Cotter, John and Dowd, Kevin (2007): Evaluating the Precision of Estimators of QuantileBased Risk Measures.

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Abstract
This paper examines the precision of estimators of QuantileBased 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.
Item Type:  MPRA Paper 

Original Title:  Evaluating the Precision of Estimators of QuantileBased Risk Measures 
Language:  English 
Subjects:  G  Financial Economics > G0  General > G00  General 
Item ID:  3504 
Depositing User:  John Cotter 
Date Deposited:  13. Jun 2007 
Last Modified:  18. Feb 2013 11:31 
References:  Acerbi, C., 2002, Spectral measures of risk: a coherent representation of subjective risk aversion, Journal of Banking and Finance, 26, 15051518. Acerbi, C., 2004, Coherent representations of subjective riskaversion, Pp. 147207 in G. Szegö (Ed,) Risk Measures for the 21st Century, (Wiley: New York). Artzner, P., F. Delbaen, J.M. Eber, and D. Heath, 1999, Coherent measures of risk, Mathematical Finance, 9, 203228. Butler, J. S., and B. Schachter, 1998, Estimating Value at Risk with a precision measure by combining kernel estimation with historical simulation, Review of Derivatives Research, 1, 371390. Chappell, D., and K. Dowd, 1999, Confidence intervals for VaR, Financial Engineering News, March 1999, pp. 12. Chen, S. X., 2005, Nonparametric estimation of expected shortfall, mimeo, Iowa State University. Chen, S. X., and C. Y. Tang, 2005, Nonparametric inference of value at risk for dependent financial returns, Journal of Financial Econometrics, 3, 227255. Cotter, J., and K. Dowd, 2006, Extreme quantilebased risk measures: an application to futures clearinghouse margin requirements, Journal of Banking and Finance, Forthcoming. Dowd, K., 2000, Assessing VaR accuracy, Derivatives Quarterly, 6 (3), 6163. Dowd, K., 2001, Estimating VaR with order statistics, Journal of Derivatives, 8, 23 30. Dowd, K., 2005, Measuring Market Risk, 2nd edition. (Wiley: Chichester and New York) Evans, M., N. Hastings, and B. Peacock, 2000, Statistical Distributions, 3rd edition. (Wiley: Chichester and New York) Frey, R. and A. J. McNeil, 2002, VaR and expected shortfall in portfolios of dependent credit risks: conceptual and practical insights, Journal of Banking and Finance, 26, 13171334. Giannopoulos, K., and R. Tunaru, 2004, Coherent risk measures under filtered historical simulation, Journal of Banking and Finance, 29, 979996. Gourieroux, C., and W. Liu, 2006, Sensitivity analysis of distortion risk measures, mimeo, University of Toronto. 17 Gouriéroux, C., Scaillet, O. and J. P. Laurent, 2000, Sensitivity analysis of values at risk, Journal of Empirical Finance, 7, 225245. Inui, K., and M. Kijima, 2004, On the significance of expected shortfall as a coherent risk measure, Journal of Banking and Finance, 29, 853864. John, S., 1982, The threeparameter twopiece normal family of distributions and its fitting, Communications in Statistics – Theory and Methods, 11, 879885. Jorion, P., 1996, Risk2: Measuring the risk in value at risk, Financial Analysts Journal 52, November/December, 4756. Kendall, M., and A. Stuart, 1972, The Advanced Theory of Statistics, Vol. 1: Distribution Theory, 4th edition. (Charles Griffin and Co. Ltd: London) Manistre, B. J., and G. H. Hancock, 2005, Variance of the CTE estimator, North American Actuarial Journal, 9, 129156. Mason, D. M., 1981, Asymptotic normality of linear combinations of order statistics with a smooth score function, Annals of Statistics, 9, 899908. Mausser, H., 2001, Calculating Quantilebased Risk Analytics with Lestimators, Algo Research Quarterly, 4, 3347. McNeil, A. J., and R. Frey, 2000, Estimation of tailrelated risk measures for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance, 7, 271300. McNeil, A. J., R. Frey, and P. Embrechts, 2005, Quantitative Risk Management. (Princeton University Press: Princeton) Pritzker, M., 1997, Evaluating value at risk methodologies: accuracy versus computational time, Journal of Financial Services Research, 12, 201242. Reiss, R.D., 1976, Asymptotic expansions for sample quantiles, Annals of Probability, 76, 4, 249258. Scaillet, O., 2004, Nonparametric estimation and sensitivity analysis of expected shortfall, Mathematical Finance, 14, 115129. Siu, T. K., H. Tong, and H. Yang, 2001, On Bayesian value at risk: from linear to nonlinear portfolios, mimeo, National University of Singapore. Stiegler, S. M., 1974, Linear functions of order statistics with smooth weight functions, Annals of Statistics, 2, 676693. Yamai, Y., and T. Yoshiba, 2002, Comparative analyses of expected shortfall and valueatrisk: their estimation error, decomposition, and optimization, Monetary and Economic Studies, January, 87122. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/3504 