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Robustness and sensitivity analysis of risk measurement procedures

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Author Info

  • Rama Cont
  • Romain Deguest
  • Giacomo Scandolo

Abstract

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a 'risk measure' that summarizes the risk of the portfolio. We define the notion of 'risk measurement procedure', which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 10 (2010)
Issue (Month): 6 ()
Pages: 593-606

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Handle: RePEc:taf:quantf:v:10:y:2010:i:6:p:593-606

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Related research

Keywords: Risk management; Risk measurement; Coherent risk measures; Law invariant risk measures; Value-at-Risk; Expected shortfall;

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Citations

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Cited by:
  1. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
  2. Sibbertsen, Philipp & Stahl, Gerhard & Luedtke, Corinna, 2008. "Measuring Model Risk," Hannover Economic Papers (HEP) dp-409, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  3. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
  4. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Post-Print hal-00921283, HAL.
  5. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
  6. Pablo Koch-Medina & Cosimo Munari, 2014. "Law-invariant risk measures: extension properties and qualitative robustness," Papers 1401.3121, arXiv.org.
  7. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
  8. Volker Kr\"atschmer & Alexander Schied & Henryk Z\"ahle, 2014. "Quasi-Hadamard differentiability of general risk functionals and its application," Papers 1401.3167, arXiv.org.
  9. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, Open Access Journal, vol. 2(1), pages 25-48, February.
  10. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
  11. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
  12. Volker Kr\"atschmer & Alexander Schied & Henryk Z\"ahle, 2012. "Comparative and qualitative robustness for law-invariant risk measures," Papers 1204.2458, arXiv.org, revised Jan 2014.
  13. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Feb 2014.
  14. Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Working Papers hal-00629929, HAL.
  15. Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
  16. Ruodu Wang & Johanna F. Ziegel, 2014. "Distortion Risk Measures and Elicitability," Papers 1405.3769, arXiv.org, revised May 2014.
  17. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Dec 2013.
  18. Hirbod Assa, 2014. "On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums," Papers 1406.2950, arXiv.org.
  19. Jun-ya Gotoh & Akiko Takeda, 2011. "On the role of norm constraints in portfolio selection," Computational Management Science, Springer, vol. 8(4), pages 323-353, November.

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