The column generation approach to the mean-risk model for the portfolio selection problem with spillover risk aversion

Abstract

In this article, we propose extensions of the general mean-risk portfolio selection models to limit the spillover effect of risk. We use the conditional value at risk (CoVaR) as a measure to identify the spillover risk contribution of securities. The goal is to find a portfolio that minimizes general risk measures while the spillover risk contribution is limited. Based on the frameworks of the general mean-risk models, we additionally guarantee that a portfolio has limited spillover risk contributions. To solve these problems efficiently, we propose a Dantzig-Wolfe decomposition reformulation that yields a strong continuous relaxation bound by introducing a set of feasible investment patterns. We develop an algorithm that incorporates a column generation procedure to reduce the spillover effect of tail risk in subproblems. Finally, we present the performance of the portfolios using real historical data. The results show that our model can provide better portfolios than the general mean-risk models.