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Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization

Author

Listed:
  • Yamai, Yasuhiro

    (Institute for Monetary & Econ Studies, Bank of Japan)

  • Yoshiba, Toshinao

    (Institute for Monetary & Econ Studies, Bank of Japan)

Abstract

We compare expected shortfall with value-at-risk (VaR) in three aspects: estimation errors, decomposition into risk factors, and optimization. We describe the advantages and the disadvantages of expected shortfall over VaR. We show that expected shortfall is easily decomposed and optimized while VaR is not. We also show that expected shortfall needs a larger size of sample than VaR for the same level of accuracy.

Suggested Citation

  • Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
  • Handle: RePEc:ime:imemes:v:20:y:2002:i:1:p:87-121
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    File URL: http://www.imes.boj.or.jp/research/papers/english/me20-1-4.pdf
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    References listed on IDEAS

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    1. Okina, Kunio & Shirakawa, Masaaki & Shiratsuka, Shigenori, 2001. "The Asset Price Bubble and Monetary Policy: Japan's Experience in the Late 1980s and the Lessons: Background Paper," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 395-450, February.
    2. Rudebusch, Glenn D. & Svensson, Lars E. O., 2002. "Eurosystem monetary targeting: Lessons from U.S. data," European Economic Review, Elsevier, vol. 46(3), pages 417-442, March.
    3. Higo, Masahiro & Nakada, Sachiko-Kuroda, 1999. "What Determines the Relation between the Output Gap and Inflation ? An International Comparison of Inflation Expectations and Staggered Wage Adjustment," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 17(3), pages 129-155, December.
    4. Mori, Naruki & Shiratsuka, Shigenori & Taguchi, Hiroo, 2001. "Policy Responses to the Post-bubble Adjustments in Japan: A Tentative Review," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 53-102, February.
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    Citations

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    Cited by:

    1. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Esfandiar Maasoumi & Michael McAleer & Teodosio Pérez-Amaral, 2015. "A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?," Tinbergen Institute Discussion Papers 15-056/III, Tinbergen Institute.
    2. Silvia Stanescu & Radu Tunaru, 2013. "Quantifying the uncertainty in VaR and expected shortfall estimates," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 15, pages 357-372 Edward Elgar Publishing.
    3. Juan Carlos Escanciano & Zaichao Du, 2015. "Backtesting Expected Shortfall: Accounting for Tail Risk," Caepr Working Papers 2015-001, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    4. Cotter, John & Dowd, Kevin, 2007. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," MPRA Paper 3504, University Library of Munich, Germany.
    5. Marius ACATRINEI, 2015. "Individual contributions to portfolio risk: risk decomposition for the BET-FI index," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 3(1), pages 75-80, June.
    6. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-14, February.
    7. Kerkhof, F.L.J. & Melenberg, B. & Schumacher, J.M., 2003. "Testing Expected Shortfall Models for Derivative Positions," Discussion Paper 2003-24, Tilburg University, Center for Economic Research.
    8. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo Group Munich.
    9. Gyöngyi Bugár & Anita Ratting, 2016. "Revision of the quantification of market risk in the Basel III regulatory framework," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 15(1), pages 33-50.
    10. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.
    11. Takashi Isogai, 2014. "Benchmarking of Unconditional VaR and ES Calculation Methods: A Comparative Simulation Analysis with Truncated Stable Distribution," Bank of Japan Working Paper Series 14-E-1, Bank of Japan.
    12. Luting Li & Hao Xing, 2018. "Capital allocation under Fundamental Review of Trading Book," Papers 1801.07358, arXiv.org.
    13. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer;Vienna University of Economics and Business, vol. 66(2), pages 75-115, April.
    14. Takaaki Koike & Mihoko Minami, 2017. "Estimation of Risk Contributions with MCMC," Papers 1702.03098, arXiv.org.
    15. 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.
    16. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    17. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    18. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.

    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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