IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v234y2014i2p481-490.html
   My bibliography  Save this article

Inverse portfolio problem with mean-deviation model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713003822
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.04.056?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Roell, Ailsa A, 1987. "Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 97(388a), pages 143-159, Supplemen.
    4. Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2009. "Maximum Entropy Principle with General Deviation Measures," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 445-467, May.
    5. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    8. Rose‐Anne Dana, 2005. "A Representation Result For Concave Schur Concave Functions," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 613-634, October.
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    10. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    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. 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.

    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. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
    2. Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2012. "Mean‐Deviation Analysis in the Theory of Choice," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1277-1292, August.
    3. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    4. Bogdan Grechuk & Michael Zabarankin, 2012. "Optimal risk sharing with general deviation measures," Annals of Operations Research, Springer, vol. 200(1), pages 9-21, November.
    5. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    6. Allen, D.E. & McAleer, M.J. & Powell, R.J. & Singh, A.K., 2015. "Down-side Risk Metrics as Portfolio Diversification Strategies across the GFC," Econometric Institute Research Papers EI2015-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Benati, S. & Conde, E., 2022. "A relative robust approach on expected returns with bounded CVaR for portfolio selection," European Journal of Operational Research, Elsevier, vol. 296(1), pages 332-352.
    8. Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    10. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    11. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2014. "European Market Portfolio Diversifcation Strategies across the GFC," Working Papers in Economics 14/25, University of Canterbury, Department of Economics and Finance.
    12. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    13. Grechuk, Bogdan & Zabarankin, Michael, 2018. "Direct data-based decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 267(1), pages 200-211.
    14. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    15. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    16. Marcelo Brutti Righi, 2017. "Closed spaces induced by deviation measures," Economics Bulletin, AccessEcon, vol. 37(3), pages 1781-1784.
    17. David E. Allen & Michael McAleer & Shelton Peiris & Abhay K. Singh, 2014. "Hedge Fund Portfolio Diversification Strategies Across the GFC," Working Papers in Economics 14/27, University of Canterbury, Department of Economics and Finance.
    18. Berkhouch, Mohammed & Lakhnati, Ghizlane, 2017. "Extended Gini-type measures of risk and variability," MPRA Paper 80329, University Library of Munich, Germany.
    19. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
    20. Palczewski, Andrzej & Palczewski, Jan, 2019. "Black–Litterman model for continuous distributions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 708-720.

    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:eee:ejores:v:234:y:2014:i:2:p:481-490. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.