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VaR is subject to a significant positive bias

Author

Listed:
  • Inui, Koji
  • Kijima, Masaaki
  • Kitano, Atsushi

Abstract

This article shows that value-at-risk (VaR), the most popular risk measure in financial practice, has a considerable positive bias when used for a portfolio with fat-tail distribution. The bias increases with higher confidence level, heavier tails, and smaller sample size. Also, the Harrell-Davis quantile estimator and its simulation counterpart, called the bootstrap estimator, tend to have a more significant positive bias for fat-tail distributions.

Suggested Citation

  • Inui, Koji & Kijima, Masaaki & Kitano, Atsushi, 2005. "VaR is subject to a significant positive bias," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 299-311, May.
  • Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:299-311
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    References listed on IDEAS

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    1. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    2. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Computational Statistics, Springer, vol. 18(3), pages 355-373, September.
    3. Masaaki Kijima & Masamitsu Ohnishi, 1996. "Portfolio Selection Problems Via The Bivariate Characterization Of Stochastic Dominance Relations," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 237-277.
    4. 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.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    6. Inui, Koji & Kijima, Masaaki, 2005. "On the significance of expected shortfall as a coherent risk measure," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 853-864, April.
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    Citations

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    Cited by:

    1. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
    2. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-25, July.

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