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Sparse and robust portfolio selection via semi-definite relaxation

Author

Listed:
  • Yongjae Lee
  • Min Jeong Kim
  • Jang Ho Kim
  • Ju Ri Jang
  • Woo Chang Kim

Abstract

In investment management, especially for automated investment services, it is critical for portfolios to have a manageable number of assets and robust performance. First, portfolios should not contain too many assets in order to reduce the management fees, transaction costs, and taxes. Second, portfolios should be robust as investment environments change rapidly. In this study, therefore, we propose two convex portfolio selection models that provide portfolios that are sparse and robust. We first perform semi-definite relaxation to develop a sparse mean-variance portfolio selection model, and further extend the model by using L2-norm regularization and worst-case optimization to formulate two sparse and robust portfolio selection models. Empirical analyses with historical stock returns demonstrate the effectiveness of the proposed models in forming sparse and robust portfolios.

Suggested Citation

  • Yongjae Lee & Min Jeong Kim & Jang Ho Kim & Ju Ri Jang & Woo Chang Kim, 2020. "Sparse and robust portfolio selection via semi-definite relaxation," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(5), pages 687-699, May.
    • Handle: RePEc:taf:tjorxx:v:71:y:2020:i:5:p:687-699
    DOI: 10.1080/01605682.2019.1581408
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    Cited by:

    1. Gaete, Michael & Herrera, Rodrigo, 2023. "Diversification benefits of commodities in portfolio allocation: A dynamic factor copula approach," Journal of Commodity Markets, Elsevier, vol. 32(C).
    2. Ni, Xuanming & Zheng, Tiantian & Zhao, Huimin & Zhu, Shushang, 2023. "High-dimensional portfolio optimization based on tree-structured factor model," Pacific-Basin Finance Journal, Elsevier, vol. 81(C).
    3. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    4. Li, Xuepeng & Xu, Fengmin & Jing, Kui, 2022. "Robust enhanced indexation with ESG: An empirical study in the Chinese Stock Market," Economic Modelling, Elsevier, vol. 107(C).
    5. Pier Francesco Procacci & Tomaso Aste, 2022. "Portfolio optimization with sparse multivariate modeling," Journal of Asset Management, Palgrave Macmillan, vol. 23(6), pages 445-465, October.
    6. Farshad Noravesh, 2022. "Sparse Non-Convex Optimization For Higher Moment Portfolio Management," Papers 2201.01227, arXiv.org, revised Jan 2022.
    7. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    8. Lioui, Abraham & Tarelli, Andrea, 2022. "Chasing the ESG factor," Journal of Banking & Finance, Elsevier, vol. 139(C).

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