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Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors

Author

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  • Dobrislav Dobrev∗

    (Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USA)

  • Travis D. Nesmith

    (Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USA)

  • Dong Hwan Oh

    (Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USA)

Abstract

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the recent survey by Nadarajah et al. (2014) on estimation methods for expected shortfall. In particular, we show that the correction we provide in the popular multivariate Student t setting eliminates understatement of expected shortfall by a factor varying from at least four to more than 100 across different tail quantiles and degrees of freedom. As such, the resulting economic impact in financial risk management applications could be significant. We further correct such errors encountered also in closely related results in Kamdem (2007 and 2009) for mixtures of elliptical distributions. More generally, our findings point to the extra scrutiny required when deploying new methods for expected shortfall estimation in practice.

Suggested Citation

  • Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.
    • Handle: RePEc:gam:jjrfmx:v:10:y:2017:i:1:p:5-:d:89239
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    References listed on IDEAS

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    Cited by:

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    3. Janine Balter & Alexander J. McNeil, 2018. "On the Basel Liquidity Formula for Elliptical Distributions," Risks, MDPI, vol. 6(3), pages 1-13, September.
    4. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2019. "Quantifying Risk in Traditional Energy and Sustainable Investments," Sustainability, MDPI, vol. 11(3), pages 1-22, January.
    5. Maria Grazia Zoia & Gianmarco Vacca & Laura Barbieri, 2020. "Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions," Risks, MDPI, vol. 8(4), pages 1-21, November.

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    More about this item

    Keywords

    expectedshortfall; ellipticaldistributions; multivariateStudent t distribution; mixturesof elliptical distributions; accurate closed-form expression;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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