converging to the optimal solution. Our empirical study, utilizing industry portfolios, demonstrates the efficacy of our approach by consistently identifying an optimal portfolio within a few iterations. Furthermore, comparative analysis against other decision criteria, such as mean-variance, second-degree stochastic dominance, and third-degree stochastic dominance, reveals that ASSD generally leads to portfolios with higher out-of-sample average excess returns but also entails increased variations and risks. This paper was accepted by Agostino Capponi, finance. Funding: C. Luo acknowledges financial support from the National Natural Science Foundation of China [Grant 72101070] and the Zhejiang Provincial Natural Science Foundation of China [Grant LY23G010001]. P. Chen acknowledges financial support from the National Natural Science Foundation of China [Grant 72401253]. P. Jaillet acknowledges financial support from the Office of Naval Research [Grant N00014-18-1-2122 and N00014-24-1-2470] and the Air Force Office of Scientific Research [Grant FA9550-23-1-0182 and Grant FA9550-23-1-0190]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.01092 .