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5689The Basel Committee on Banking Supervision(BIS)has recently sanctioned Expected Shortfall(ES)as the market risk measure to be used for banking regulatory purposes, replacing the well-known Value-at-Risk(VaR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor properties of VaR. In particular, VaR fails to control for "tail risk". In this transition, the major challenge faced by financial institutions is the unavailability of simple tools for evaluation of ES forecasts(i.e. backtesting ES). The main purpose of this article is to propose such tools. Specifically, we propose backtests for ES based on cumulative violations, which are the natural analogue of the commonly used backtests for VaR. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to three major stock indexes shows that VaR is generally unresponsive to extreme events such as those experienced during the recent financial crisis, while ES provides a more accurate description of the risk involved.
/ Journals / Journal of Finance and Economics
Journal of Finance and Economics
LiuYuanchun, Editor-in-Chief
ZhengChunrong, Vice Executive Editor-in-Chief
YaoLan BaoXiaohua HuangJun, Vice Editor-in-Chief
Backtesting Expected Shortfall:Accounting for Tail Risk
Journal of Finance and Economics Vol. 43, Issue 12, pp. 74 - 99 (2017) DOI:10.16538/j.cnki.jfe.2017.12.006
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References
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2 Acerbi C, Szekely B. Backtesting expected shortfall[N]. Risk Magazine, 2014.
4 Artzner P, Delbaen F, Eber M., et al. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3):203-228. DOI:10.1111/mafi.1999.9.issue-3
5 Bai J. Testing parametric conditional distributions of dynamic models[J]. Review of Economics and Statistics, 2003, 85(3):531-549. DOI:10.1162/003465303322369704
6 Basak S, Shapiro A. Value-at-risk based risk management:Optimal policies and asset prices[J]. Review of Financial Studies, 2001, 14(2):371-405. DOI:10.1093/rfs/14.2.371
7 Basel Committee on Banking Supervision. Consultative document:Fundamental review of the trading book[R]. Basel, Switzerland, 2012.
8 Berkowitz J. Testing density forecasts with applications to risk management[J]. Journal of Business and Economic Statistics, 2001, 19(4):465-474. DOI:10.1198/07350010152596718
9 Berkowitz J, Christoffersen P, Pelletier D. Evaluating value-at-risk models with desk-level data[J]. Management Science, 2011, 57(12):2213-2227. DOI:10.1287/mnsc.1080.0964
10 Bose A. Bahadur representation of mestimates[J]. Annals of Statistics, 1998, 26(2):771-777. DOI:10.1214/aos/1028144859
11 Box G, Pierce D. Distribution of residual autocorrelations in autoregressive integrated moving average time series models[J]. Journal of American Statistical Association, 1970, 65(332):1509-1527. DOI:10.1080/01621459.1970.10481180
12 Christoffersen P. Evaluating interval forecasts[J]. International Economic Review, 1998, 39(4):841-862. DOI:10.2307/2527341
13 Christoffersen P, Goncalves P.Estimation risk in financial risk management[J]. Journal of Risk, 2005, 7(3):1-28. DOI:10.21314/JOR.2005.112
14 Christoffersen P.Value-at-risk models[M]. Handbook of Financial Time Series, 2009.
15 Colletaz G, Hurlin C, Perignon C. The risk map:A new tool for validating risk models[J]. Journal of Banking and Finance, 2013, 37(10):3843-3854. DOI:10.1016/j.jbankfin.2013.06.006
16 Du Z. Nonparametric bootstrap tests for the independence of generalized errors[R]. CAEPR Working Paper No. 023-2009, 2015.
17 Emmer S, Kratz M, Tasche D. What is the best risk measure in practice? A comparison of standard measures[R]. ESSEC Business School:Paris, France, 2014.
18 Escanciano J.Weak convergence of non-stationary multivariate marked processes with applications to martingale testing[J]. Journal of Multivariate Analysis, 2007, 98(7):1321-1336. DOI:10.1016/j.jmva.2007.03.004
19 Escanciano J, Lobato I. Testing the martingale hypothesis[M]. Palgrave Handbook of Econometrics, 2009a.
20 Escanciano J, Lobato I.An automatic portmanteau test for serial correlation[J]. Journal of Econometrics, 2009b, 151(2):140-149. DOI:10.1016/j.jeconom.2009.03.001
21 Escanciano J, Olmo J. Backtesting parametric value-at-risk with estimation risk[J]. Journal of Business and Economic Statistics, 2010, 28(1):36-51. DOI:10.1198/jbes.2009.07063
22 Escanciano J, Velasco C. Specification tests of parametric dynamic conditional quantiles[J]. Journal of Econometrics, 2010, 159(1):209-221. DOI:10.1016/j.jeconom.2010.06.003
23 Escanciano J, Pei P. Pitfalls in backtesting historical simulation models[J]. Journal of Banking and Finance, 2012, 36(8):2233-2244. DOI:10.1016/j.jbankfin.2012.04.004
24 Francq C, Zakoian J.Risk-parameter estimation in volatility models[J]. Journal of Econometrics, 2015, 184(1):158-173. DOI:10.1016/j.jeconom.2014.06.019
25 Gourieroux C, Zakoian J.Estimation-adjusted VaR[J]. Econometric Theory, 2013, 29(4):735-770. DOI:10.1017/S0266466612000680
26 Hansen B.Autoregressive conditional density estimation[J]. International Economic Review, 1994, 35(3):705-730. DOI:10.2307/2527081
27 Hong Y, Lee T. Diagnostic checking for adequacy of linear and nonlinear time series models[J]. Econometric Theory, 2003, 19(6):1065-1121.
28 Hong Y, Li H. Nonparametric specification testing for continuous-time modelswith applications to term structure of interest rates[J]. The Review of Financial Studies, 2005, 18(1):37-84. DOI:10.1093/rfs/hhh006
30 Jorion P. Value at risk:The new benchmark for managing financial risk[M]. New York:McGraw-Hill, 2006.
31 Kerkhof J, Melenberg B. Backtesting for risk-based regulatory capital[J].Journal of Banking and Finance, 2004, 28(8):1845-1865. DOI:10.1016/j.jbankfin.2003.06.007
32 Kourouma L, Dupre D, Sanfilippo G, et al. Extreme value at risk and expected shortfall during financial crisis[R]. Working Paper, 2011.
33 Kupiec P. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2):73-84. DOI:10.3905/jod.1995.407942
35 O'Brien J, Szerszen P. An evaluation of bank VaR measures for market risk during and before the financial crisis[R]. FEDS Working Paper No. 2014-21, 2014.
36 Perignon C, Smith D. A new approach to comparing VaR estimation methods[J]. Journal of Derivatives, 2008, 16(2):54-66. DOI:10.3905/JOD.2008.16.2.054
37 Rosenblatt M. Remarks on a multivariate transformation[J]. Annals of Mathematical Statistics, 1952, 23:470-472. DOI:10.1214/aoms/1177729394
38 Shiryaev A. Probability[M]. New York:Springer, 1996.
39 van der Vaart A, Wellner J.Weak convergence and empirical processes[M]. New York:Springer, 1996.
41 Wong W.Backtesting value-at-risk based on tail losses[J]. Journal of Empirical Finance, 2010, 17(3):526-538. DOI:10.1016/j.jempfin.2009.11.004
Cite this article
Du Zaichao, Juan Carlos Escanciano. Backtesting Expected Shortfall:Accounting for Tail Risk[J]. Journal of Finance and Economics, 2017, 43(12): 74–99.
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