An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization

Wei Xu (), Jie Tang (), Ka Fai Cedric Yiu () and Jian Wen Peng ()
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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

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 690-704

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.

Keywords: portfolio selection; cardinality constraint; lower bound analysis; branch and bound method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:2:p:690-704

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