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

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  • Roberto Baviera
  • Giulia Bianchi

Abstract

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (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. In the minimum-variance case, we prove that the analytical solution is significantly different from the one found numerically by Glasserman and Xu (2014) and that model risk reduces to an estimation risk. A detailed numerical example is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1902.06623
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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.
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    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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