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A new global algorithm for factor-risk-constrained mean-variance portfolio selection

Author

Listed:
  • Huixian Wu

    (Hangzhou Dianzi University)

  • Hezhi Luo

    (Zhejiang Sci-Tech University)

  • Xianye Zhang

    (Zhejiang Sci-Tech University)

  • Jianzhen Liu

    (Hangzhou Dianzi University)

Abstract

We consider the factor-risk-constrained mean-variance portfolio-selection (MVPS) problem that allows managers to construct portfolios with desired factor-risk characteristics. Its optimization model is a non-convex quadratically constrained quadratic program that is known to be NP-hard. In this paper, we investigate the new global algorithm for factor-risk-constrained MVPS problem based on the successive convex optimization (SCO) method and the semi-definite relaxation (SDR) with a second-order cone (SOC) constraint. We first develop an SCO algorithm and show that it converges to a KKT point of the problem. We then develop a new global algorithm for factor-risk-constrained MVPS, which integrates the SCO method, the SDR with an SOC constraint, the branch-and-bound framework and the adaptive branch-and-cut rule for factor-related variables, to find a globally optimal solution to the underlying problem within a pre-specified $$\epsilon $$ ϵ -tolerance. We establish the global convergence of the proposed algorithm and its complexity. Preliminary numerical results demonstrate the effectiveness of the proposed algorithm in finding a globally optimal solution to medium- and large-scale instances of factor-risk-constrained MVPS.

Suggested Citation

  • Huixian Wu & Hezhi Luo & Xianye Zhang & Jianzhen Liu, 2023. "A new global algorithm for factor-risk-constrained mean-variance portfolio selection," Journal of Global Optimization, Springer, vol. 87(2), pages 503-532, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01218-z
    DOI: 10.1007/s10898-022-01218-z
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