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Why risk is so hard to measure

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  • Danielsson, Jon
  • Zhou, Chen

Abstract

This paper analyzes the robustness of standard risk analysis techniques, with a special emphasis on the specifications in Basel III. We focus on the difference between Value– at–Risk and expected shortfall, the small sample properties of these risk measures and the impact of using an overlapping approach to construct data for longer holding periods. Overall, risk forecasts are extremely uncertain at low sample sizes. By comparing the estimation uncertainty, we find that Value–at–Risk is superior to expected shortfall and the time-scaling approach for risk forecasts with longer holding periods is preferable to using overlapping data.

Suggested Citation

  • Danielsson, Jon & Zhou, Chen, 2015. "Why risk is so hard to measure," LSE Research Online Documents on Economics 62002, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:62002
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    File URL: http://eprints.lse.ac.uk/62002/
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    References listed on IDEAS

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    1. 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.
    2. Danielsson, Jon & James, Kevin R. & Valenzuela, Marcela & Zer, Ilknur, 2016. "Model risk of risk models," Journal of Financial Stability, Elsevier, vol. 23(C), pages 79-91.
    3. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    4. Danielsson, Jon & Jorgensen, Bjorn N. & Sarma, Mandira & de Vries, Casper G., 2006. "Comparing downside risk measures for heavy tailed distributions," Economics Letters, Elsevier, vol. 92(2), pages 202-208, August.
    5. 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.
    6. 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.
    7. Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
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    Cited by:

    1. Alexandra-Maria Chiper, 2023. "Financial Risk Optimisation Methods: A Survey," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 31, pages 155-168, June.
    2. Bengtsson, Elias & Grothe, Magdalena & Lepers, Etienne, 2020. "Home, safe home: Cross-country monitoring framework for vulnerabilities in the residential real estate sector," Journal of Banking & Finance, Elsevier, vol. 112(C).
    3. Semih Atakan & Kerem Bülbül & Nilay Noyan, 2017. "Minimizing value-at-risk in single-machine scheduling," Annals of Operations Research, Springer, vol. 248(1), pages 25-73, January.
    4. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    5. Kubitza, Christian & Gründl, Helmut, 2016. "Systemic risk: Time-lags and persistence," ICIR Working Paper Series 20/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    6. Magdalena Grothe, 2020. "Monitoring Vulnerabilities in the Residential Real Estate Sector in Poland," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 2, pages 5-24.

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    More about this item

    Keywords

    value–at–risk; expected shortfall; finite sample properties; Basel II;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation

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