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An analysis of the distribution of extremes in indices of share returns in the US, UK and Japan from 1963 to 2000

Listed author(s):
  • G. D. Gettinby

    (Department of Accountancy and Business Finance, The University of Dundee, UK)

  • C. D. Sinclair

    (Department of Accountancy and Business Finance, The University of Dundee, UK)

  • D. M. Power

    (Department of Accountancy and Business Finance, The University of Dundee, UK)

  • R. A. Brown

    (Department of Accountancy and Business Finance, The University of Dundee, UK)

Registered author(s):

    This paper seeks to characterize the distribution of extreme returns for US, UK and Japanese equity indices over the years 1963-2000. In particular, the suitability of the following distributions is investigated: Normal, Frechet, Gumbel, Weibull, Generalized Extreme Value (GEV), Generalized Pareto and Generalized Logistic (GL). Daily returns were obtained for each of the countries, and the minima over a variety of selection intervals were calculated. Plots of higher moment statistics for the minima on statistical distribution maps suggested that the best fitting distribution would be either the GEV or the GL. The results from fitting each of these distributions to extremes of a series of US, UK and Japanese share returns supported the preliminary evidence that the GL distribution best fitted the data in all three countries over the period of study. The GL distribution has fatter tails than the GEV distribution; hence this finding is of importance to investors who are concerned with assessing the risk of a portfolio. The paper highlights the important finance implications and in particular the potential for underestimation of risk if distributions without fat enough tails are employed. Copyright © 2006 John Wiley & Sons, Ltd.

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    Article provided by John Wiley & Sons, Ltd. in its journal International Journal of Finance & Economics.

    Volume (Year): 11 (2006)
    Issue (Month): 2 ()
    Pages: 97-113

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    Handle: RePEc:ijf:ijfiec:v:11:y:2006:i:2:p:97-113
    DOI: 10.1002/ijfe.280
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    1. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
    2. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    3. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    4. Phillipe Lambert & J. K. Lindsey, 1999. "Analysing Financial Returns by Using Regression Models Based on Non-Symmetric Stable Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 409-424.
    5. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
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