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

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/fin/papers/9810/9810002.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 9810002.

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Length: 31 pages
Date of creation: 08 Oct 1998
Date of revision:
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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Keywords: Value-at-Risk;

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References

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  1. Jon Danielsson, 1997. "Extreme Returns, Tail Estimation, and Value-at-Risk," FMG Discussion Papers dp273, Financial Markets Group.
  2. repec:wop:ilucae:9604 is not listed on IDEAS
  3. J. S. Butler & Barry Schachter, 1996. "Improving Value-At-Risk Estimates By Combining Kernel Estimation With Historical Simulation," Finance 9605001, EconWPA.
  4. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Staff Reports 33, Federal Reserve Bank of New York.
  5. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69.
  6. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Proceedings 512, Federal Reserve Bank of Chicago.
  7. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
  8. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  9. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, EconWPA.
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Cited by:
  1. Philippe Jorion, 2005. "Bank Trading Risk and Systemic Risk," NBER Working Papers 11037, National Bureau of Economic Research, Inc.
  2. Cornelis A Los, 2005. "Why VaR FailsLong Memory and Extreme Events in Financial Markets," The IUP Journal of Financial Economics, IUP Publications, vol. 0(3), pages 19-36, September.

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