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

Huixian Wu (), Hezhi Luo (), Xianye Zhang () and Jianzhen Liu ()
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Huixian Wu: Hangzhou Dianzi University
Hezhi Luo: Zhejiang Sci-Tech University
Xianye Zhang: Zhejiang Sci-Tech University
Jianzhen Liu: Hangzhou Dianzi University

Journal of Global Optimization, 2023, vol. 87, issue 2, No 9, 503-532

Abstract: 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.

Keywords: Factor-risk-constrained mean-variance portfolio selection; Global optimization; Successive convex optimization; Semi-definite relaxation; Branch-and-bound (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01218-z

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