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Estimation Risk in Financial Risk Management

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  • Peter Christoffersen

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  • Sílvia Gonçalves

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Abstract

Value-at-Risk (VaR) and Expected Shortfall (ES) are increasingly used in portfolio risk measurement, risk capital allocation and performance attribution. Financial risk managers are therefore rightfully concerned with the precision of typical VaR and ES techniques. The purpose of this paper is exactly to assess the precision of common models and to quantify the magnitude of the estimation error by constructing confidence bands around the point VaR and ES forecasts. A key challenge in constructing proper confidence bands arises from the conditional variance dynamics typically found in speculative returns. Our paper suggests a resampling technique which accounts for parameter estimation error in dynamic models of portfolio variance. In a Monte Carlo study we find that commonly used practitioner methods such as Historical Simulation, which calculates the empirical quantile on a moving window of returns, implies 90% VaR confidence intervals that are too narrow and that contain as few as 20% of the true VaRs. Other methods which properly account for conditional variance dynamics, such as Filtered Historical Simulation instead imply 90% VaR confidence intervals that contain close to 90% of the true VaRs. ES measures are generally less accurate than VaR measures and the confidence bands around ES are also less reliable. La valeur-à-risque (VaR) et la mesure ES (Expected Shortfall) sont de plus en plus utilisées pour la mesure du risque d'un portefeuille, l'allocation de capital de risque et la détermination des performances. Les gestionnaires de risques financiers sont donc légitimement intéressés par la précision des techniques classiques de la valeur-à-risque et de la mesure ES. Le but de cet article est précisément d'évaluer la précision des modèles classiques et de mesurer l'importance de l'erreur d'estimation en construisant des intervalles de confiance autour des prévisions de la valeur-à-risque et de la mesure ES. Un des problèmes clés dans la construction d'intervalles de confiance appropriés provient de la dynamique de la variance conditionnelle typiquement observée pour les rendements spéculatifs. Notre article propose donc une technique de ré-échantillonnage qui tient compte de l'erreur d'estimation des paramètres des modèles dynamiques de la variance d'un portefeuille. Une analyse Monte Carlo nous montre que les méthodes généralement utilisées par les praticiens, telles que la simulation historique qui calcule le quantile empirique à l'aide d'une fenêtre mobile des rendements, génèrent des intervalles de confiance pour la valeur-à-risque à 90% qui sont trop étroits et qui contiennent seulement 20% des vraies valeurs-à-risque. D'autres méthodes qui tiennent compte correctement de la dynamique conditionnelle de la variance, telles que la simulation historique filtrée, génèrent quant à elles des intervalles de confiance de la valeur-à-risque à 90% qui contiennent près de 90% des vraies valeurs-à-risque. Les mesures ES sont généralement moins précises que les mesures de valeur-à-risque et les intervalles de confiance autour de la mesure ES sont également moins fiables.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-15.

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Date of creation: 01 Apr 2004
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Handle: RePEc:cir:cirwor:2004s-15

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Keywords: Risk management; boostrapping; GARCH; gestion des risques; Bootstrap; GARCH;

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References

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  1. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
  2. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  3. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  4. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
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  6. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
  7. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
  8. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
  9. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
  10. Jin-Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  12. 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.).
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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Citations

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Cited by:
  1. Bauwens, Luc, 2009. "A component GARCH model with time varying weights," Open Access publications from Université catholique de Louvain info:hdl:2078.1/28904, Université catholique de Louvain.
  2. Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría.
  3. Imola Driga, 2012. "Financial Risks Analysis For A Commercial Bank In The Romanian Banking System," Annales Universitatis Apulensis Series Oeconomica, Faculty of Sciences, "1 Decembrie 1918" University, Alba Iulia, vol. 1(14), pages 14.
  4. Henry Dannenberg, 2011. "The Importance of Estimation Uncertainty in a Multi-Rating Class Loan Portfolio," IWH Discussion Papers 11, Halle Institute for Economic Research.
  5. Loriano Mancini & Fabio Trojani, 2007. "Robust Value at Risk Prediction," University of St. Gallen Department of Economics working paper series 2007 2007-36, Department of Economics, University of St. Gallen.
  6. Peter Christoffersen & Jeremy Berkowitz & Denis Pelletier, 2008. "Evaluating Value-at-Risk Models with Desk-Level Data," CREATES Research Papers 2009-35, School of Economics and Management, University of Aarhus.
  7. Christoph Hartz & Stefan Mittnik & Marc S. Paolella, 2006. "Accurate Value-at-Risk Forecast with the (good old) Normal-GARCH Model," CFS Working Paper Series 2006/23, Center for Financial Studies.
  8. Boudt, Kris & Peterson, B. & Croux, Christophe, 2008. "Estimation and Decomposition of Downside Risk for Portfolios with Non-normal Returns," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/200168, Katholieke Universiteit Leuven.
  9. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
  10. Gaglianone, Wagner Piazza & Linton, Oliver & Lima, Luiz Renato Regis de Oliveira, 2008. "Evaluating Value-at-Risk models via Quantile regressions," Economics Working Papers (Ensaios Economicos da EPGE) 679, Graduate School of Economics, Getulio Vargas Foundation (Brazil).
  11. María Rosa Nieto & Esther Ruiz, 2010. "Bootstrap prediction intervals for VaR and ES in the context of GARCH models," Statistics and Econometrics Working Papers ws102814, Universidad Carlos III, Departamento de Estadística y Econometría.
  12. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series 1115, Economics, The University of Manchester.

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