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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.

In defence of mean variance optimisation

Adock C. J.

Management

2001

Vol. 5, no 1

107-118

The construction of optimised portfolios of risky financial assets is usually carried out using quadratic programming. The use of this optimisation method is justified by the assumption that returns follow a multivariate normal distribution and/or the investor espouses a quadratic utility function. Such utility functions are criticised on the grounds that, according to the quadratic model, there are situations in which the investor will prefer less wealth to more wealth and that risky assets are regarded as an inferior good. In this paper, it is shown that, for normally distributed retums, this criticism of the quadratic utility function is unjustified. A number of relevant results are summarised and some extensions are given. These show that any utility function willlead to a point on the Markowitz mean-variance efficient frontier. The same property also holds in the presence of transactions costs. The paper discusses the implication of these results and concludes with a brief summary of the problems that arise when return s are not normal.