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Backtesting Expected Shortfall: a simple recipe?

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  • Felix Moldenhauer
  • Marcin Pitera

Abstract

We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of Expected Shortfall with respect to its target confidence level we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient backtesting framework for unconditional coverage of Expected Shortfall in a natural extension of the regulatory traffic-light approach for Value-at-Risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures.

Suggested Citation

  • Felix Moldenhauer & Marcin Pitera, 2017. "Backtesting Expected Shortfall: a simple recipe?," Papers 1709.01337, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1709.01337
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    References listed on IDEAS

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    1. Wong, Woon K., 2008. "Backtesting trading risk of commercial banks using expected shortfall," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1404-1415, July.
    2. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    3. Tobias Fissler & Johanna F. Ziegel & Tilmann Gneiting, 2015. "Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting," Papers 1507.00244, arXiv.org, revised Jul 2015.
    4. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
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    Cited by:

    1. Spring, Konstantin, 2021. "Backtesting the Expected Shortfall," Junior Management Science (JUMS), Junior Management Science e. V., vol. 6(3), pages 590-636.

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