Risk Measures and Portfolio Choices for Gain-Loss Dependent Objectives

This study advances the understanding of risk measures and portfolio choice for investors exhibiting gain-loss dependent risk attitudes by integrating stochastic dominance (SD) concepts, including prospect stochastic dominance (PSD) and Markowitz stochastic dominance (MSD). We demonstrate that partial moments serve as effective risk measures, aligning with various SD criteria to capture diverse investor attitudes toward gains and losses. One contribution of this paper is the development of a decision-making criterion to identify the segment of the mean-variance efficient frontier that is efficient under different SD conditions, applicable to elliptical distributions. Leveraging partial moments, we adopt a portfolio optimization method that constructs portfolios dominating a benchmark from multiple SD perspectives, facilitating comparisons across gain-loss utility models. This approach enables a more direct comparison of alternative gain-loss utility models without relying on parameter assumptions, which often lead to differing risk-return priorities within a model.