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Backtesting for risk-based regulatory capital

  • Kerkhof, Jeroen
  • Melenberg, Bertrand

In this paper we present a framework for backtesting all currently popular risk measurement methods (including value-at-risk and expected shortfall) using the functional delta method.Estimation risk can be taken explicitly into account.Based on a simulation study we provide evidence that tests for expected shortfall with acceptable low levels have a better performance than tests for value-at-risk in realistic financial sample sizes.We propose a way to determine multiplication factors, and find that the resulting regulatory capital scheme using expected shortfall compares favorably to the current Basle Accord backtesting scheme.

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Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 28 (2004)
Issue (Month): 8 (August)
Pages: 1845-1865

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Handle: RePEc:eee:jbfina:v:28:y:2004:i:8:p:1845-1865
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  1. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  2. Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO.
  3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  6. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  7. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, 06.
  8. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  9. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  10. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  11. Kerkhof, F.L.J. & Melenberg, B. & Schumacher, J.M., 2002. "Model Risk and Regulatory Capital," Discussion Paper 2002-27, Tilburg University, Center for Economic Research.
  12. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558,, revised Oct 2002.
  13. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295,, revised May 2002.
  14. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  15. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  16. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  17. 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.
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