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Portfolio Optimization by a Bivariate Functional of the Mean and Variance

Author

Listed:
  • Z. Landsman

    (University of Haifa
    Holon Institute of Technology)

  • U. Makov

    (University of Haifa)

  • T. Shushi

    (Ben Gurion University)

Abstract

We consider the problem of maximization of functional of expected portfolio return and variance portfolio return in its most general form and present an explicit closed-form solution of the optimal portfolio selection. This problem is closely related to expected utility maximization and two-moment decision models. We show that most known risk measures, such as mean–variance, expected shortfall, Sharpe ratio, generalized Sharpe ratio and the recently introduced tail mean variance, are special cases of this functional. The new results essentially generalize previous results by the authors concerning the maximization of combination of expected portfolio return and a function of the variance of portfolio return. Our general mean–variance functional is not restricted to a concave function with a single optimal solution. Thus, we also provide optimal solutions to a fractional programming problem, that is arising in portfolio theory. The obtained analytic solution of the optimization problem allows us to conclude that all the optimization problems corresponding to the general functional have efficient frontiers belonged to the efficient frontier obtained for the mean–variance portfolio.

Suggested Citation

  • Z. Landsman & U. Makov & T. Shushi, 2020. "Portfolio Optimization by a Bivariate Functional of the Mean and Variance," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 622-651, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01664-3
    DOI: 10.1007/s10957-020-01664-3
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    References listed on IDEAS

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    Cited by:

    1. Huang, Zhenzhen & Wei, Pengyu & Weng, Chengguo, 2024. "Tail mean-variance portfolio selection with estimation risk," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 218-234.
    2. Nicola Loperfido & Tomer Shushi, 2023. "Optimal Portfolio Projections for Skew-Elliptically Distributed Portfolio Returns," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 143-166, October.
    3. Eini, Esmat Jamshidi & Khaloozadeh, Hamid, 2021. "The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 44-50.

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