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Portfolio optimization under Expected Shortfall: contour maps of estimation error

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  • Fabio Caccioli
  • Imre Kondor
  • Gábor Papp

Abstract

The contour maps of the error of historical and parametric estimates of the global minimum risk for large random portfolios optimized under the Expected Shortfall (ES) risk measure are constructed. Similar maps for the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.

Suggested Citation

  • Fabio Caccioli & Imre Kondor & Gábor Papp, 2018. "Portfolio optimization under Expected Shortfall: contour maps of estimation error," Quantitative Finance, Taylor & Francis Journals, vol. 18(8), pages 1295-1313, August.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:8:p:1295-1313
    DOI: 10.1080/14697688.2017.1390245
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    Citations

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    Cited by:

    1. Papp, Gábor & Kondor, Imre & Caccioli, Fabio, 2021. "Optimizing expected shortfall under an ℓ1 constraint—an analytic approach," LSE Research Online Documents on Economics 111051, London School of Economics and Political Science, LSE Library.
    2. Shanshan Jiang & Jie Wang & Ruiting Dong & Yutong Li & Min Xia, 2023. "Systemic Risk with Multi-Channel Risk Contagion in the Interbank Market," Sustainability, MDPI, vol. 15(3), pages 1-24, February.
    3. Cesarone, Francesco & Mango, Fabiomassimo & Mottura, Carlo Domenico & Ricci, Jacopo Maria & Tardella, Fabio, 2020. "On the stability of portfolio selection models," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 210-234.
    4. Anand Deo & Karthyek Murthy, 2020. "Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives," Papers 2008.09818, arXiv.org.
    5. G'abor Papp & Imre Kondor & Fabio Caccioli, 2021. "Optimizing Expected Shortfall under an $\ell_1$ constraint -- an analytic approach," Papers 2103.04375, arXiv.org.
    6. Axel Pruser & Imre Kondor & Andreas Engel, 2021. "Aspects of a phase transition in high-dimensional random geometry," Papers 2105.04395, arXiv.org, revised Jun 2021.

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