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Testing, Comparing, and Combining Value at Risk Measures

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  • Peter Christoffersen
  • Jinyong Hahn
  • Atsushi Inoue

Abstract

Value-at-Risk (VaR) has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems which report VaR-like measures. Risk managers are therefore often left with the daunting task of having to choose from this plethora of risk measures. Accordingly, this paper develops a framework for answering the following questions about VaRs: 1) How can a risk manager test that the VaR measure at hand is properly specified, given the history of asset returns? 2) Given two different VaR measures, how can the risk manager compare the two and pick the best in a statistically meaningful way? Finally, 3) How can the risk manager combine two or more different VaR measures in order to obtain a single statistically superior measure? The usefulness of the methodology is illustrated in an application to daily returns on the S&P500. In the application, competing VaR measures are calculated from either historical or option-price based volatility measures, and the VaRs are then tested and compared.

Suggested Citation

  • Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 1999. "Testing, Comparing, and Combining Value at Risk Measures," Center for Financial Institutions Working Papers 99-44, Wharton School Center for Financial Institutions, University of Pennsylvania.
    • Handle: RePEc:wop:pennin:99-44
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    Cited by:

    1. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    2. Chen, Xiaohong & Hong, Han & Shum, Matthew, 2007. "Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models," Journal of Econometrics, Elsevier, vol. 141(1), pages 109-140, November.
    3. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    4. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    5. Shcherba, Alexandr, 2011. "Comparison of VaR estimation methods for different forecasting samples for Russian stocks," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 58-70.
    6. Dany Rogers Silva & Karem Cristina de Sousa Ribeiro & Hsia Hua Sheng, 2011. "Trade credit profitability measurement: application in a wholesalerdistributor case," Brazilian Business Review, Fucape Business School, vol. 8(2), pages 22-41, April.
    7. Mauro Bernardi & Leopoldo Catania & Lea Petrella, 2014. "Are news important to predict large losses?," Papers 1410.6898, arXiv.org, revised Oct 2014.
    8. Kilic, Ekrem, 2006. "Violation duration as a better way of VaR model evaluation : evidence from Turkish market portfolio," MPRA Paper 5610, University Library of Munich, Germany.

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