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The aim of this study is to model the probabilistic behaviour of unusually large financial losses (extreme-risk) and gains of the South African Financial Index (J580). Risk is defined as uncertainty in return in this paper. This study makes use of Extreme Value Theory (EVT) for the period years: 1995-2018 to build models that are used to estimate extreme losses and gains. The quarterly block maxima/minima of monthly returns are fitted to the Generalised Extreme Value Distribution (GEVD). Return levels (maximum loss/gain) based on the parameters from the GEVD are estimated. A comparative analysis with the Generalised Pareto Distribution (GPD) is carried out. The study reveals that EVT provides an efficient method of forecasting potentially high risks in advance. The conclusion is that analysing extreme risk in the South African Financial Index helps investors understand its riskness better and manage to reduce the risk exposure in this portfolio. Highlights: According to the GEVD model, for one invested in the South African financial index: i. The maximum potential losses are lower than the maximum potential gains in the short term. ii. The maximum potential gains are lower than the maximum potential losses in the long term. The comparative GPD model on the other hand suggests that: the maximum potential losses are greater than the maximum potential gains both in the short and long term.

Analysing Extreme Risk in the South African Financial Index (J580) using the Generalised Extreme Value Distribution