IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v81y2021i2d10.1007_s10898-021-01039-6.html
   My bibliography  Save this article

Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach

Author

Listed:
  • Roberto Baviera

    (Politecnico di Milano)

  • Giulia Bianchi

    (Politecnico di Milano)

Abstract

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach and for the special case with the additional constraint of a constant mean vector considered in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Moreover, we prove in two relevant cases—the minimum-variance case and the symmetric case, i.e. when all assets have the same mean—that the analytical solutions in the alternative model and in the nominal one are equal; we show that this corresponds to the situation when model risk reduces to estimation risk.

Suggested Citation

  • Roberto Baviera & Giulia Bianchi, 2021. "Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach," Journal of Global Optimization, Springer, vol. 81(2), pages 469-491, October.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-01039-6
    DOI: 10.1007/s10898-021-01039-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01039-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-021-01039-6?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. Penev, Spiridon & Shevchenko, Pavel V. & Wu, Wei, 2019. "The impact of model risk on dynamic portfolio selection under multi-period mean-standard-deviation criterion," European Journal of Operational Research, Elsevier, vol. 273(2), pages 772-784.
    2. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
    3. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    4. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    7. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    8. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
    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. Zhijun Xu & Jing Zhou, 2023. "A simultaneous diagonalization based SOCP relaxation for portfolio optimization with an orthogonality constraint," Computational Optimization and Applications, Springer, vol. 85(1), pages 247-261, May.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.

    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. Roberto Baviera & Giulia Bianchi, 2019. "Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach," Papers 1902.06623, arXiv.org, revised Dec 2019.
    2. Spiridon Penev & Pavel V. Shevchenko & Wei Wu, 2021. "The impact of model risk on dynamic portfolio selection under multi-period mean-standard-deviation criterion," Papers 2108.02633, arXiv.org.
    3. Penev, Spiridon & Shevchenko, Pavel V. & Wu, Wei, 2019. "The impact of model risk on dynamic portfolio selection under multi-period mean-standard-deviation criterion," European Journal of Operational Research, Elsevier, vol. 273(2), pages 772-784.
    4. Detering, Nils & Packham, Natalie, 2018. "Model risk of contingent claims," IRTG 1792 Discussion Papers 2018-036, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Yu Feng & Ralph Rudd & Christopher Baker & Qaphela Mashalaba & Melusi Mavuso & Erik Schlögl, 2021. "Quantifying the Model Risk Inherent in the Calibration and Recalibration of Option Pricing Models," Risks, MDPI, vol. 9(1), pages 1-20, January.
    6. Sebastian Jaimungal & Silvana M. Pesenti & Leandro S'anchez-Betancourt, 2022. "Minimal Kullback-Leibler Divergence for Constrained L\'evy-It\^o Processes," Papers 2206.14844, arXiv.org, revised Aug 2022.
    7. Mohammed Berkhouch & Fernanda Maria Müller & Ghizlane Lakhnati & Marcelo Brutti Righi, 2022. "Deviation-Based Model Risk Measures," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 527-547, February.
    8. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    9. Jan Obłój & Johannes Wiesel, 2021. "Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1454-1493, October.
    10. Yu Feng, 2019. "Non-Parametric Robust Model Risk Measurement with Path-Dependent Loss Functions," Papers 1903.00590, arXiv.org.
    11. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    12. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    13. Valeriane Jokhadze & Wolfgang M. Schmidt, 2020. "Measuring Model Risk In Financial Risk Management And Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-37, April.
    14. Mariano González-Sánchez & Eva M. Ibáñez Jiménez & Ana I. Segovia San Juan, 2022. "Market and model risks: a feasible joint estimate methodology," Risk Management, Palgrave Macmillan, vol. 24(3), pages 187-213, September.
    15. Li, Jing, 2018. "Essays on model uncertainty in financial models," Other publications TiSEM 202cd910-7ef1-4db4-94ae-d, Tilburg University, School of Economics and Management.
    16. Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2015. "What's in a ball? Constructing and characterizing uncertainty sets," Papers 1510.01675, arXiv.org.
    17. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    18. Tunaru, Radu & Zheng, Teng, 2017. "Parameter estimation risk in asset pricing and risk management: A Bayesian approach," International Review of Financial Analysis, Elsevier, vol. 53(C), pages 80-93.
    19. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    20. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.

    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:spr:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-01039-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.