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Inverse portfolio problem with mean-deviation model

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  • Grechuk, Bogdan
  • Zabarankin, Michael

Abstract

A Markowitz-type portfolio selection problem is to minimize a deviation measure of portfolio rate of return subject to constraints on portfolio budget and on desired expected return. In this context, the inverse portfolio problem is finding a deviation measure by observing the optimal mean-deviation portfolio that an investor holds. Necessary and sufficient conditions for the existence of such a deviation measure are established. It is shown that if the deviation measure exists, it can be chosen in the form of a mixed CVaR-deviation, and in the case of n risky assets available for investment (to form a portfolio), it is determined by a combination of (n+1) CVaR-deviations. In the later case, an algorithm for constructing the deviation measure is presented, and if the number of CVaR-deviations is constrained, an approximate mixed CVaR-deviation is offered as well. The solution of the inverse portfolio problem may not be unique, and the investor can opt for the most conservative one, which has a simple closed-form representation.

Suggested Citation

  • Grechuk, Bogdan & Zabarankin, Michael, 2014. "Inverse portfolio problem with mean-deviation model," European Journal of Operational Research, Elsevier, vol. 234(2), pages 481-490.
    • Handle: RePEc:eee:ejores:v:234:y:2014:i:2:p:481-490
    DOI: 10.1016/j.ejor.2013.04.056
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    References listed on IDEAS

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    Cited by:

    1. Saeed Shavvalpour & Hossein Khanjarpanah & Farhad Zamani & Armin Jabbarzadeh, 2017. "Petrochemical Products Market and Stock Market Returns: Empirical Evidence from Tehran Stock Exchange," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 21(2), pages 383-403, Spring.
    2. Bogdan Grechuk & Michael Zabarankin, 2017. "Synergy effect of cooperative investment," Annals of Operations Research, Springer, vol. 249(1), pages 409-431, February.
    3. Angelini, Pierpaolo & Maturo, Fabrizio, 2022. "The price of risk based on multilinear measures," International Review of Economics & Finance, Elsevier, vol. 81(C), pages 39-57.
    4. Martijn Pistorius & Mitja Stadje, 2016. "On Dynamic Deviation Measures and Continuous-Time Portfolio Optimisation," Papers 1604.08037, arXiv.org.
    5. Akhilesh KUMAR & Mohammad SHAHID, 2021. "Portfolio selection problem: Issues, challenges and future prospectus," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(4(629), W), pages 71-90, Winter.
    6. Bogdan Grechuk & Andrzej Palczewski & Jan Palczewski, 2018. "On the solution uniqueness in portfolio optimization and risk analysis," Papers 1810.11299, arXiv.org, revised Oct 2020.
    7. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
    8. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    9. Grechuk, Bogdan & Zabarankin, Michael, 2014. "Risk averse decision making under catastrophic risk," European Journal of Operational Research, Elsevier, vol. 239(1), pages 166-176.
    10. Hosseini-Nodeh, Zohreh & Khanjani-Shiraz, Rashed & Pardalos, Panos M., 2023. "Portfolio optimization using robust mean absolute deviation model: Wasserstein metric approach," Finance Research Letters, Elsevier, vol. 54(C).
    11. Grechuk, Bogdan & Zabarankin, Michael, 2018. "Direct data-based decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 267(1), pages 200-211.

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