Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Zhang-Lei Shi; Xiao Peng Li; Chi-Sing Leung; Hing Cheung So

doi:10.1109/TNNLS.2022.3192065

Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Zhang-Lei Shi, Xiao Peng Li^*, Chi-Sing Leung^*, Hing Cheung So

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

261 Downloads (CityUHK Scholars)

Abstract

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality (ℓ₀-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

Original language	English
Pages (from-to)	2901-2909
Number of pages	9
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	35
Issue number	2
Online published	27 Jul 2022
DOIs	https://doi.org/10.1109/TNNLS.2022.3192065
Publication status	Published - Feb 2024

Funding

This work was supported by a grant from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. CityU 11207922]. (Corresponding Authors: Xiao Peng Li and Chi-Sing Leung)

Research Keywords

ℓ0-norm
alternating direction method of multipliers (ADMMs)
Convex functions
Covariance matrices
Heuristic algorithms
Indexes
mean-variance model
Neural networks
Optimization
Portfolios
sparse portfolio

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Shi, Z-L., Li, X. P., Leung, C-S., & So, H. C. (2022). Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers. IEEE Transactions on Neural Networks and Learning Systems. https://doi.org/10.1109/TNNLS.2022.3192065.

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title = "Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers",

abstract = "Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality (ℓ0-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.",

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author = "Zhang-Lei Shi and Li, {Xiao Peng} and Chi-Sing Leung and So, {Hing Cheung}",

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N2 - Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality (ℓ0-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

AB - Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality (ℓ0-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

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KW - alternating direction method of multipliers (ADMMs)

KW - Convex functions

KW - Covariance matrices

KW - Heuristic algorithms

KW - Indexes

KW - mean-variance model

KW - Neural networks

KW - Optimization

KW - Portfolios

KW - sparse portfolio

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JF - IEEE Transactions on Neural Networks and Learning Systems

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ER -

Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

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Research Keywords

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GRF: Advanced Factorization Approaches for Low-Rank Matrix Recovery

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Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

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Research Keywords

Publisher's Copyright Statement

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GRF: Advanced Factorization Approaches for Low-Rank Matrix Recovery

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