AN EXAMINATION OF THE EFFECTS OF MAJOR POLITICAL CHANGEON STOCK MARKET VOLATILITY: THE SOUTH AFRICANEXPERIENCE

Robert D. Brooks, Sinclair Davidson and Robert W. Faff1

Department of Economics and Finance, Royal Melbourne Institute ofTechnology, GPO Box 2476V, Melbourne Victoria 3001, Australia.

ABSTRACT

Prior to President de Klerk's historic announcement on February 2 1990, South Africawas the subject of extreme economic and political isolation. As a result of thisannouncement, it would be expected that South Africa's financial markets transformedfrom a state of segmentation to a degree of integration in world markets. One meansof assessing the possible effects of this major political change is by investigating stockmarket volatility. Specifically, we would expect that the post-announcement volatilitywould behave more like that observed in other developed markets. Accordingly, inthis paper we investigate the applicability of the ARCH family of models to SouthAfrican stock return data, over the period March 20 1986 to February 23 1996. Ourresults support the applicability of ARCH models. Further, more complex volatilitymodels can be supported in the post-announcement period, suggesting greaterinternational integration of the Johannesburg Stock Exchange in the post-1990s period.

JEL Classifications: G12, G15Key Words: Political Change; Volatility; GARCH.; South Africa.

* The authors wish to thank Gabrielle Berman for her helpful research assistancethat required low monitoring costs and an anonymous referee for some veryhelpful comments which have significantly improved the paper.

1 Professor Robert Faff, RMIT Business, Department of Economics and Finance, GPO Box 2476V,Melbourne, 3001, Victoria, Australia. Telephone: +61 3 9660 5905, Facsimile: +61 0 9660 5986.Email: robertf@bf.rmit.edu.au.

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1. INTRODUCTION

On February 2 1990, President de Klerk announced to the world that South

Africa would undergo a fundamental change to its political structure. Of

course, for several years prior to his announcement, South Africa was the

subject of an extreme form of political and economic isolation from the

international community. Most notably, this took the form of trade and

financial sanctions (including disinvestment campaigns and pressures for the

withdrawal of foreign funds). In addition, South African domestic residents

are legally restrained from investing offshore. These considerations imply, at

least, mild segmentation from international capital markets. Indeed, this

provides an ample a priori basis for believing that the major capital market in

South Africa, the Johannesburg Stock Exchange (JSE), was, until recently,

segmented from international capital markets. Accordingly, the primary aim of

this paper is to investigate this hypothesis.

Having identified our aim, we need to establish the methodology by which the

analysis will be conducted. For a number of related reasons, our choice is to

investigate the behaviour of stock market volatility. A well established stylised

fact of high frequency financial time series is that they exhibit volatility

clustering. This implies that periods of high volatility are likely to be followed

by subsequent periods of high volatility, and periods of low volatility are likely

to be followed by subsequent periods of low volatility. In essence, this

clustering phenomena suggests that volatility possesses an important

predictable component. As Engle (1993, p.72) argues this predictability has a

3

very real practical importance - investors can use knowledge of the

predictability of volatility to make improved portfolio adjustment and hedging

decisions. While the role of volatility is most clearly evident in derivative

markets such as options and futures, it also has an important role to play in

equity markets.

From the foregoing discussion, improving our understanding of how volatility

changes over time is an interesting and potentially very rewarding area of

research activity in finance. One technique for doing this is the class of

autoregressive conditional heteroscedasticity (ARCH) models introduced by

Engle (1982). In a comprehensive survey of modelling volatility in empirical

finance, Bollerslev, Chou and Kroner (1992) find that ARCH models and their

various generalisations (see inter alia Bollerslev (1986)) have proven to be

very successful in modelling volatility. Bollerslev, Chou and Kroner (1992)

discuss a number of key papers which have analysed US stock returns. A

legitimate research extension is to determine the applicability of the ARCH

class of models to other markets. Indeed Bollerslev et al (1992, p.31) make a

call for further investigations in markets beyond the US. Despite its age;

despite it being the largest stock market in Africa and (in 1995) being the

fourteenth largest stock market in the world; and despite the availability of

data; the JSE has received relatively little attention in the (international)

literature in any form. Indeed, to the best of our knowledge, the time varying

volatility aspects of this market have not been previously examined.

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To some extent this line of research is already developing with studies

analysing ARCH effects in the Australian market (see Brailsford and Faff

(1993, 1996), Kearns and Pagan (1993)), the Dutch market (see De Jong,

Kemna and Kloek (1992)), the Japanese market (see Tse (1991)), the

Singaporean market (see Tse and Tung (1992)) and the UK market (see Poon

and Taylor (1992)). Accordingly, in the present paper we assess the general

applicability of ARCH/GARCH models to the JSE.

However, analysing volatility on the JSE is more than just a simple extension

of this line of research. By studying the possible ARCH-related effects

associated with the political changes occurring in South Africa this presents

the opportunity of examining the "emergence" of a sophisticated and developed

capital market which was isolated from the international community.

Specifically, we would expect that the volatility characteristics of the market would

change and that the post-announcement volatility would behave more like that

observed in other developed markets. Many studies of this type investigate

markets that are well integrated and well developed (see previous references).

