Risk quantification using skewed distributions: An application to the South African Financial Index (J580)

Department of Mathematical Statistics and Mathematical Statistics, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, 9301, South Africa

^* Corresponding author: shongwesc@ufs.ac.za

Abstract

This study assesses the reproducibility of a recent publication on the risk quantification of the South African Financial Index (J580) using skewed distributions. That is, four skewed distributions (Burr, exponential, gamma and Weibull) are fitted to the returns (split into losses and gains) of the J580 dataset. In this paper, we redo the analysis in an effort to highlight some of the quantifiable differences in the values of the descriptives, goodness-of-fit and risk measures for all four distributions. In addition, other goodness-of-fit tests are computed for all four distributions to check consistency, and based on this extension, it is observed that the Weibull is a better model for gains due to a majority of the goodness-of-fit test inferring that and yields better risk measures. Finally, the Burr distribution is recommended for losses as it better captures the heavy tail of the loss returns.