IDEAS home Printed from https://ideas.repec.org/p/arx/papers/cond-mat-0203558.html
   My bibliography  Save this paper

Expected Shortfall and Beyond

Author

Listed:
  • Dirk Tasche

Abstract

Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is defined as a fixed level quantile of the random variable under consideration, is the most popular risk measure. Unfortunately, it fails to reward diversification, as it is not "subadditive". In the search for a suitable alternative to value-at-risk, "Expected Shortfall" (or "conditional value-at-risk" or "tail value-at-risk") has been characterized as the smallest "coherent" and "law invariant" risk measure to dominate value-at-risk. We discuss these and some other properties of Expected Shortfall as well as its generalization to a class of coherent risk measures which can incorporate higher moment effects. Moreover, we suggest a general method on how to attribute Expected Shortfall "risk contributions" to portfolio components. Key words: Expected Shortfall; Value-at-Risk; Spectral Risk Measure; coherence; risk contribution.

Suggested Citation

  • Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
  • Handle: RePEc:arx:papers:cond-mat/0203558
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/cond-mat/0203558
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    2. Winfried G. Hallerbach, 1999. "Decomposing Portfolio Value-at-Risk: A General Analysis," Tinbergen Institute Discussion Papers 99-034/2, Tinbergen Institute.
    3. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    5. Dirk Tasche, 2001. "Conditional Expectation as Quantile Derivative," Papers math/0104190, arXiv.org.
    6. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tasche, Dirk, 2002. "Expected shortfall and beyond," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1519-1533, July.
    2. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    3. Inui, Koji & Kijima, Masaaki, 2005. "On the significance of expected shortfall as a coherent risk measure," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 853-864, April.
    4. Alexandre Kurth & Dirk Tasche, 2002. "Credit Risk Contributions to Value-at-Risk and Expected Shortfall," Papers cond-mat/0207750, arXiv.org, revised Nov 2002.
    5. Cossette, Hélène & Mailhot, Mélina & Marceau, Étienne, 2012. "TVaR-based capital allocation for multivariate compound distributions with positive continuous claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 247-256.
    6. Alexis Bonnet & Isabelle Nagot, 2005. "Methodology of measuring performance in alternative investment," Cahiers de la Maison des Sciences Economiques b05078, Université Panthéon-Sorbonne (Paris 1).
    7. Monica Billio & Lorenzo Frattarolo & Loriana Pelizzon, 2016. "Hedge Fund Tail Risk: An investigation in stressed markets, extended version with appendix," Working Papers 2016:01, Department of Economics, University of Venice "Ca' Foscari".
    8. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
    9. Leitner Johannes, 2006. "Monetary utility over coherent risk ratios," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-15, July.
    10. So Yeon Chun & Alexander Shapiro & Stan Uryasev, 2012. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," Operations Research, INFORMS, vol. 60(4), pages 739-756, August.
    11. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2009. "Stable allocations of risk," Games and Economic Behavior, Elsevier, vol. 67(1), pages 266-276, September.
    12. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    13. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    14. Brian Tomlin & Yimin Wang, 2005. "On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 37-57, June.
    15. Cossette, Hélène & Côté, Marie-Pier & Marceau, Etienne & Moutanabbir, Khouzeima, 2013. "Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 560-572.
    16. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2015. "Linear vs. quadratic portfolio selection models with hard real-world constraints," Computational Management Science, Springer, vol. 12(3), pages 345-370, July.
    17. Melnikov, Alexander & Smirnov, Ivan, 2012. "Dynamic hedging of conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 182-190.
    18. Brandtner, Mario & Kürsten, Wolfgang, 2014. "Decision making with Conditional Value-at-Risk and spectral risk measures: The problem of comparative risk aversion," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100615, Verein für Socialpolitik / German Economic Association.
    19. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    20. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0203558. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.