A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN–VARIANCE OPTIMIZATION

Xiaoyue Liu (), Zhenzhong Huang (), Biwei Song () and Zhen Zhang
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Xiaoyue Liu: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Zhenzhong Huang: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
Biwei Song: Huawei Technologies Company Ltd., Shenzhen 518100, P. R. China
Zhen Zhang: Department of Mathematics, International Center for Mathematics, National Center for Applied Mathematics (Shenzhen ), Southern University of Science and Technology, Shenzhen 518055, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 04n05, 1-23

Abstract: In the Markowitz mean–variance portfolio optimization problem, the estimation of the inverse covariance matrix is not trivial and can even be intractable, especially when the dimension is very high. In this paper, we propose a linear-programming portfolio optimizer (LPO) to solve the Markowitz optimization problem in both low-dimensional and high-dimensional settings. Instead of directly estimating the inverse covariance matrix Σ−1, the LPO method estimates the portfolio weights Σ−1μ through solving an l1-constrained optimization problem. Moreover, we further prove that the LPO estimator asymptotically yields the maximum expected return while preserving the risk constraint. To offer a practical insight into the LPO approach, we provide a comprehensive implementation procedure of estimating portfolio weights via the Dantzig selector with sequential optimization (DASSO) algorithm and selecting the sparsity parameter through cross-validation. Simulations on both synthetic data and empirical data from Fama–French and the Center for Research in Security Prices (CRSP) databases validate the performance of the proposed method in comparison with other existing proposals.

Keywords: Markowitz mean–variance portfolio optimization; sparsity; asymptotic consistency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0219024923500127

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