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Estimation Risk in Financial Risk Management

Listed author(s):
  • Peter Christoffersen
  • Sílvia Gonçalves

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

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Length: 30 pages
Date of creation: 01 Apr 2004
Handle: RePEc:cir:cirwor:2004s-15
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  1. 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.
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  4. Christoffersen, Peter, 2003. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 1, number 9780121742324.
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  7. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
  8. 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.
  9. 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 542-547, August.
  10. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
  11. 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.
  12. Jin-Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167.
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