Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach
提出一种非参数效率测量方法，在均值-方差-偏度空间中评估静态投资组合选择问题，通过短缺函数寻找收益和偏度增加、方差减少的改进方向，并建立与间接效用函数的联系，可区分组合效率与配置效率，并揭示投资者的风险厌恶和审慎程度。
This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.