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A review of backtesting and backtesting procedures

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  • Sean D. Campbell

Abstract

This paper reviews a variety of backtests that examine the adequacy of Value-at-Risk (VaR) measures. These backtesting procedures are reviewed from both a statistical and risk management perspective. The properties of unconditional coverage and independence are defined and their relation to backtesting procedures is discussed. Backtests are then classified by whether they examine the unconditional coverage property, independence property, or both properties of a VaR measure. Backtests that examine the accuracy of a VaR model at several quantiles, rather than a single quantile, are also outlined and discussed. The statistical power properties of these tests are examined in a simulation experiment. Finally, backtests that are specified in terms of a pre-specified loss function are reviewed and their use in VaR validation is discussed.

Suggested Citation

  • 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.).
  • Handle: RePEc:fip:fedgfe:2005-21
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    References listed on IDEAS

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    1. 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, June.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    4. Jose A. Lopez, 1996. "Regulatory Evaluation of Value-at-Risk Models," Center for Financial Institutions Working Papers 96-51, Wharton School Center for Financial Institutions, University of Pennsylvania.
    5. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    6. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    7. Katerina Simons, 1996. "Value at risk: new approaches to risk management," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 3-13.
    8. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    9. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 201-242, October.
    10. Colleen Cassidy & Marianne Gizycki, 1997. "Measuring Traded Market Risk: Value-at-risk and Backtesting Techniques," RBA Research Discussion Papers rdp9708, Reserve Bank of Australia.
    11. Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
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    Citations

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    Cited by:

    1. Kulp-Tåg, Sofie, 2007. "An Empirical Investigation of Value-at-Risk in Long and Short Trading Positions," Working Papers 526, Hanken School of Economics.
    2. CARPANTIER, Jean - François, 2010. "Commodities inventory effect," CORE Discussion Papers 2010040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Ergün, A. Tolga & Jun, Jongbyung, 2010. "Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(3), pages 264-272, August.
    4. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    5. Pérignon, Christophe & Deng, Zi Yin & Wang, Zhi Jun, 2008. "Do banks overstate their Value-at-Risk?," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 783-794, May.
    6. Sabrina Khanniche, 2009. "Evaluation of Hedge Fund Returns Value at Risk Using GARCH Models," EconomiX Working Papers 2009-46, University of Paris Nanterre, EconomiX.
    7. repec:eee:empfin:v:42:y:2017:i:c:p:175-198 is not listed on IDEAS
    8. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    9. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    10. Gonzales-Martínez, Rolando, 2009. "La Gestión de Riesgo de Liquidez en Economías Emergentes: Un Modelo Valor-en-Riesgo (VaR) Paramétrico de Calibración Indirecta y una Aplicación al Sistema Financiero Boliviano
      [Liquidity Risk Manag
      ," MPRA Paper 14247, University Library of Munich, Germany.
    11. Christos Agiakloglou & Charalampos Agiropoulos, 2011. "The sensitivity of Value-at-Risk estimates using Monte Carlo approach," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 61(1-2), pages 7-12, January -.
    12. Evers, Corinna & Rohde, Johannes, 2014. "Model Risk in Backtesting Risk Measures," Hannover Economic Papers (HEP) dp-529, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2012. "Commodities volatility and the theory of storage," CORE Discussion Papers 2012037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    15. Christophe HURLIN & Sessi TOKPAVI, 2006. "Backtesting VaR Accuracy: A Simple and Powerful Test," LEO Working Papers / DR LEO 268, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.

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    Keywords

    Risk management ; Bank investments;

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