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Estimation Risk in Financial Risk Management

Author

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  • Peter Christoffersen
  • Sílvia Gonçalves

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.

Suggested Citation

  • Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.
  • Handle: RePEc:cir:cirwor:2004s-15
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    File URL: http://www.cirano.qc.ca/files/publications/2004s-15.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nieto, María Rosa & Ruiz, Esther, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Audrino, Francesco & Trojani, Fabio, 2011. "A General Multivariate Threshold GARCH Model With Dynamic Conditional Correlations," Journal of Business & Economic Statistics, American Statistical Association, pages 138-149.
    3. Alexandros Gabrielsen & Axel Kirchner & Zhuoshi Liu & Paolo Zagaglia, 2015. "Forecasting Value-At-Risk With Time-Varying Variance, Skewness And Kurtosis In An Exponential Weighted Moving Average Framework," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., pages 1-29.
    4. International Monetary Fund, 2014. "Switzerland; Technical Note-Systemic Risk and Contagion Analysis," IMF Staff Country Reports 14/268, International Monetary Fund.
    5. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, pages 2295-2312.
    6. Silvia Stanescu & Radu Tunaru, 2013. "Quantifying the uncertainty in VaR and expected shortfall estimates," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 15, pages 357-372 Edward Elgar Publishing.
    7. 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, pages 150-160.
    8. Genest, Benoit & Cao, Zhili, 2014. "Value-at-Risk in turbulence time," MPRA Paper 62906, University Library of Munich, Germany.
    9. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 281-313, Spring.
    10. Bauwens Luc & Storti Giuseppe, 2009. "A Component GARCH Model with Time Varying Weights," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 1-33.
    11. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc S., 2006. "Accurate Value-at-Risk forecast with the (good old) normal-GARCH model," CFS Working Paper Series 2006/23, Center for Financial Studies (CFS).
    12. Nieto, María Rosa & Ruiz, Esther, 2010. "Bootstrap prediction intervals for VaR and ES in the context of GARCH models," DES - Working Papers. Statistics and Econometrics. WS ws102814, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. 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.
    14. 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, pages 1-14.
    15. Adrián F. Rossignolo & Víctor A. Álvarez, 2015. "Has the Basel Committee Got it Right? Evidence from Commodity Positions in Turmoil," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, March.
    16. Dannenberg, Henry, 2011. "The Importance of Estimation Uncertainty in a Multi-Rating Class Loan Portfolio," IWH Discussion Papers 11/2011, Halle Institute for Economic Research (IWH).

    More about this item

    Keywords

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

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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