Portfolio Risk Management with CVaR-Like Constraints

Recently, a lot of attention has been focused on developing portfolio allocation models that take into account the asymmetric nature of asset return distributions. In this paper, we extend Krokhmal, Palmquist, and Uryasev's approach by using CVaR-like constraints in the traditional portfolio optimization problem to reshape either the left or right tail of a portfolio return distribution while not significantly affecting other portfolio properties. We illustrate how to apply this approach, called the “MV CVaR approach”, to manage tail risk of an insurer's asset-liability portfolios. Finally, we compare the MV CVaR approach with the traditional Markowitz method and a method recently introduced by Boyle and Ding. Our numerical analysis provides empirical support for the effectiveness of the MV CVaR approach in controlling downside risk. Moreover, we find that the MV CVaR approach can improve skewness of mean-variance portfolios, especially for the high-variance portfolios