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VaR is subject to a significant positive bias

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  • Inui, Koji
  • Kijima, Masaaki
  • Kitano, Atsushi
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4FM3582-3/2/c244d768637a7cac12682013d2907c27
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 72 (2005)
    Issue (Month): 4 (May)
    Pages: 299-311

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    Handle: RePEc:eee:stapro:v:72:y:2005:i:4:p:299-311

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    Related research

    Keywords: Value-at-risk Harrell-Davis estimator Historical simulation Concave ordering;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. 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.
    2. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Research Paper Series 91, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. 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.
    4. 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.
    5. 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, 06.
    6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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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.

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