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Risk Measure Inference

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  • Christophe Hurlin
  • Sébastien Laurent
  • Rogier Quaedvlieg
  • Stephan Smeekes

Abstract

We propose a bootstrap-based test of the null hypothesis of equality of two firms’ conditional risk measures (RMs) at a single point in time. The test can be applied to a wide class of conditional risk measures issued from parametric or semiparametric models. Our iterative testing procedure produces a grouped ranking of the RMs, which has direct application for systemic risk analysis. Firms within a group are statistically indistinguishable from each other, but significantly more risky than the firms belonging to lower ranked groups. A Monte Carlo simulation demonstrates that our test has good size and power properties. We apply the procedure to a sample of 94 U.S. financial institutions using ΔCoVaR, MES, and %SRISK. We find that for some periods and RMs, we cannot statistically distinguish the 40 most risky firms due to estimation uncertainty.

Suggested Citation

  • Christophe Hurlin & Sébastien Laurent & Rogier Quaedvlieg & Stephan Smeekes, 2017. "Risk Measure Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 499-512, October.
    • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:4:p:499-512
    DOI: 10.1080/07350015.2015.1127815
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    1. Bajgrowicz, Pierre & Scaillet, Olivier, 2012. "Technical trading revisited: False discoveries, persistence tests, and transaction costs," Journal of Financial Economics, Elsevier, vol. 106(3), pages 473-491.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    3. Boudt, Kris & Daníelsson, Jón & Laurent, Sébastien, 2013. "Robust forecasting of dynamic conditional correlation GARCH models," International Journal of Forecasting, Elsevier, vol. 29(2), pages 244-257.
    4. Sylvain Benoît & Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2013. "A Theoretical and Empirical Comparison of Systemic Risk Measures," Working Papers halshs-00746272, HAL.
    5. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    6. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    7. Castro, Carlos & Ferrari, Stijn, 2014. "Measuring and testing for the systemically important financial institutions," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 1-14.
    8. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    9. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Dimitrios Bisias & Mark Flood & Andrew W. Lo & Stavros Valavanis, 2012. "A Survey of Systemic Risk Analytics," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 255-296, October.
    12. Pilar Olave Robio, 1999. "Forecast intervals in ARCH models: bootstrap versus parametric methods," Applied Economics Letters, Taylor & Francis Journals, vol. 6(5), pages 323-327.
    13. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    14. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 417-442, November.
    15. Shimizu Kenichi, 2013. "The bootstrap does not alwayswork for heteroscedasticmodels," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 189-204, August.
    16. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    17. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    18. Viral Acharya & Robert Engle & Matthew Richardson, 2012. "Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risks," American Economic Review, American Economic Association, vol. 102(3), pages 59-64, May.
    19. Hidalgo, Javier & Zaffaroni, Paolo, 2007. "A goodness-of-fit test for ARCH([infinity]) models," Journal of Econometrics, Elsevier, vol. 141(2), pages 835-875, December.
    20. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    21. Gourieroux, Christian & Zakoïan, Jean-Michel, 2013. "Estimation-Adjusted Var," Econometric Theory, Cambridge University Press, vol. 29(4), pages 735-770, August.
    22. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    23. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    24. Reeves, Jonathan J., 2005. "Bootstrap prediction intervals for ARCH models," International Journal of Forecasting, Elsevier, vol. 21(2), pages 237-248.
    25. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    26. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    27. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    28. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Rejoinder on: Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 461-471, November.
    29. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    30. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    31. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    32. J. Carlos Escanciano & Jose Olmo, 2011. "Robust Backtesting Tests for Value-at-risk Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 132-161, Winter.
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    Cited by:

    1. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    2. Wided Khiari & Salim Ben Sassi, 2019. "On Identifying the Systemically Important Tunisian Banks: An Empirical Approach Based on the △CoVaR Measures," Risks, MDPI, vol. 7(4), pages 1-15, December.
    3. Sarlin, Peter & Holopainen, Markus, 2016. "Toward robust early-warning models: a horse race, ensembles and model uncertainty," Working Paper Series 1900, European Central Bank.
    4. Ophélie Couperier & Jérémy Leymarie, 2020. "Backtesting Expected Shortfall via Multi-Quantile Regression," Working Papers halshs-01909375, HAL.
    5. Saidane, Dhafer & Sène, Babacar & Désiré Kanga, Kouamé, 2021. "Pan-African banks, banking interconnectivity: A new systemic risk measure in the WAEMU," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    6. Hurlin, Christophe & Leymarie, Jérémy & Patin, Antoine, 2018. "Loss functions for Loss Given Default model comparison," European Journal of Operational Research, Elsevier, vol. 268(1), pages 348-360.
    7. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    8. Raphaëlle BELLANDO & Oana TOADER, 2017. "An analysis of banks’ weaknesses in the light of stress tests," LEO Working Papers / DR LEO 2479, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    9. Francq, Christian & Zakoian, Jean-Michel, 2015. "Looking for efficient qml estimation of conditional value-at-risk at multiple risk levels," MPRA Paper 67195, University Library of Munich, Germany.
    10. Markus Holopainen & Peter Sarlin, 2015. "Toward robust early-warning models: A horse race, ensembles and model uncertainty," Papers 1501.04682, arXiv.org, revised Apr 2016.

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