n Management Dynamics : Journal of the Southern African Institute for Management Scientists - An investigation into the return distributions of the South African general equity universe

Volume 16, Issue 3
  • ISSN : 1019-567X



The purpose of this study was to investigate the return distributions evident in the general equity universe,comprising the All-share Index and sub indices, consisting of the Industrial, Financial and Gold/Mining indices over a 5-year and 10-year period.

Alternative distributions evaluated are the logistic, lognormal, extreme value and the stable distributions. The descriptive statistics of the returns are calculated and the fit of alternative distributions evaluated graphically. Lastly, the alternative distributions' goodness-of-fit is evaluated by calculating the respective parameters through the application of maximum likelihood estimation, and by calculating the Anderson-Darling statistics.
The results of this study reveal that over the 5-year period,where marginal skewness and kurtosis are evident, the normal/stable alpha 2 distributions best fit the returns. However, over the longer period, the stable distribution best fits the return distributions, by accurately discounting the higher moments of the returns. This conclusion is important, because one of the key assumptions in the Capital Asset Pricing Model (CAPM) is the assumption that asset returns are normally distributed. It therefore is important that tools are applied which take this non normality into account in both the portfolio selection process and theoretical analyses in South Africa.

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