Distributionally Robust and Robust Second-Order Stochastic Dominance Portfolio Models Based on Support Vector Clustering
TL;DR
A novel SSD-based portfolio optimization framework that incorporates support vector clustering (SVC) to construct data-driven uncertainty sets that consistently outperform benchmark approaches in terms of robustness and profitability across a wide range of market conditions.
Abstract
Traditional second-order stochastic dominance (SSD) portfolio optimization models typically rely on precisely specified return data and probability distributions. However, these assumptions are often violated in real financial markets. To address this issue, we develop a novel SSD-based portfolio optimization framework that incorporates support vector clustering (SVC) to construct data-driven uncertainty sets. Specifically, we propose two models: the SVC-DRSSD model, which addresses ambiguity in return distributions, and the SVC-RSSD model, which accounts for uncertainty in return levels. Both models can be reformulated as tractable convex quadratic or linear programming problems. Numerical experiments conducted on constituent stocks of the DJIA, DAX, and HSI indices demonstrate that the proposed SVC-DRSSD and SVC-RSSD models consistently outperform benchmark approaches in terms of robustness and profitability across a wide range of market conditions. Notably, during periods of market downturn, the proposed models effectively mitigate downside risk while maintaining competitive return performance.