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

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.