Conversely, studies of less well integrated markets are constrained to examine

markets that are relatively underdeveloped (see for example, Yu (1996) on

China’s emerging markets). The JSE provides an instance where a well

developed market is (at least mildly) segmented. For these reasons, the JSE is

an opportunity to investigate a unique example of an "emerging" market, and,

hence of considerable interest and importance in a finance research setting.

The plan of this paper is as follows. In section two we outline some

background detail about the JSE. Section three contains our empirical

5

framework and discusses our results. Section four contains some concluding

remarks.

2. SOME DETAILS OF THE JSE

The JSE was established in 1887 making it the oldest surviving stock market in

Africa. In terms of market capitalisation it is the largest on the African

continent, being 57 times larger than the second largest market (Egypt) (see

Clark 1996, p.43). In 1995, it was ranked the world’s fourteenth largest stock

market, with a market capitalisation of R809.1 billion (US$149.2 billion).

Despite its relatively large size, historically, the turnover ratio has been low

(usually less than ten per cent) and the JSE is thinly traded. Bradfield (1989,

p.4-16) reports that approximately one third of the stocks listed on the

exchange do not trade for at least one out of every four week period, on

average. There are a number of factors which may be responsible for this,

inter alia, the Marketable Securities Tax, stamp tax, a lack of foreign investor

participation due to sanctions imposed during the apartheid era and high levels

of cross ownership (see Barr, Gerson and Kantor (1995) for a discussion of

ownership structures in South Africa and French and Poterba (1991) for the

effects of cross ownership on market capitalisation in Japan).

Roll (1992, p.6) reports that of the 24 FT Actuaries/Goldman Sacks national

Equity Market indices in his study, South Africa had the highest

(unconditional) volatility over the period April 1988 to March 1991. This was

6

30.20 per cent in US dollar terms. The second and third highest volatility were

in Hong Kong (24.85%) and Mexico (24.35%). In addition to the factors that

Roll (1992) investigates as contributing to (index) volatility, thin trading and

South African specific risk must contribute substantially to volatility. South

Africa has experienced substantial change since February 1990, when the

(then) President F. W. de Klerk removed the legal prohibition on the existence

of various political organisations and set in motion the process leading to the

multi-racial election and installation of a democratic government in 1994.

Roll’s (1992) sample period covers a period of substantial political uncertainty

in South African history.

To the extent that volatility is a measure of risk and the JSE was segmented

from global capital markets, we expect the structure of volatility to be very

different from that of other (integrated) countries. Bekaert and Harvey (1995)

write that for segmented countries, risk may be difficult to quantify as the

sources of risk may be very different from those in integrated markets. As

South African has moved away from apartheid toward a more democratic

society, it is reasonable to assume that its markets have become more

integrated to the world capital markets. Moreover, given the well developed

and highly sophisticated nature of the JSE prior to the de Klerk announcement,

other things being equal, we would expect a more readily detectable move to

integration. However, given that domestic investors remain constrained by

exchange controls, integration must come in the form of increased foreign

participation.

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In December 1994, the JSE was granted “designation status” by the Japan

Securities Dealers Association indicating that the JSE is an “appropriate”

market for Japanese investors. In March of 1995, the JSE was added to the

Morgan Stanley Index, while in April 1995 it was included in the IFC

Emerging Markets Global and Investable Indices. The JSE reports that for the

year ending February 1996, that gross foreign purchases had increased by 35.2

per cent over the previous year. The JSE President’s Review (1996) ascribes

this increase to improved perceptions of the South African economy, inclusion

of South Africa in emerging markets indices and renewed interest in emerging

markets after the Mexican crisis.

Issues of interest then are firstly, does the ARCH/GARCH methodology apply

to South African data and secondly, if so, has the structure of volatility

changed as South Africa moved from an apartheid system to a more democratic

system? As it reasonable to assume that during the apartheid years South

Africa capital markets would (largely) have been mildly segmented from global

markets, in essence we are investigating the effect of segmentation on stock

market returns volatility. A priori we expect that the time-varying nature of

the JSE market volatility will have changed from the pre- and post-

announcement periods. More particularly, we expect the behaviour of

conditional volatility over the latter period to conform more closely to the

specifications well documented for the developed markets in recent years.

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3. EMPIRICAL FRAMEWORK AND RESULTS

3.1 Data

We gathered daily data on three South African indices (the All Share Index

(ALSI), the Industrials Index (IND) and the Gold Index (GOLD)) over the

period March 20 1986 to February 23 1996. This data was obtained from the

I-Net database. (The I-Net database is maintained by the firm of Ivor, Jones,

Roy & Co., a firm of stockbrokers in Johannesburg, which has recently been

taken over by Deutsche Morgan Grenfell.) While we include a full analysis of

all three share market indices, our main results pertain to the overall market

impact, as reflected by the ALSI.

