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An analysis of skewness and kurtosis in Polish stock returns and the estimation of beta using the generalised skew student distribution

Adock C. J., Shutes K.

Management

2003

Vol. 7, no 1

213-225

This paper uses the generalised skew Student (GST) distribution to model returns on Polish stocks that are constituents of the WIG20 index. A basic analysis of returns provides strong evidence of skewness and kurtosis, both of which can be accommodated by the generalised skew Student model. Three specific forms of the GST distribution are used. These are Student's t itself, the symmetric generalised Student distribution and a specific version of the generalised skew Student distribution. The models are first used to estimate the location parameter and other parameters of the return distribution separately for each stock. Secondly, stock betas are estimated for each security by assuming that the stock specific residuals in the market model follow one of the specified forms of GST distribution. The paper also reports the results of a short portfolio selection study in which the minimum variance portfolio is constructed using the different sets of parameter estimates.