Fitting Statistical Parent Distributions to Quantify Financial Risk in the South African Financial Index (J580)

Authors

D. Chikobvu, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South AfricaFollow
O. Jakata, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

The purpose of this study is to investigate and describe the riskiness of an investment in the South African Financial Index (J580) using four relatively heavy tailed statistical parent distributions, viz: the Exponential, Weibull, Gamma and Burr distributions. The statistical distributions describe the Index returns, and quantify the riskiness of the monthly South African Financial Index (J580) for the period 1995-2018. The Maximum Likelihood Estimation (MLE) method is used to estimate the distribution parameters. The heavier-tailed Burr distribution in the heavy tailed Frétchet domain distribution is the best fitting statistical parent distribution for losses as evidenced by the AIC, BIC and other graphical measures of goodness of fit. The lighter tailed Exponential distribution is the best fitting statistical parent distribution for the positive returns (gains). The Exponential distribution is in the light tailed Gumbel domain distribution. Summary measures of financial risk, such as the Value at Risk (VaR) and Expected Shortfall (ES) are calculated using the two best fitting distributions. Financial risk (VaR and ES) quantification and risk mitigation is topical in light of the failure of the Normal distribution-based risk models, which under estimated risk in leading up to the Global Financial Crisis (GFC) of 2008-2009. The practical implications are that the Normal distribution-based risk measures ought to be replaced with other statistical parent distributions and even extreme value distributions (EVD) in order to accurately estimate financial risk. Given the limited empirical investigations on the South Africa Financial Index (J580), the results from this research provide additional and valuable information for both investors and practitioners on how to accurately estimate and assess financial risk. The study extends the empirical literature on more accurate financial risk assessment, more specifically in the context of the Financial Index in South Africa.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/120329

Recommended Citation

Chikobvu, D. and Jakata, O. (2023) "Fitting Statistical Parent Distributions to Quantify Financial Risk in the South African Financial Index (J580)," Journal of Statistics Applications & Probability: Vol. 12: Iss. 3, Article 29.
DOI: http://dx.doi.org/10.18576/jsap/120329
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss3/29