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Expected Shortfall: a natural coherent alternative to Value at Risk

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  • Carlo Acerbi
  • Dirk Tasche

Abstract

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

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  • Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0105191
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    File URL: http://arxiv.org/pdf/cond-mat/0105191
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    2. Dirk Tasche, 2001. "Conditional Expectation as Quantile Derivative," Papers math/0104190, arXiv.org.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
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