Factor-risk-constrained mean-variance portfolio selection: formulation and global optimization solution approach

Shushang Zhu, Xueting Cui, Xiaoling Sun, Duan Li

Abstract

ABSTRACT

Adopting an appropriate factor model enables us to pinpoint the hidden forces that drive the movement of the market and contribute to its systematic risk. We argue that risk management should be performed at the fundamental level of factor risks. We therefore propose a factor-risk-constrained mean-variance portfolio-selection formulation that allows managers to construct portfolios with desired factor-risk characteristics. As the resulting optimization problem is a nonconvex quadratically constrained quadratic program, we devise a branch-and-bound method by exploiting the special structure of the formulation. The features of our solution algorithm include a tight and relatively cheap lower bound by second-order cone relaxation and a special branching rule for factor-related variables. To examine the properties of the new formulation, we carry out empirical experiments that reveal certain benefits in applying the proposed factor-risk-constrained portfolioselection formulation in risk management.We also demonstrate the computational power of our proposed solution scheme by comparing it with the state-of-the-art global optimization package Baron.