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

Author

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  • 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
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    References listed on IDEAS

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    1. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
    2. 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.
    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. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. 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.
    8. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
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    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.

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