Page 250 - Contributed Paper Session (CPS) - Volume 6

CPS1909 Retius C. et al.
largest stock exchange with more than 400 listed firms and offering a wide
range of products. The South African stock market is significantly robust and
is able to make the list of the first twenty largest stock markets in the world
consistently (Hassan, 2013). This market value is unavoidably significant
among world stock indexes, making it respond to the global economic
meltdown surrounding emerging markets.
The FTSE/JSE All Share Price Index (ALSI) is designed to represent the
performance of South African companies, providing investors with a
comprehensive and complementary set of indices, which measure the
performance of the major capital and industry segments of the South African
stock market. It has 164 listed companies and it is about 99% of the full South
African market capitalization value i.e. before the application of any
investability weightings, of all ordinary securities listed on the main board of
JSE, subject to minimum free-float and liquidity criteria. ALSI, as an equity
index portrays the operational activities of a typical ordinary share in the South
African market. The ALSI also evaluates the operationalization of the entire
market (Makhwiting, 2014). The major volume of all securities listed on the JSE
is an integral function of the market index because the share prices flow of the
listed companies is what drives the market.
There are many types of empirical models which have been used to
describe the stylized facts in stock returns. These include, ARCH (Engle, 1982),
GARCH (Bollerslev, 1986), IGARCH (Engle and Bollerslev, 1986), EGARCH
(Nelson, 1991), TARCH (Glosten et al., 1993a), APARCH (Ding et al., 1993),
FIGARCH (Baillie et al., 1996), FIEGARCH (Bollerslev and Mikkelsen, 1996),
FIAPARCH (Tse, 1998) and HYGARCH (Davidson, 2004). In order to obtain
good estimates for risk management, the challenge is to choose the
appropriate GARCH-type model which adequately captures volatility
clustering and at the same type be able to capture the non-normality property
of financial returns. Paolella (2016) used stable-APARCH model to model
four stocks from DJIA index. Sin et al. (2017) used of the TGARCH combined
with the generalized error distribution (GED) to model crude oil index. In the
literature, there is no agreement of the type of the heavy-tailed distribution
to be used in order to capture the non-normality of the residuals of the
GARCH-type models. In this paper, we are interested in the relative
performance of the asymmetric power auto-regressive conditional
heteroscedastic (APARCH) model combined with heavy-tailed distributions,
namely; generalized Pareto (GPD), Pearson type-IV (PIVD) and stable
distributions (SD) in estimating the value-at-risk (VaR) for South Africa stock
market.
We are not aware of any literature relating to an application of APARCH-
GPD, APARCH- PIVD model and APARCH-SD model to the FTSE/JSE All Share
Price Index. To the best of our knowledge, there are limited research on

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