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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

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2006. "An analysis of the distribution of extremes in indices of share returns in the US, UK and Japan from 1963 to 2000," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 11(2), pages 97-113.
    • Handle: RePEc:ijf:ijfiec:v:11:y:2006:i:2:p:97-113
    DOI: 10.1002/ijfe.280
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    References listed on IDEAS

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    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., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    6. 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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    Cited by:

    1. Hussain, Saiful Izzuan & Li, Steven, 2015. "Modeling the distribution of extreme returns in the Chinese stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 34(C), pages 263-276.
    2. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    3. Emmanuel Afuecheta & Chigozie Utazi & Edmore Ranganai & Chibuzor Nnanatu, 2023. "An Application of Extreme Value Theory for Measuring Financial Risk in BRICS Economies," Annals of Data Science, Springer, vol. 10(2), pages 251-290, April.
    4. Kengo Kayaba & Yui Hirano & Naoki Ueda & Nobuki Matsui, 2018. "An investigation of fat-tailed distributions in fitting the Japanese stock market returns," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 8(2), pages 1399-1399.
    5. Tolikas, Konstantinos & Gettinby, Gareth D., 2009. "Modelling the distribution of the extreme share returns in Singapore," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 254-263, March.
    6. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    7. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.

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