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On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall

Author

Listed:
  • Yamai, Yasuhiro

    (Institute for Monetary and Economic Studies, Bank of Japan)

  • Yoshiba, Toshinao

    (Institute for Monetary and Economic Studies, Bank of Japan)

Abstract

Value-at-risk (VaR) has become a standard measure used in financial risk management due to its conceptual simplicity, computational facility, and ready applicability. However, many authors claim that VaR has several conceptual problems. Artzner et al. (1997, 1999), for example, have cited the following shortcomings of VaR. (1) VaR measures only percentiles of profit-loss distributions, and thus disregards any loss beyond the VaR level ("tail risk"), and (2) VaR is not coherent since it is not sub-additive. To alleviate the problems inherent in VaR, the use of expected shortfall is proposed. In this paper, we provide an overview of studies comparing VaR and expected shortfall to draw practical implications for financial risk management. In particular, we illustrate how tail risk can bring serious practical problems in some cases.

Suggested Citation

  • Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 57-85, January.
    • Handle: RePEc:ime:imemes:v:20:y:2002:i:1:p:57-85
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    Cited by:

    1. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & Maasoumi, Esfandiar & McAleer, Michael & Pérez-Amaral, Teodosio, 2019. "Choosing expected shortfall over VaR in Basel III using stochastic dominance," International Review of Economics & Finance, Elsevier, vol. 60(C), pages 95-113.
    2. Fermanian, Jean-David & Scaillet, Olivier, 2005. "Sensitivity analysis of VaR and Expected Shortfall for portfolios under netting agreements," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 927-958, April.
    3. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
    4. Mario Domingues de Paula Simões & Marcelo Cabus Klotzle & Antonio Carlos Figueiredo Pinto & Leonardo Lima Gomes, 2016. "Electricity prices forecast analysis using the extreme value theory," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 1-22.
    5. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, March.
    6. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.
    7. Kim, Minjo & Lee, Sangyeol, 2016. "Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 1-19.
    8. Srečko Devjak & Andraž Grum, 2006. "Third Moment of Yield Probability Distributions for Instruments on Slovenian Financial Markets," Prague Economic Papers, Prague University of Economics and Business, vol. 2006(4), pages 364-373.
    9. Yam Wing Siu, 2018. "Volatility Forecast by Volatility Index and Its Use as a Risk Management Tool Under a Value-at-Risk Approach," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-48, June.
    10. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    11. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    12. Deepak K. Jadhav & Ramanathan Thekke Variyam, 2023. "Modified Expected Shortfall: a Coherent Risk Measure for Elliptical Family of Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 234-256, May.
    13. Annalisa Di Clemente, 2019. "Comparing Different Systemic Risk Measures for European Banking System," International Business Research, Canadian Center of Science and Education, vol. 12(1), pages 35-53, January.
    14. Kerkhof, F.L.J. & Melenberg, B., 2002. "Backtesting for Risk-Based Regulatory Capital," Other publications TiSEM 2363cf81-9720-41f2-913c-f, Tilburg University, School of Economics and Management.
    15. Sasa Zikovic & Randall Filer, 2009. "Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets," CESifo Working Paper Series 2820, CESifo.
    16. Su, Jung-Bin, 2014. "Empirical analysis of long memory, leverage, and distribution effects for stock market risk estimates," The North American Journal of Economics and Finance, Elsevier, vol. 30(C), pages 1-39.
    17. Juraj Pekár & Mário Pčolár, 2022. "Empirical distribution of daily stock returns of selected developing and emerging markets with application to financial risk management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 699-731, June.
    18. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    19. Andrea Rigamonti, 2020. "Mean-Variance Optimization Is a Good Choice, But for Other Reasons than You Might Think," Risks, MDPI, vol. 8(1), pages 1-16, March.
    20. Sebastian Bayer & Timo Dimitriadis, 2022. "Regression-Based Expected Shortfall Backtesting [Backtesting Expected Shortfall]," Journal of Financial Econometrics, Oxford University Press, vol. 20(3), pages 437-471.
    21. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    22. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    23. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    24. 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.
    25. Hammadi Zouari, 2022. "On the Effectiveness of Stock Index Futures for Tail Risk Protection," International Journal of Economics and Financial Issues, Econjournals, vol. 12(3), pages 38-52, May.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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