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Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm

Author

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  • Hoai An Le Thi

    (University of Lorraine)

  • Mahdi Moeini

    (Technische Universität Braunschweig)

Abstract

In the matter of Portfolio selection, we consider an extended version of the Mean-Absolute Deviation (MAD) model, which includes discrete asset choice constraints (threshold and cardinality constraints) and one is allowed to sell assets short if it leads to a better risk-return tradeoff. Cardinality constraints limit the number of assets in the optimal portfolio and threshold constraints limit the amount of capital to be invested in (or sold short from) each asset and prevent very small investments in (or short selling from) any asset. The problem is formulated as a mixed 0–1 programming problem, which is known to be NP-hard. Attempting to use DC (Difference of Convex functions) programming and DCA (DC Algorithms), an efficient approach in non-convex programming framework, we reformulate the problem in terms of a DC program, and investigate a DCA scheme to solve it. Some computational results carried out on benchmark data sets show that DCA has a better performance in comparison to the standard solver IBM CPLEX.

Suggested Citation

  • Hoai An Le Thi & Mahdi Moeini, 2014. "Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 199-224, April.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-012-0197-0
    DOI: 10.1007/s10957-012-0197-0
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    References listed on IDEAS

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    Cited by:

    1. Mahdi Moeini, 2022. "Solving the index tracking problem: a continuous optimization approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 807-835, June.
    2. E. Grizickas Sapkute & M. A. Sánchez-Granero & M. N. López García & J. E. Trinidad Segovia, 2022. "The impact of regulation-based constraints on portfolio selection: The Spanish case," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-14, December.
    3. Le Thi, H.A. & Pham Dinh, T. & Le, H.M. & Vo, X.T., 2015. "DC approximation approaches for sparse optimization," European Journal of Operational Research, Elsevier, vol. 244(1), pages 26-46.
    4. Vrinda Dhingra & Shiv Kumar Gupta & Amita Sharma, 2023. "Norm constrained minimum variance portfolios with short selling," Computational Management Science, Springer, vol. 20(1), pages 1-35, December.

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