Tail nonlinearly transformed risk measure and its application

This paper discusses risk measurement and portfolio selection under the mean‐risk framework. Through introducing a nonlinear convex transformation to large losses, we propose a new class of risk measures which are convex and monotone. We demonstrate the new risk measure’s favorable financial and mathematical properties, and consider its estimation in practice and relevant consistent and asymptotic issues. A realistic portfolio selection model based on the new risk measure is then established with typical market frictions taken into account simultaneously. Based on trade data from Chinese stock markets and American stock markets over stable and volatile periods, respectively, both in‐sample and out‐of‐sample empirical studies are carried out. Theoretical and empirical results show that the new risk measure and the corresponding portfolio selection model can not only reflect different investors’ risk averse attitudes and control the fat‐tail phenomenon of the return distribution, but also find a realistic optimal portfolio with superior performance and robustness than the corresponding optimal portfolio obtained under the expected shortfall risk measure.