An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000

Abstract

This paper seeks to characterise the distribution of extreme returns for a UK share index over the years 1975 to 2000. In particular, the suitability of the following distributions is investigated: Gumbel, Frechet, Weibull, Generalised Extreme Value, Generalised Pareto, Log‐Normal and Generalised Logistic. Daily returns for the FT All Share index were obtained from Datastream, and the maxima and minima of these daily returns over a variety of selection intervals were calculated. Plots of summary statistics for the weekly maxima and minima on statistical distribution maps suggested that the best fitting distribution would be either the Generalised Extreme Value or the Generalised Logistic. The results from fitting each of these two distributions to extremes of a series of UK share returns support the conclusion that the Generalised Logistic distribution best fits the UK data for extremes over the period of the study. The Generalised Logistic distribution has fatter tails than either the log‐normal or the Generalised Extreme Value distribution, hence this finding is of importance to investors who are concerned with assessing the risk of a portfolio.