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.

Keywords:

• Portfolio optimization
• spillover effect
• Danzig-Wolfe decomposition
• column generation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2022M3J6A1063021, RS-2023-00249931). CL was supported by the Hankuk University of Foreign Studies Research Fund and the National Research Foundation of Korea (NRF) under the Basic Science Research Program (NRF-2021R1F1A1 048540).