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A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution

Author

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  • Zinoviy Landsman

    (Actuarial Research Center, Department of Statistics, University of Haifa, Mount Carmel, 3498838 Haifa, Israel)

  • Udi Makov

    (Actuarial Research Center, Department of Statistics, University of Haifa, Mount Carmel, 3498838 Haifa, Israel)

  • Tomer Shushi

    (Actuarial Research Center, Department of Statistics, University of Haifa, Mount Carmel, 3498838 Haifa, Israel
    Department of Economics and Business Management, Ariel University, Ariel 40700, Israel)

Abstract

In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ).

Suggested Citation

  • Zinoviy Landsman & Udi Makov & Tomer Shushi, 2018. "A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution," Risks, MDPI, vol. 6(1), pages 1-15, March.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:1:p:19-:d:134997
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    References listed on IDEAS

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    1. Best, Michael J. & Grauer, Robert R., 1990. "The efficient set mathematics when mean-variance problems are subject to general linear constraints," Journal of Economics and Business, Elsevier, vol. 42(2), pages 105-120, May.
    2. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    3. Zinoviy Landsman & Udi Makov, 2016. "Minimization of a Function of a Quadratic Functional with Application to Optimal Portfolio Selection," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 308-322, July.
    4. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    5. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    6. Ray, Pritee & Jenamani, Mamata, 2016. "Mean-variance analysis of sourcing decision under disruption risk," European Journal of Operational Research, Elsevier, vol. 250(2), pages 679-689.
    7. Castellano, Rosella & Cerqueti, Roy, 2014. "Mean–Variance portfolio selection in presence of infrequently traded stocks," European Journal of Operational Research, Elsevier, vol. 234(2), pages 442-449.
    8. Fulga, Cristinca, 2016. "Portfolio optimization under loss aversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 310-322.
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    Cited by:

    1. Nicole Bauerle & Tomer Shushi, 2019. "Risk Management with Tail Quasi-Linear Means," Papers 1902.06941, arXiv.org, revised Jan 2020.
    2. 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.
    3. Aditya Maheshwari & Traian A. Pirvu, 2020. "Portfolio Optimization under Correlation Constraint," Risks, MDPI, vol. 8(1), pages 1-18, February.

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