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. Copyright Blackwell Publishers Ltd, 2004.

The financial performance of the FTSE4Good indices

“…The kurtosis results are even more emphatic, with all eight FTSE 4 Good indices containing significantly more extreme tail observations than one would expect with the normal distribution. Such a finding is not unusual for share indices (Gettingby et al, 2004) and simply indicates that equity returns tend to be volatile. Finally, the findings for the base universe indices suggest that the FTSE 4 Good indices have outperformed their non-FTSE 4 Good counterparts; in each instance, the mean returns for the 'universe' indices are lower than those for their FTSE 4 Good counterparts.…”

Modelling the distribution of the extreme share returns in Singapore

“…The distribution whose theoretical τ 4 and τ 3 curve passes closest to the data set 9 is then selected. In environmental studies, the usefulness of L-moment ratio diagrams in identifying appropriate distributions is well illustrated in Hosking (1990) and Peel et al (2001) while in finance, this approach has received attention by Gettinby et al (2004Gettinby et al ( , 2006 and Tolikas (2008).…”

“…Pownall and Koedijk (1999) and Bali (2003) presented evidence that EVT-based VaR outperformed models based on the assumption that returns are normally distributed, while Cotter and Dowd (2006) showed that EVT can be valuable when calculating clearinghouse margin requirements for future contracts. Gettinby et al (2004Gettinby et al ( , 2006 found that the Generalized Logistic (GL) distribution characterized the extreme daily share returns in the US, UK and Japan better than the highly documented GEV distribution. Recently, Tolikas (2008) provided further evidence of the ability of the GL distribution to fit adequately extreme returns and illustrated that the GL can lead to more accurate VaR estimates compared to those based on the GEV or the normal distribution.…”

Modeling the distribution of extreme returns in the Chinese stock market

“…However, Tolikas (2008) and Gettinby et al (2004) suggest the use of probability weighted moments (PWM) to estimate parameters for GEV, GL and GP in modeling the extreme returns of financial series.…”

“…Studies by Longin (1996), Jondeau and Rockinger (2003) and Gencay and Selcuk (2004) find that extreme stock returns in the US can be characterized by the GEV distribution, which can be used for calculating VaR measures and capital requirements. Gettinby et al (2004Gettinby et al ( & 2006 find Generalized Logistic (GL) distribution fits better for extreme daily share return in the US, UK and Japan compared…”