IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1910.00640.html
   My bibliography  Save this paper

On the Concavity of Expected Shortfall

Author

Listed:
  • Mikhail Tselishchev

Abstract

It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this short paper we prove that Expected Shortfall is a concave risk measure with respect to probability distributions, i. e. Expected Shortfall of a finite mixture of arbitrary risk positions is not lower than the linear combination of Expected Shortfalls of the same risk positions (with the same weights as in the mixture).

Suggested Citation

  • Mikhail Tselishchev, 2019. "On the Concavity of Expected Shortfall," Papers 1910.00640, arXiv.org.
    • Handle: RePEc:arx:papers:1910.00640
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1910.00640
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. Carlo Acerbi, 2001. "Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem," Papers cond-mat/0107190, arXiv.org.
    3. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maria Logvaneva & Mikhail Tselishchev, 2022. "On a Stochastic Model of Diversification," Papers 2204.01284, arXiv.org.

    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. 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).
    2. Alexis Bonnet & Isabelle Nagot, 2005. "Methodology of measuring performance in alternative investment," Post-Print halshs-00196443, HAL.
    3. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
    4. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    5. Maria Logvaneva & Mikhail Tselishchev, 2022. "On a Stochastic Model of Diversification," Papers 2204.01284, arXiv.org.
    6. Manuel Kleinknecht & Wing Lon Ng, 2015. "Minimizing Basel III Capital Requirements with Unconditional Coverage Constraint," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 22(4), pages 263-281, October.
    7. 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.
    8. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    9. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    10. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    11. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    12. Eric Beutner & Henryk Zähle, 2018. "Bootstrapping Average Value at Risk of Single and Collective Risks," Risks, MDPI, vol. 6(3), pages 1-30, September.
    13. Panna, Miskolczi, 2017. "Note On Simple And Logarithmic Return," APSTRACT: Applied Studies in Agribusiness and Commerce, AGRIMBA, vol. 11(1-2), September.
    14. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    15. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    16. Gürtler, Marc & Hibbeln, Martin & Vöhringer, Clemens, 2007. "Measuring concentration risk for regulatory purposes," Working Papers IF26V4, Technische Universität Braunschweig, Institute of Finance.
    17. S. Broda & Juan Carlos Arismendi-Zambrano, 2020. "On Quadratic Forms in Multivariate Generalized Hyperbolic Random Vectors∗," Economics Department Working Paper Series n302-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    18. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    19. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    20. Carlo Acerbi, 2001. "Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem," Papers cond-mat/0107190, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1910.00640. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.