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An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization

Author

Listed:
  • Wei Xu

    (Research Institute for Risk Governance and Emergency Decision-Making, School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China)

  • Jie Tang

    (School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China)

  • Ka Fai Cedric Yiu

    (Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong 999077, P.R. China)

  • Jian Wen Peng

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R. China)

Abstract

This paper focuses on the cardinality constrained mean-variance portfolio optimization, in which only a small number of assets are invested. We first treat the covariance matrix of asset returns as a diagonal matrix with a special matrix processing technique. Using the dual theory, we formulate the lower bound problem of the original problem as a max-min optimization. For the inner minimization problem with the cardinality constraint, we obtain its analytical solution for the portfolio weights. Then, the lower bound problem turns out to be a simple concave optimization with respect to the Lagrangian multipliers. Thus, the interval split method and the supergradient method are developed to solve it. Based on the precise lower bound, the depth-first branch and bound method are designed to find the global optimal investment selection strategy. Compared with other lower bounds and the current popular mixed integer programming solvers, such as CPLEX and SCIP, the numerical experiments show that our method has a high searching efficiency.

Suggested Citation

  • Wei Xu & Jie Tang & Ka Fai Cedric Yiu & Jian Wen Peng, 2024. "An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 690-704, March.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:690-704
    DOI: 10.1287/ijoc.2022.0344
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