Forecasting Financial Risk using Statistical Parent Distributions in the South African Industrial Index (J520) Returns

Owen  Jakata; Delson  Chikobvu

Authors

Owen Jakata Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
Delson Chikobvu Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa

Keywords:

Value-at-Risk, exponential distribution, Weibull distribution, gamma distribution, Burr distribution

Abstract

This study investigates suitable models for forecasting financial risk of the monthly South African industrial index (J520) returns. Financial returns are leptokurtic (heavy-tailed) relative to the normal distribution. This study proposes some important alternatives to the normal distribution often used in fitting to financial returns and to forecast financial risk more accurately than suggested by the normal distribution. The study identifies the best-fitting parent distributions to the South African industrial index (J520) returns data and quantifies the financial risk of this index. South Africa is a stable developing country and such information is crucial in developing a diversified portfolio for the international investor inclusive of a developing country’s assets. This study uses four relatively heavy-tailed parent distributions, viz: the exponential, Weibull, gamma and the Burr distributions in contrast to past studies, if any, used to describe this particular index returns. The exponential and Weibull distributions are the best fitting parent distributions for the gains and losses respectively. The exponential and the Weibull distributions are in the light tailed Gumbel distribution domain. The study provides the framework on how parent distributions are used to quantify and forecast the financial risk, inclusive of the value-at-risk (VaR) and the expected shortfall (ES) measures. The results reveal that the prospects of potential gains are greater than the prospects of potential losses for one invested in the index. This is useful information for investors who wish to participate in the South African stock market.

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