Clearly, gold mining and the gold sector have an important role to play in the

South African economy. It is a widely held view in South Africa that gold (and

mining shares in general) and industrial share returns are driven by different

risk factors (see for example, Gilbertson and Goldberg 1981). The basis for

this view is that mining firms sell their output into the integrated global

commodity market and are exposed to international "shocks". Hence, the

pervasive international nature of gold markets represents an added

complication in our study, since this will tend to bias our analysis against

finding a "volatility effect". That is, the gold sector will most likely be largely

immune from the political and economic isolation experienced by the rest of

the South African economy. Accordingly, a separate analysis of IND and

GOLD will help to finesse this issue. In summary, we expect the ALSI and

IND to reveal the greatest evidence of a "volatility effect" reflecting the

9

political change in South Africa. In effect our analysis of the GOLD index is

included more as a control than anything else.

Our period of analysis contains February 2 1990, the date on which the then

President de Klerk made a number of significant announcements regarding the

dismantling of the apartheid regime in South Africa. This enables analysis of

whether this date is associated with any structural break in the process driving

returns and volatility. While it took another four years before democratic

elections were held and some political uncertainty and violence were

experienced in the interim, assuming that the market is informationally

efficient, this date is the appropriate choice to evaluate the effects of

democratisation on the JSE. Hence we analyse three samples in our analysis, (i)

March 20 1986 to February 23 1996, which we refer to as the full sample

period (ii) March 20 1986 to February 1 1990 which we refer to as the “pre-

announcement” period, and (iii) February 5 1990 to February 23 1996 referred

to as the “post-announcement” period.

3.2 Stationarity

The first stage of the analysis involves determining the stationarity

characteristics of the index data. For each of the three indices in each of the

three samples we calculated the test of Dickey and Fuller (1979). The results

of the Dickey-Fuller (DF) tests are presented in table 1. As expected they

clearly show that the index data contains a unit root and is non-stationary.

Further analysis requires a stationary variable. Hence we focus on analysing

10

returns. By assuming continuous compounding we approximate returns as,

rt=log(Pt/Pt-1).

3.3 Descriptive Statistics

For the returns series on each index we calculated a number of descriptive

statistics. Specifically the statistics calculated were mean, variance, skewness,

kurtosis, the Dickey-Fuller (DF) test on returns, first order autocorrelation

coefficient (ρ1), the Box and Pierce (1970) Q statistic on the first twenty

autocorrelations of returns (Q20(r)), and the Box-Pierce Q statistic on the first

twenty autocorrelations of squared returns (Q20(r2)).

The mean and variance of daily returns for all three indices in all three samples

are fairly low. The mean in South African Rand terms is not as high as that

reported in Roll (1992) and the variance is substantially lower. It is interesting

to note that despite the increased political uncertainty following de Klerk’s

announcement that the unconditional variance of the time series decline. Both

the ALSI and IND returns have distributions with negative skewness although

this becomes less pronounced in the post-announcement sample (5/2/90 to

23/2/96). The GOLD returns exhibit a very slight positive skewness in all

three samples. The IND returns are very leptokurtic in the full sample

(20/3/86 to 23/2/96) and in the pre-announcement sample (20/3/86 to 1/2/90).

The IND returns only show slight excess kurtosis in the post-announcement

sample (5/2/90 to 23/2/96). The ALSI returns are also leptokurtic in all three

samples although this tendency is less pronounced in the post-announcement

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sample. However GOLD returns have a kurtosis which does not appear to

differ significantly from the normal distribution value of three.

The distributional characteristics of the GOLD index are very different from

those of the ALSI and IND indices. This is consistent with our earlier

argument that despite the political isolation, gold is priced internationally and,

hence, the South African gold sector will be driven more by global than by

domestic factors. This view finds some support in Roll (1992, p. 34 and 35)

where he adjusts market correlation coefficients for industrial structure. South

Africa’s correlation coefficient, which usually is low, increases dramatically

(especially compared to Australia which also has a large resource sector). All

return and squared return series show significant autocorrelation. This is

consistent with the extent of thin trading on the JSE.

An inspection of the autocorrelation and partial autocorrelation of the three

returns series in each of the three samples suggested that there was an

autocorrelation structure in returns that needed to be modelled. Therefore to

model this autocorrelation structure we used the general AR(k) model:

rt = φ1 rt-1 + φ2 rt-2 + ...... + φk rt-k + εt ... (1)

We note Nelson's (1992) result that precise specification of the conditional

mean is not critical for estimation of the conditional variance parameters.

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The estimated AR models for the ALSI are presented in the first row of tables

2, 3 and 4, for the IND in the first row of tables 5, 6 and 7, and for GOLD in

the first row of tables 8, 9 and 10. An examination of these results indicates

that the autoregressive structure in GOLD returns is very low relative to the

other series. For the full sample period (20/3/86 to 23/2/96) all of the return

series can reasonably be modelled as following an AR(1) model. For the ALSI

and IND returns there is more autocorrelation structure in the pre-

announcement period (20/3/86 to 1/2/90) than in the post-announcement

period (5/2/90 to 23/2/96). This is consistent with greater market integration

in the post-announcement sample as any autocorrelation induced by thin

trading would be reduced in the more integrated market. For the pre-

announcement period the ALSI appears to require a model with returns at lags

1 and 7, but only returns at lag 1 in the post-announcement period. For the

pre-announcement period the IND appears to require a model with returns at

lags of 1, 2, 3, 4, and 7, but only returns at lags of 1 and 2 in the post-

announcement period. In contrast, the model for GOLD appears to be an

AR(1) model for all three samples. Interestingly, this result further re-enforces

our earlier view that the global nature of the gold market will see the GOLD

index reveal little, if any, impact of any structural change between our two

sample periods.

