24/10/2025 - D.251

Leo Zhang

Portfolio Selection with Downside Risk Optimization: Distributional Robustness and Ambiguity Aversion

Downside risk and ambiguity aversion are central concerns in portfolio selection. In this paper, we measure downside risk around an $m$-order lower partial moment (LPM) and capture ambiguity aversion through a Wasserstein ball centered at a reference distribution of asset returns. We show that, in general, the distributionally robust mean-downside risk minimization (mean-DRDRM) can be formulated as a tractable convex program. Closed-form solutions are derived when the Wasserstein ball employs the Mahalanobis distance as the ground metric, which integrate the mean-variance theory and ambiguity aversion into the downside risk minimization framework. Building on these explicit portfolio solutions, we employ the target return of the LPM to characterize the risk aversion parameter in mean–variance theory and the degree of ambiguity aversion, two notions that are conceptually important yet often abstract for practical investment. More importantly, this connection links Knightian uncertainty with traditional measures of risk. Finally, a numerical study demonstrates that the proposed portfolios effectively control downside risk, mitigate the impact of market crashes, preserve upside potential, and outperform naive benchmarks.