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Unexpected shortfalls of Expected Shortfall: Extreme default profiles and regulatory arbitrage

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  • Koch-Medina, Pablo
  • Munari, Cosimo

Abstract

The purpose of this paper is to dispel some common misunderstandings about capital adequacy rules based on Expected Shortfall. We establish that, from a theoretical perspective, Expected Shortfall based regulation can provide a misleading assessment of tail behavior, does not necessarily protect liability holders’ interests much better than Value-at-Risk based regulation, and may also allow for regulatory arbitrage when used as a global solvency measure. We also show that, for a value-maximizing financial institution, the benefits derived from protecting its franchise may not be sufficient to disincentivize excessive risk taking. We further interpret our results in the context of portfolio risk measurement. Our results do not invalidate the possible merits of Expected Shortfall as a risk measure but instead highlight the need for its cautious use in the context of capital adequacy regimes and of portfolio risk control.

Suggested Citation

  • Koch-Medina, Pablo & Munari, Cosimo, 2016. "Unexpected shortfalls of Expected Shortfall: Extreme default profiles and regulatory arbitrage," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 141-151.
    • Handle: RePEc:eee:jbfina:v:62:y:2016:i:c:p:141-151
    DOI: 10.1016/j.jbankfin.2015.11.006
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    Citations

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    Cited by:

    1. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    2. Matteo Burzoni & Cosimo Munari & Ruodu Wang, 2020. "Adjusted Expected Shortfall," Papers 2007.08829, arXiv.org, revised Aug 2021.
    3. Polyzos, Stathis & Samitas, Aristeidis & Kampouris, Ilias, 2021. "Economic stimulus through bank regulation: Government responses to the COVID-19 crisis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    4. Burzoni, Matteo & Munari, Cosimo & Wang, Ruodu, 2022. "Adjusted Expected Shortfall," Journal of Banking & Finance, Elsevier, vol. 134(C).
    5. Enrique Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2021. "Backtesting expected shortfall for world stock index ETFs with extreme value theory and Gram–Charlier mixtures," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4163-4189, July.
    6. Cosimo Munari & Stefan Weber & Lutz Wilhelmy, 2023. "Capital requirements and claims recovery: A new perspective on solvency regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 329-380, June.
    7. Martin Herdegen & Nazem Khan, 2022. "Mean‐ρ$\rho$ portfolio selection and ρ$\rho$‐arbitrage for coherent risk measures," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 226-272, January.
    8. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.
    9. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.
    10. Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised Feb 2024.
    11. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    12. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Documents de travail du Centre d'Economie de la Sorbonne 16034rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    13. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Post-Print halshs-01317391, HAL.
    14. Gómez, Fabio & Tang, Qihe & Tong, Zhiwei, 2022. "The gradient allocation principle based on the higher moment risk measure," Journal of Banking & Finance, Elsevier, vol. 143(C).
    15. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.
    16. Asimit, Alexandru V. & Li, Jinzhu, 2016. "Extremes for coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 332-341.
    17. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Risk quantification for commodity ETFs: Backtesting value-at-risk and expected shortfall," International Review of Financial Analysis, Elsevier, vol. 70(C).
    18. M. Burzoni & I. Peri & C. M. Ruffo, 2017. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1735-1743, November.
    19. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    20. Osmundsen, Kjartan Kloster, 2018. "Using expected shortfall for credit risk regulation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 57(C), pages 80-93.

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    More about this item

    Keywords

    Expected Shortfall; Value-at-risk; Financial regulation; Tail behavior; Default behavior;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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