3.4 Models of Time-Varying Volatility

Having identified an appropriate model for the mean of returns, we now

consider modelling the variance or volatility. Clearly the simplest possible

model is a model where the variance is constant. Further to this if the variance

13

is constant it makes OLS an efficient technique for estimating the AR models

discussed in the previous paragraph. Therefore a constant variance model is to

be preferred unless we can find evidence to suggest that the variance is time

varying. However as noted in the introduction many researchers have found

autoregressive conditional heteroscedasticity (ARCH) effects in other stock

markets.

The ARCH model introduced by Engle (1982) is of the form,

rt = φ1 rt-1 + φ2 rt-2 + ...... + φk rt-k + εt ... (2)

εt ∼ N(0,ht)

ht = α0 + α1 ε2t-1 + α2 ε2

t-2 + .... + αp ε2t-q ... (3)

Since ht is the conditional variance, all of the α parameters are constrained to

be strictly non-negative. A problem with the standard ARCH model is that it

typically requires a long lag of q values to fit the data. A more parsimonious

model is the generalised (GARCH) model introduced by Bollerslev (1986)

where a GARCH (p,q) model is given by:

ht = α0 + α1 ε2t-1 + α2 ε2

t-2 + .... + αp ε2t-q + β1 ht-1 + β2 ht-2 + βp ht-p ... (4)

14

Again, since ht is the conditional variance, all of the α and β parameters are

now restricted to be non-negative. Bollerslev (1987, p.544) points out that the

GARCH(p,q) model can readily be interpreted as a generalisation of Engle's

(1982) ARCH(q) model which includes p moving average terms in the

autoregressive equation for the conditional expectation of εt2.

3.5 Diagnostic Tests of ARCH effects

Prior to investigating these models we apply diagnostic tests to the residuals of

the estimated AR models from table 2 to determine if their are ARCH or

GARCH effects in the data. The simplest diagnostic test for the presence of

ARCH effects is the Lagrange Multiplier (LM) test suggested by Engle (1982).

Lee (1991) has demonstrated that Engle’s (1982) LM test for ARCH effects is

also the LM test for GARCH effects. This test which has an asymptotic χ2

distribution is calculated from an auxiliary regression of the squared residuals

from the AR model on a constant and the lagged squared residuals. The

calculated values of the LM test are presented in table 1.

These results show a clear presence of ARCH/GARCH effects at the 5%

significance level in all returns series and in all samples except for GOLD

returns in the post-announcement period (5/2/90 to 23/2/96). A potential

problem with the LM test is that it is a two-sided test, whereas we know that

ARCH/GARCH parameters must be non-negative. Therefore the use of a two-

sided test fails to use all the relevant information that a researcher has about

ARCH/GARCH models. To exploit the one-sided nature of the diagnostic

testing problem for ARCH/GARCH effects Lee and King (1993) have

15

suggested a one-sided test for ARCH/GARCH effects. They have a standard

version of their test, which is denoted LBS1, and a version of their test which

is robust to non-normality in the data, which is denoted LBS2. Both of their

test statistics have an asymptotic standard normal distribution. The calculated

values of the LBS tests are also presented in table 1. Consistent with the LM

test the results again show a clear presence of ARCH/GARCH effects in all

return series in all samples with the exception of GOLD returns in the post-

announcement period (5/2/90 to 23/2/96).

3.6 Estimated ARCH/GARCH Models

Having identified the presence of ARCH/GARCH effects in the data we now

estimate the models with ARCH/GARCH effects. For each return series in

each sample we started with an ARCH(1) model, that is, an ARCH model

where q=1, and then moved to successively more complex models such as

ARCH(2), ARCH(3) and so on. We stopped estimating ARCH models when

our TSP estimation routine failed to converge due to singularity in the data.

The presence of singularity in the data indicates that there is not enough

information in the data to identify and estimate further parameters.

We followed a similar approach to the estimation of GARCH models. We

started with the simple GARCH(1,1) model, that is, a GARCH model where

p=1 and q=1 and then increased p and q successively to produce more complex

GARCH models. Again, we ceased estimating GARCH models when our TSP

estimation routine failed to converge due to singularity in the data. This leads

to a range of ARCH and GARCH models being estimated.

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An obvious question is which is the best model of the conditional variance. To

answer this question we used the criteria suggested by Pagan and Schwert

(1990). Specifically, Pagan and Schwert (1990) suggested choosing the model

with the highest R2 from an auxiliary regression of the squared residuals on a

constant and the fitted conditional variance from the ARCH model. For each

ARCH/GARCH model estimated we report the calculated Pagan and Schwert

R2. The estimated ARCH/GARCH models for the ALSI are presented in tables

2, 3 and 4, for the IND in tables 5, 6 and 7, and for GOLD in tables 8, 9 and

10.

