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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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    References listed on IDEAS

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    1. Xiaodong Ding & Hezhi Luo & Huixian Wu & Jianzhen Liu, 2021. "An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation," Computational Optimization and Applications, Springer, vol. 80(1), pages 89-120, September.
    2. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    3. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    4. Cheng Lu & Zhibin Deng & Jing Zhou & Xiaoling Guo, 2019. "A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 73(2), pages 371-388, February.
    5. F. Palacios-Gomez & L. Lasdon & M. Engquist, 1982. "Nonlinear Optimization by Successive Linear Programming," Management Science, INFORMS, vol. 28(10), pages 1106-1120, October.
    6. M. V. Solodov, 2004. "On the Sequential Quadratically Constrained Quadratic Programming Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 64-79, February.
    7. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    8. William F. Sharpe, 2002. "Budgeting and Monitoring Pension Fund Risk," Financial Analysts Journal, Taylor & Francis Journals, vol. 58(5), pages 74-86, September.
    9. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    10. Samuel Burer & Dieter Vandenbussche, 2009. "Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound," Computational Optimization and Applications, Springer, vol. 43(2), pages 181-195, June.
    11. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    12. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    13. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    14. Li, Yingjie & Zhu, Shushang & Li, Donghui & Li, Duan, 2013. "Active allocation of systematic risk and control of risk sensitivity in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 228(3), pages 556-570.
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