A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN-VARIANCE OPTIMIZATION

Liu, Xiaoyue1; Huang, Zhenzhong2; Song, Biwei3; Zhang, Zhen4

2023-08-01

10.1142/S0219024923500127

INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE   影响因子和分区

0219-0249

1793-6322

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 sigma-1, the LPO method estimates the portfolio weights sigma-1 mu 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.

Markowitz mean-variance portfolio optimization sparsity asymptotic consistency

ESCI

英语

通讯

NSFC[12071207] ; Guangdong Basic and Applied Basic Research Foundation[2021A1515010359]

Business & Economics

Business, Finance

WOS:001146424000006

WORLD SCIENTIFIC PUBL CO PTE LTD

Web of Science

1.Georgia Inst Technol, H Milton Stewart Sch Ind & Syst Engn, Atlanta, GA 30332 USA
2.Univ Warwick, Dept Stat, Coventry CV4 7AL, Warwickshire, England
3.Huawei Technol Co Ltd, Shenzhen 518100, Peoples R China
4.Southern Univ Sci & Technol, Nat Ctr Appl Math Shenzhen, Int Ctr Mathemat, Dept Math, Shenzhen 518055, Peoples R China

Liu, Xiaoyue,Huang, Zhenzhong,Song, Biwei,et al. A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN-VARIANCE OPTIMIZATION[J]. INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE,2023,26(04N05).

Liu, Xiaoyue,Huang, Zhenzhong,Song, Biwei,&Zhang, Zhen.(2023).A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN-VARIANCE OPTIMIZATION.INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE,26(04N05).

Liu, Xiaoyue,et al."A LINEAR-PROGRAMMING PORTFOLIO OPTIMIZER TO MEAN-VARIANCE OPTIMIZATION".INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE 26.04N05(2023).