An examination of the results reveals the following information. A number of

ARCH and GARCH models are successfully fitted to each of the data series in

each of the three samples. A general finding is that the more complex

ARCH/GARCH models can only be fitted to the post-announcement sample

(5/2/90 to 23/2/96) for the ALSI and IND returns. For instance for the ALSI

returns models up to ARCH (12) can be fitted in the post-announcement

sample, but models beyond ARCH (4) fail to estimate in the pre-announcement

sample. For the IND returns models up to ARCH (8) can be fitted in the post-

announcement sample, but models beyond ARCH (2) fail to estimate in the

pre-announcement sample. This more complex volatility structure post-

announcement, is consistent with findings for other developed stock markets.

Moreover, as outlined earlier in this paper, it supports the hypothesis of

greater market integration.

17

Interestingly, for the GOLD returns the reverse pattern is observed with

models up to ARCH (9) fitted in the pre-announcement sample, but models

beyond ARCH (4) fail to estimate in the post-announcement sample. The

complexity of models which can be successfully fitted to the full sample lies

between the pre-announcement and post-announcement results, again with the

exception of the results for GOLD.

A number of features are common to the results of all indices and all samples.

First, the parameter estimates for αi and βi are fairly insensitive to the

changing complexity of the model. Secondly, the Pagan-Schwert R2 measures

are low and fairly similar across the range of models. Finally, the estimated

ARCH and GARCH models are stationary in that the sum of αi and βi

parameters in the model are less than unity. This implies that the impact of a

shock on volatility declines as we move away from the shock. The only

exception in this regard is the GARCH (1,2) model for ALSI returns in the

post-announcement sample where the parameters sum to the explosive value of

1.084. This implies, the counter-intuitive result that the impact of a shock on

volatility is amplified as we move away from the shock. In general the sum of

the αi and βi parameters in the GARCH models is greater than 0.95 for ALSI

and GOLD returns. However, for IND returns the GARCH models are much

less persistent typically summing to between 0.7 and 0.8. The ARCH models

are much less persistent with the sum of the αi values increasing with the lag

length but only up to a maximum value of about 0.8.

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3.7 Preferred ARCH/GARCH Models

Comparing across the different indices shows that the IND returns supports a

lower complexity of ARCH models than the ALSI and GOLD returns. Indeed,

applying the Pagan-Schwert R2 criteria to IND returns selects an ARCH (1)

model as the preferred model in both the pre-announcement and post-

announcement but ARCH (3) in overall period. This contrasts with the ALSI

returns where the ARCH (4) model is the preferred model in the pre-

announcement sample and the GARCH (1,2) model is the preferred model in

the post-announcement sample. A different finding is reached with respect to

GOLD returns where the ARCH (3) model is the preferred model in both the

pre-announcement and post-announcement sample, yet again re-enforcing the

evidence that the gold sector is least affected by the political change in South

Africa. In general results for other stock markets tend to support the more

complex models which suggests that the volatility patterns for South African

stocks are much less complex. However, we note that the preferred model for

ALSI returns has become more complex in the post-announcement sample,

which again is consistent with the hypothesis of greater market integration.

3.8 POLITICAL CHANGE AND VOLATILITY

As argued earlier, a priori we expected to find that the time-varying nature of

the JSE market volatility will have changed from the pre- and post-

announcement periods. More particularly, we expected the behaviour of

conditional volatility over the latter period to conform more closely to the

specifications well documented for the developed markets in recent years. In

19

essence, these predictions relate to an hypothesis of market integration in the

post-announcement sample.

Our primary findings have been based on the All Share Index (ALSI) which

support the "political change volatility effect". This began with the finding

that the autocorrelation structure of returns became less complex in the post-

announcement sample, consistent with the notion that market integration had

reduced thin trading effects. This was re-enforced by the final key finding that

the conditional volatility specification became more complex - from an ARCH

(4) model in the pre-announcement sample to a GARCH (1,2) model in the

post-announcement sample. Notably, the GARCH specification is more in line

with models found in other developed countries, again consistent with our

integration prediction.

4. CONCLUSION

On February 2 1990, President de Klerk announced to the world that South

Africa would undergo a fundamental change to its political structure. For

several years prior to his announcement, South Africa was the subject of an

extreme form of political and economic isolation from the international

community. As a result of this announcement, it would be expected that South

Africa's financial markets transformed from a state of segmentation to a degree of

integration in world markets.

20

One means of assessing the possible effects of this major political change is by

investigating the time-varying behaviour of stock market volatility. Specifically, we

would expect that the volatility characteristics of the market would change and that the

post-announcement volatility would behave more like that observed in other developed

markets. Accordingly, in this paper we have investigated the applicability of the

autoregressive conditional heteroscedasticity (ARCH) family of models to South

African stock return data.

By studying the possible ARCH-related effects associated with the political

changes occurring in South Africa this presents the opportunity of examining

the "emergence" of a sophisticated and developed capital market which was

isolated from the international community. Many studies of this type

investigate markets that are well integrated and well developed (see previous

references). Conversely, studies of less well integrated markets are

constrained to examine markets that are relatively underdeveloped. The JSE

provides an instance where a well developed market is (at least mildly)

segmented. For these reasons, the JSE is an opportunity to investigate a

unique example of an "emerging" market, and, hence of considerable interest

and importance in a finance research setting.

