The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution

Abstract

In the insurance and financial markets, events of extreme losses happen in the tail of return distributions, and investors are sensitive to these losses. The Tail Mean–Variance (TMV) criterion focuses on the rare risk but large losses, and it has recently been used in financial management for portfolio selection. In this paper, the proposed TMV criterion is based on the two measures of risk, i.e., the Tail Conditional Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution. We obtain an explicit solution with simple implementation and use a convex optimization approach for the TMV optimization problem under the GSE distribution. We also provide a practical example of a portfolio optimization problem using the proposed TMV criterion. The empirical results show that the optimal portfolio performance can be improved by controlling the tail variability of returns distribution.