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Backtesting for Risk-Based Regulatory Capital

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Author Info

  • Kerkhof, F.L.J.
  • Melenberg, B.

    (Tilburg University, Center for Economic Research)

Abstract

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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2002-110.

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Date of creation: 2002
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Handle: RePEc:dgr:kubcen:2002110

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Keywords: risk management; capital;

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References

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  1. 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.
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  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
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  7. 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.
  8. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
  9. Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO.
  10. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  11. 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.
  12. 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.
  13. 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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  16. 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.
  17. 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.
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Citations

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Cited by:
  1. Aramonte, Sirio & Giudice Rodriguez, Marius del & Wu, Jason, 2013. "Dynamic factor Value-at-Risk for large heteroskedastic portfolios," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4299-4309.
  2. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
  3. Clara Cardone-Riportella & Antonio Trujillo-Ponce & Anahí Briozzo, 2013. "Analyzing the role of mutual guarantee societies on bank capital requirements for small and medium-sized enterprises," Journal of Economic Policy Reform, Taylor & Francis Journals, vol. 16(2), pages 142-159, June.
  4. Clara Cardone Riportella & Antonio Trujillo Ponce & Maria Jose Casasola, 2008. "Credit risk mitigation and SMEs bank financing in Basel II : the case of the Loan Guarantee Associations," Business Economics Working Papers wb084011, Universidad Carlos III, Departamento de Economía de la Empresa.
  5. Wong, Woon K., 2010. "Backtesting value-at-risk based on tail losses," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 526-538, June.
  6. Kerkhof, F.L.J., 2003. "Model Risk Analysis for Risk Management and Option Pricing," Open Access publications from Tilburg University urn:nbn:nl:ui:12-119331, Tilburg University.
  7. Escanciano, J. C. & Olmo, J., 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," Working Papers 07/11, Department of Economics, City University London.
  8. Lönnbark, Carl, 2013. "On the role of the estimation error in prediction of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 847-853.
  9. Memmel, Christoph & Wehn, Carsten, 2005. "The supervisor's portfolio: the market price risk of German banks from 2001 to 2003 - Analysis and models for risk aggregation," Discussion Paper Series 2: Banking and Financial Studies 2005,02, Deutsche Bundesbank, Research Centre.
  10. Almeida, Caio & Vicente, José, 2009. "Are interest rate options important for the assessment of interest rate risk?," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1376-1387, August.
  11. Wong, Woon K., 2008. "Backtesting trading risk of commercial banks using expected shortfall," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1404-1415, July.
  12. Chen, Qian & Gerlach, Richard H., 2013. "The two-sided Weibull distribution and forecasting financial tail risk," International Journal of Forecasting, Elsevier, vol. 29(4), pages 527-540.
  13. Melenberg, B. & Polbennikov, S.Y., 2005. "Testing for Mean-Coherent Regular Risk Spanning," Discussion Paper 2005-99, Tilburg University, Center for Economic Research.
  14. Wong, Woon K & Copeland, Laurence, 2008. "Risk Measurement and Management in a Crisis-Prone World," Cardiff Economics Working Papers E2008/14, Cardiff University, Cardiff Business School, Economics Section.
  15. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
  16. Sean D. Campbell, 2005. "A review of backtesting and backtesting procedures," Finance and Economics Discussion Series 2005-21, Board of Governors of the Federal Reserve System (U.S.).
  17. Polbennikov, S.Y. & Melenberg, B., 2005. "Mean-Coherent Risk and Mean-Variance Approaches in Portfolio Selection: An Empirical Comparison," Discussion Paper 2005-100, Tilburg University, Center for Economic Research.

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