Specifically, we examine whether ARCH/GARCH models can be fitted to daily returns

data on the All Stocks Index (ALSI), the Industrials Index (IND) and the Gold Index

(GOLD) over the period March 20 1986 to February 23 1996. Our results support the

applicability of ARCH/GARCH models. Further, we find that with the exception of

GOLD returns, more complex volatility models can be supported by the data in the

21

post-announcement period. As these more complex models are typically supported by

ARCH studies in other stock markets, this suggests greater international integration of

the Johannesburg Stock Exchange in the post-1990s period.

22

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TABLE 1: SUMMARY STATISTICS ON RETURNS

This table presents summary statistics for returns on the ALSI, IND and GOLD for daily data over three sample periods: (1) 20/3/86 to 23/2/96: (2) 20/3/86 to 1/2/90: (3) 5/2/90 to 23/2/96.

ALSI IND GOLD

Full Sample20/3/86-23/2/96

Pre-AnnouncementSample

20/3/86 - 1/2/90

Post-AnnouncementSample

5/2/90 - 23/2/96Full Sample

20/3/86 - 23/2/96

Pre-AnnouncementSample

20/3/86 - 1/2/90

Post-AnnouncementSample

5/2/90 - 23/2/96Full Sample

20/3/86 - 23/2/96

Pre-AnnouncementSample

20/3/86 - 1/2/90Post-Announcement5/2/90 - 23/2/96

DF test (index) 3.31351 1.81720 2.65715 5.07271 2.64135 4.03371 -0.298112 0.523319 -0.08795

Mean 0.00060935 0.00079245 0.00046423 0.00078018 0.00091972 0.00064366 0.00013555 0.00055759 -0.00015128

Variance 0.00011895 0.00018125 0.00007875 0.00007509 0.00010853 0.00005214 0.00050397 0.00042423 0.00055497

Skewness -1.48471 -1.85177 -0.4628 -3.20337 -4.55158 -0.55906 0.22590 0.00083612 0.32917

Kurtosis 16.40858 16.75958 3.31745 48.94106 57.87405 5.76445 2.56635 3.11905 2..27907

DF test(returns)

-42.882 -27.477 -32.318 -39.195 -25.589 -29.392 -46.421 -28.969 -36.218

ρ1 0.147 0.121 0.183 0.230 0.186 0.270 0.072 0.070 0.072

Q20(r) 131 86.9 87.8 278 147 173 35.1 41.8 34.6

Q20(r2) 545 205 87.3 326 130 85.7 342 309 133

LM 106.93669 32.94409 22.80339 153.63772 37.19096 104.85251 13.26014 45.67352 0.016627

LBS1 32.13987 18.00579 7.63657 66.15211 35.28201 20.95113 5.50314 10.87369 0.18787

LBS2 10.34009 5.73969 4.77529 12.39476 6.09844 10.23975 3.63723 6.75822 0.12895

TABLE 2: ARCH/GARCH MODELS FOR ALSI RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the ALSI index over the full sample: (1) 20/3/86 to 23/2/96.

ALSI φ1 α0 α1 α2 α3 α4 α5 α6 α7 α8 α9 β1 β2 Σ(αi + βi)

PAGAN-SCHWERT

R2

AR (1) 0.150*(7.571)

ARCH (1) 0.207*(10.715)

0.831*(69.191)

0.291*(22.762)

0.291 0.048352

ARCH (2) 0.285*(17.392)

0.725*(52.215)

0.292*(24.686)

0.123*(5.808)

0.415 0.050507

ARCH (3) 0.184*(8.262)

0.545*(28.191)

0.285*(25.869)

0.090*(5.402)

0.218*(19.187)

0.593 0.062570

ARCH (4) 0.200*(9.237)

0.489*(25.697)

0.257*(26.431)

0.092*(5.574)

0.202*(16.034)

0.090*(6.803)

0.641 0.068570

ARCH (5) 0.207*(9.361)

0.441*(22.895)

0.257*(26.145)

0.091*(5.626)

0.198*(16.394)

0.083*(6.626)

0.062*(3.723)

0.691 0.066319

ARCH (6) 0.206*(8.875)

0.407*(21.831)

0.263*(27.315)

0.090*(5.655)

0.199*(16.364)

0.077*(5.335)

0.052*(3.221)

0.053*(3.710)

0.734 0.067294

ARCH (7) 0.204*(8.823)

0.390*(21.588)

0.248*(19.155)

0.079*(4.964)

0.197*(16.392)

0.074*(5.313)

0.049*(3.150)

0.053*(3.762)

0.047*(2.675)

0.747 0.069517

ARCH (8) 0.195*(8.165)

0.382*(20.761)

0.245*(19.202)

0.057*(3.162)

0.192*(15.546)

0.076*(5.803)

0.032*(2.042)

0.023(1.543)

0.048*(2.704)

0.069*(4.062)

0.742 0.072783

ARCH (9) 0.195*(8.173)

0.374*(15.892)

0.242*(19.054)

0.056*(3.042)

0.194*(15.382)

0.078*(5.864)

0.031*(2.019)

0.022(1.485)

0.048*(2.726)

0.069*(4.044)

0.010(0.711)

0.750 0.072682

GARCH(1,1)

0.201*(8.938)

0.055*(7.327)

0.188*(25.506)

0.789*(78.188)

0.977 0.059890

GARCH(1,2)

0.193*(9.329)

0.051*(5.779)

0.232*(27.735)

0.138*(4.454)

0.616*(19.236)

0.986 0.073224

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 3: ARCH/GARCH MODELS FOR ALSI RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the ALSI index over the pre-announcement sample: (2) 20/3/86 to 1/2/90.

