IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i1p19-d134997.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/1/19/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/6/1/19/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    9. Graham, John R. & Harvey, Campbell R. & Puri, Manju, 2015. "Capital allocation and delegation of decision-making authority within firms," Journal of Financial Economics, Elsevier, vol. 115(3), pages 449-470.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicole Bauerle & Tomer Shushi, 2019. "Risk Management with Tail Quasi-Linear Means," Papers 1902.06941, arXiv.org, revised Jan 2020.
    2. Amen Aissi Harzallah & Mouna Boujelbene Abbes, 2020. "The Impact of Financial Crises on the Asset Allocation: Classical Theory Versus Behavioral Theory," Journal of Interdisciplinary Economics, , vol. 32(2), pages 218-236, July.
    3. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    4. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    5. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    6. 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.
    7. Wang, Haijun & Tan, Jie & Guo, Shuojia & Wang, Shenhao, 2018. "High-value transportation disruption risk management: Shipment insurance with declared value," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 293-310.
    8. Cristinca FULGA, 2017. "Integrated Decision Support System for Portfolio Selection with Enhanced Behavioral Content," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(3), pages 127-142.
    9. Ulrike Malmendier & Vincenzo Pezone & Hui Zheng, 2023. "Managerial Duties and Managerial Biases," Management Science, INFORMS, vol. 69(6), pages 3174-3201, June.
    10. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    11. Marc Peter Radke & Manuel Rupprecht, 2021. "Household Wealth: Low-Yielding and Poorly Structured?," JRFM, MDPI, vol. 14(3), pages 1-40, March.
    12. repec:cep:stieop:49 is not listed on IDEAS
    13. Laura Alfaro & Nick Bloom & Paola Conconi & Harald Fadinger & Patrick Legros & Andrew F Newman & Raffaella Sadun & John Van Reenen, 2024. "Come Together: Firm Boundaries and Delegation," Journal of the European Economic Association, European Economic Association, vol. 22(1), pages 34-72.
    14. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2016. "Efficient skewness/semivariance portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 331-346, September.
    15. Oriana Bandiera & Renata Lemos & Andrea Prat & Raffaella Sadun, 2018. "Managing the Family Firm: Evidence from CEOs at Work," The Review of Financial Studies, Society for Financial Studies, vol. 31(5), pages 1605-1653.
    16. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    17. Bastien Drut, 2010. "Sovereign Bonds and Socially Responsible Investment," Journal of Business Ethics, Springer, vol. 92(1), pages 131-145, April.
    18. Zhe Li & Oksana Pryshchepa & Bo Wang, 2023. "Financial experts on the top management team: Do they reduce investment inefficiency?," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 50(1-2), pages 198-235, January.
    19. Leslie A. Robinson & Phillip C. Stocken, 2013. "Location of Decision Rights Within Multinational Firms," Journal of Accounting Research, Wiley Blackwell, vol. 51(5), pages 1261-1297, December.
    20. Dongmin Kong & Ling Zhu & Ni Qin, 2022. "Does corruption shape firm centralisation? Evidence from state‐owned enterprises in China," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 62(3), pages 3365-3395, September.
    21. Dasgupta, Amil & Fos, Vyacheslav & Sautner, Zacharias, 2021. "Institutional investors and corporate governance," LSE Research Online Documents on Economics 112114, London School of Economics and Political Science, LSE Library.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:6:y:2018:i:1:p:19-:d:134997. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.