Portfolio Risk Management with CVaR-like Constraints

In his original monograph on portfolio selection, Markowitz (1952) discusses the tradeoff between the mean and variance of a portfolio. Since then, especially recently, much attention has been focused on asymmetric distributions to minimize risks with given return goal for investors who have special skewness preferences. To address this issue, we extend Krokhmal et al. (2002)’s approach by adding CVaR-like constraints to the traditional portfolio optimization problem. The CVaR optimization technique has the advantage of reshaping either the left or right tail of a distribution while not significantly affecting the other. Specifically, this approach is used to manage the skewness of asset-liability portfolios of financial institutions. In addition, we compare the CVaR-like constraints approach with traditional Markowitz method and some other alternatives such as, the CVaR approach(directly optimize CVaR), the Boyle-Ding approach as well as the mean-absolute deviation(MAD) approach. Our numerical analysis provides empirical support for the superiority of CVaR-like constraints approach in terms of skewness improvement of mean-variance portfolios.

Publication Information
Article Title: Portfolio Risk Management with CVaR-like Constraints
Journal: North American Actuarial Journal (Sep, 2008)
Author(s): Cox, Samuel H.;  Lin, Yijia;  Tian, Ruilin;  Zuluaga, Luis F.
Researcher Information
Lin, Yijia
Lin, Yijia
N. Z. Snell Life Insurance Professor
HLH 425 V
P.O. Box 880490
University of Nebraska-Lincoln
Lincoln, NE 68588-0490, USA
Phone: (402) 472-0093
Fax: (402) 472-5140