ALSI φ1 φ7 α0 α1 α2 α3 α4 β1 β2 Σ(αi + βi)

PAGAN-SCHWERT

R2

AR (1,7) 0.129*(4.039)

0.113*(3.543)

ARCH (1) 0.189*(5.507)

0.046(1.800)

1.150*(40.735)

0.397*(14.381)

0.397 0.043027

ARCH (2) 0.315*(11.314)

0.062*(2.871)

0.945*(24.434)

0.422*(16.079)

0.152*(3.788)

0.574 0.050601

ARCH (3) 0.104*(2.685)

-0.002(0.725)

0.677*(14.344)

0.404*(16.346)

0.009*(3.601)

0.262*(12.143)

0.675 0.062001

ARCH (4) 0.140*(3.395)

0.025(0.938)

0.624*(12.344)

0.361*(15.707)

0.086*(3.654)

0.229*(9.678)

0.098*(4.643)

0.774 0.066196

GARCH(1,1)

0.135*(3.287)

0.022(0.626)

0.183*(6.830)

0.324*(15.078)

0.634(35.421)

0.958 0.050776

GARCH(1,2)

0.125*(3.095)

0.015(0.395)

0.175*(5.673)

0.365*(15.482)

0.145(3.407)

0.454(8.976)

0.964 0.065808

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 4: ARCH/GARCH MODELS FOR ALSI RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the ALSI index over the post-announcement sample: (3) 5/2/90 to 23/2/96.

ALSI φ1 α0 α1 α2 α3 α4 α5 α6 α7 α8 α9 α10 α11 α12 β1 β2

Σ(αi +βi)

PAGAN-SCHWERT R2

AR(1) 0.185*(7.323)

ARCH (1) 0.218*(7.604)

0.672*(35.141)

0.122*(4.457)

0.122 0.018211

ARCH (2) 0.225*(7.865)

0.638*(29.906)

0.122*(4.211)

0.048*(2.014)

0.170 0.017174

ARCH (3) 0.236*(8.500)

0.505*(23.260)

0.121*(13.911)

0.061*(2.629)

0.082*(7.502)

0.264 0.017208

ARCH (4) 0.246*(8.885)

0.456*(20.768)

0.119*(3.871)

0.071*(3.026)

0.171*(6.871)

0.071*(3.354)

0.432 0.020659

ARCH (5) 0.250*(9.474)

0.392*(17.996)

0.117*(3.852)

0.091*(3.720)

0.147*(6.002)

0.049*(2.645)

0.118*(4.587)

0.522 0.027376

ARCH (6) 0.245*(8.764)

0.385*(17.682)

0.110*(3.636)

0.083*(3.460)

0.134*(5.299)

0.052*(2.730)

0.107*(4.282)

0.032(1.895)

0.518 0.028565

ARCH (7) 0.239*(8.741)

0.390*(18.062)

0.098*(3.347)

0.049*(2.020)

0.124*(4.927)

0.049*(2.649)

0.102*(4.112)

0.040*(2.061)

0.037(1.791)

0.499 0.030693

ARCH (8) 0.241*(8.694)

0.372*(16.576)

0.096*(3.335)

0.046(1.870)

0.107*(4.411)

0.054*(2.792)

0.089*(3.457)

0.025(1.201)

0.043*(1.999)

0.058*(2.513)

0.518 0.033422

ARCH (9) 0.245*(8.839)

0.352*(11.887)

0.093*(3.188)

0.035(1.284)

0.113*(4.563)

0.054*(2.812)

0.087*(3.317)

0.024(1.140)

0.043*(2.046)

0.056*(2.424)

0.041*(2.072)

0.546 0.031620

ARCH (10) 0.247*(8.858)

0.342*(10.949)

0.094*(3.163)

0.038(1.341)

0.110*(4.344)

0.053*(2.803)

0.085*(3.257)

0.024(1.153)

0.041(1.951)

0.054*(2.328)

0.042*(2.077)

0.019(0.919)

0.560 0.031196

ARCH (11) 0.247*(8.882)

0.338*(10.557)

0.093*(3.162)

0.038(1.341)

0.111*(4.358)

0.053*(2.817)

0.084*(3.242)

0.026(1.227)

0.038(1.807)

0.054*(2.296)

0.043*(2.093)

0.016(0.789)

0.011(0.499)

0.567 0.031488

ARCH (12) 0.248*(8.912)

0.336*(10.256)

0.093*(3.175)

0.039(1.370)

0.111*(4.383)

0.052*(2.731)

0.084*(3.251)

0.027(1.263)

0.038(1.759)

0.052*(2.202)

0.046*(2.178)

0.017(0.842)

0.006(0.265)

0.010(0.598)

0.575 0.031043

GARCH(1,1)

0.231*(9.238)

0.007*(2.797)

0.050*(5.953)

0.932*(97.910)

0.982 0.044919

GARCH(1,2)

0.237*(8.929)

0.012*(2.632)

0.082*(5.174)

0.378(1.827)

0.624*(4.318)

1.084 0.050684

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 5: ARCH/GARCH MODELS FOR IND RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the IND index over the full sample: (1) 20/3/86 to 23/2/96.

