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Evaluating the Precision of Estimators of Quantile-Based Risk Measures

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  • Cotter, John
  • Dowd, Kevin

Abstract

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions.

Suggested Citation

  • Cotter, John & Dowd, Kevin, 2007. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," MPRA Paper 3504, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3504
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    References listed on IDEAS

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    1. B. John Manistre & Geoffrey Hancock, 2005. "Variance of the CTE Estimator," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 129-156.
    2. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
    3. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    4. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk (2): Expected Utility Maximization and Tail Risk," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(2), pages 95-115, April.
    5. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    6. Tak Siu & Howell Tong & Hailiang Yang, 2004. "On Bayesian Value at Risk: From Linear to Non-Linear Portfolios," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(2), pages 161-184, June.
    7. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    8. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    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. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    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. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 227-255.
    13. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    14. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers 2006-33, Center for Research in Economics and Statistics.
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    Cited by:

    1. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, vol. 229(2), pages 487-495.
    2. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524.

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    JEL classification:

    • G00 - Financial Economics - - General - - - General

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