Title: Extreme value modelling of the South African Industrial Index (J520) returns using the generalised extreme value distribution

Authors: Owen Jakata; Delson Chikobvu

Addresses: Department of Mathematical Statistics and Actuarial Sciences, University of the Free State (South Africa), Bloemfontein 9300, Free State, South Africa ' Department of Mathematical Statistics and Actuarial Sciences, University of the Free State (South Africa), Bloemfontein 9300, Free State, South Africa

Abstract: The aim of this study is to analyse the behaviour of extreme returns of the South African Industrial Index (J520) (years 1995-2018) and estimate extreme risk measures using the Generalised Extreme Value Distribution (GEVD). The results reveal that for the 8, 20 and 40 quarterly return periods, the estimated extreme losses are 9.28%, 13.65% and 17.03%, respectively. The extreme possible gains for the same periods are 9.81%, 11.63% and 12.68%, respectively. Therefore, in the short term (8 quarters) the extreme losses are less than the extreme gains, but in the medium to long term (20 and 40 quarterly return periods), the extreme losses are greater than the extreme gains. This study uses the GEVD to build models that can be used to estimate extreme risk measures that can act as effective decision-making tools for minimising risk exposure and maximising on the potential gains in equity portfolio risk management. Highlights: (1) In the short term the gains in the South African Industrial Index are greater than the losses. (2) However, in the medium to long term, for an investor invested in the same Index, the losses are greater than the gains.

Keywords: block maxima/minima; extreme value theory; generalised extreme value distribution; maximum likelihood estimation; return level; return period.

DOI: 10.1504/IJAMS.2022.127009

International Journal of Applied Management Science, 2022 Vol.14 No.4, pp.299 - 315

Received: 15 Feb 2020
Accepted: 17 Jun 2020
Published online: 18 Nov 2022 *

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