IDEAS home Printed from
   My bibliography  Save this paper

Testing, Comparing, and Combining Value at Risk Measures


  • Peter Christoffersen
  • Jinyong Hahn
  • Atsushi Inoue


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Ikenberry, David & Lakonishok, Josef & Vermaelen, Theo, 1995. "Market underreaction to open market share repurchases," Journal of Financial Economics, Elsevier, vol. 39(2-3), pages 181-208.
    2. Jensen, Michael C. & Ruback, Richard S., 1983. "The market for corporate control : The scientific evidence," Journal of Financial Economics, Elsevier, vol. 11(1-4), pages 5-50, April.
    3. Cohen, Michael D, et al, 1996. "Routines and Other Recurring Action Patterns of Organizations: Contemporary Research Issues," Industrial and Corporate Change, Oxford University Press, vol. 5(3), pages 653-698.
    4. Thakor, Anjan V., 1999. "Information technology and financial services consolidation," Journal of Banking & Finance, Elsevier, vol. 23(2-4), pages 697-700, February.
    5. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    6. Richard R. Nelson, 1995. "Recent Evolutionary Theorizing about Economic Change," Journal of Economic Literature, American Economic Association, vol. 33(1), pages 48-90, March.
    7. Calomiris, Charles W., 1999. "Gauging the efficiency of bank consolidation during a merger wave," Journal of Banking & Finance, Elsevier, vol. 23(2-4), pages 615-621, February.
    8. Agrawal, Anup & Jaffe, Jeffrey F & Mandelker, Gershon N, 1992. " The Post-merger Performance of Acquiring Firms: A Re-examination of an Anomaly," Journal of Finance, American Finance Association, vol. 47(4), pages 1605-1621, September.
    9. Healy, Paul M. & Palepu, Krishna G. & Ruback, Richard S., 1992. "Does corporate performance improve after mergers?," Journal of Financial Economics, Elsevier, vol. 31(2), pages 135-175, April.
    10. Raghavendra Rau, P. & Vermaelen, Theo, 1998. "Glamour, value and the post-acquisition performance of acquiring firms," Journal of Financial Economics, Elsevier, vol. 49(2), pages 223-253, August.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Shcherba, Alexandr, 2011. "Comparison of VaR estimation methods for different forecasting samples for Russian stocks," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 24(4), pages 58-70.
    2. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(01), pages 74-113, February.
    3. 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.
    4. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 559-589.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. Mauro Bernardi & Leopoldo Catania & Lea Petrella, 2014. "Are news important to predict large losses?," Papers 1410.6898,, revised Oct 2014.
    7. 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.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:pennin:99-44. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.