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Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?

Author

Listed:
  • Xiongwei Ju

    (University of Illinois at Urbana-Champaign)

  • Neil D. Pearson

    (University of Illinois at Urbana-Champaign)

Abstract

We study a source of bias in value-at-risk estimates that has not previously been recognized. Because value-at-risk estimates are based on past data, a trader will often have a good understanding of the errors in the value-at-risk estimate, and it will be possible for her to choose portfolios for which she knows that the value -at-risk is less than the "true" value at risk. Thus, The trader will be able to take on more market risk than risk limits based on value-at-risk permit. Biases can also arise if she doesn't have a good understanding of the errors, but uses the estimated covariance matrix to achieve certain portfolio objectives. We assess the magnitude of these biases for three different assumptions about the motivations and behavoir of the trader and find that in all cases, value-at-risk estimates are systematically downward biased. In some circumstances the biases can be very large. Our study of the distributions of the biases also suggests a way to adjust the estimates to "correct" the biases.

Suggested Citation

  • Xiongwei Ju & Neil D. Pearson, 1998. "Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?," Finance 9810002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:9810002
    Note: Type of Document - PDF; prepared on pc; to print on HP; pages: 31; figures: included. Office for Futures and Options Research (OFOR)at University of Illinois at Ubana -Champaign. Working Paper 98-08. For a complete list of OFOR working papers see http://w3.ag.uiuc.edu/ACE/ofor
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    References listed on IDEAS

    as
    1. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
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    Cited by:

    1. Mohammed Bilal Girach & Shashank Oberoi & Siddhartha P. Chakrabarty, 2021. "Is Being “Robust” Beneficial? A Perspective from the Indian Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(4), pages 469-497, December.
    2. Philippe Jorion, 2007. "Bank Trading Risk and Systemic Risk," NBER Chapters, in: The Risks of Financial Institutions, pages 29-57, National Bureau of Economic Research, Inc.
    3. Belhajjam, A. & Belbachir, M. & El Ouardirhi, S., 2017. "Robust multivairiate extreme value at risk allocation," Finance Research Letters, Elsevier, vol. 23(C), pages 1-11.
    4. Mohammed Bilal Girach & Shashank Oberoi & Siddhartha P. Chakrabarty, 2019. "Is being `Robust' beneficial?: A perspective from the Indian market," Papers 1908.05002, arXiv.org.
    5. Cornelis A. Los, 2004. "Why VAR Fails: Long Memory and Extreme Events in Financial Markets," Finance 0412014, University Library of Munich, Germany.

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