IND φ1 α0 α1 α2 α3 β1 Σ(αi + βi)PAGAN-

SCHWERT R2

AR(1) 0.236*(12.129)

ARCH (1) 0.280*(27.031)

0.551*(210.170)

0.208*(12.121)

0.208 0.073857

ARCH (2) 0.334*(27.190)

0.509*(204.220)

0.125*(6.747)

0.117*(11.897)

0.242 0.046978

ARCH (3) 0.335*(15.269)

0.402*(175.967)

0.134*(7.850)

0.001(0.166)

0.298*(34.050)

0.433 0.087935

GARCH (1,1) 0.337*(15.661)

0.187*(10.617)

0.131*(7.750)

0.584*(15.132)

0.7150.079115

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 6: ARCH/GARCH MODELS FOR IND RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the IND index over the pre-announcement sample: (2) 20/3/86 to 1/2/90.

IND φ1 φ2 φ3 φ4 φ7 α0 α1 α2 β1 Σ(αi +βi)

PAGAN-SCHWERT R2

AR(1,3,4,7) 0.184*(5.754)

0.029(0.900)

0.054(1.658)

0.068*(2.131)

0.144*(4.552)

ARCH (1) 0.365*(9.603)

-0.200(0.038)

0.091*(3.949)

0.021(0.645)

0.055(1.283)

0.714*(138.078)

0.272*(4.141)

0.272 0.124254

ARCH (2) 0.349*(12.872

0.056(0.947)

0.069*(2.147)

-0.046(1.556)

0.088*(2.399)

0.708*(123.081)

0.100*(3.596)

0.162*(4.976)

0.262 0.027780

GARCH (1,1) 0.330*(6.353)

0.049(0.716)

0.054(1.169)

-0.012(0.215)

0.079(1.501)

0.240*(4.990)

0.115*(3.571)

0.625*(8.410)

0.740 0.068112

GARCH (2,1) 0.308*(6.268)

0.052(0.699)

0.059(1.043)

-0.009(0.148)

0.075(1.460)

0.312*(3.800)

0.075*(3.636)

0.125*(1.966)

0.477*(3.445)

0.677 0.033000

Note: All parameter estimates in the αo column should be multiplied by 10-4.

TABLE 7: ARCH/GARCH MODELS FOR IND RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the IND index over the post-announcement sample: (3) 5/2/90 to 23/2/96

IND φ1 φ2 α0 α1 α2 α3 α4 α5 α6 α7 α8 β1 Σ(αi +βi)

PAGAN-SCHWERT

R2

AR(1,2) 0.260*(10.110)

0.063*(2.450)

ARCH (1) 0.296*(9.787)

0.047*(1.986)

0.383*(49.226)

0.210*(7.872)

0.210 0.075691

ARCH (2) 0.318*(10.310)

0.041(1.403)

0.311*(25.153)

0.236*(7.896)

0.167*(9.419)

0.403 0.053568

ARCH (3) 0.319*(10.323)

0.058(1.840)

0.286*(20.744)

0.234*(8.074)

0.171*(9.985)

0.065*(2.620)

0.470 0.05008

ARCH (4) 0.327*(10.662)

0.060(1.907)

0.274*(19.091)

0.232*(8.054)

0.175*(10.392)

0.053*(2.173)

0.037*(2.043)

0.497 0.049987

ARCH (5) 0.313*(11.098)

0.056(1.808)

0.250*(17.970)

0.216*(8.212)

0.190*(10.674)

0.055*(2.187)

0.025(1.442)

0.067*(5.100)

0.580 0.044118

ARCH (6) 0.324*(10.555)

0.042(1.310)

0.243*(17.772)

0.225*(8.416)

0.190*(10.880)

0.050*(2.099)

0.024(1.385)

0.053*(4.737)

0.017*(2.036)

0.559 0.050999

ARCH (7) 0.323*(10.547)

0.043(1.318)

0.225*(14.502)

0.238*(8.788)

0.170*(10.527)

0.032(1.437)

0.117(0.778)

0.049*(4.591)

0.013(1.790)

0.085*(4.109)

0.704 0.050999

ARCH (8) 0.327*(10.626)

0.041(1.297)

0.220*(13.654)

0.239*(8.835)

0.173*(10.687)

0.033(1.483)

0.012(0.757)

0.047*(4.361)

0.013(1.862)

0.084*(4.077)

0.013(0.990)

0.614 0.050937

GARCH (1,1) 0.325*(10.635)

0.053(1.748)

0.848*(9.330)

0.216*(10.987)

0.628*(24.020)

0.844 0.044472

GARCH (2,1) 0.326*(10.595)

0.054(1.679)

0.090*(9.203)

0.222*(8.636)

0.073(0.335)

0.606*(20.036)

0.901 0.046000

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 8: ARCH/GARCH MODELS FOR GOLD RETURNSThis table presents estimated ARCH and GARCH models for daily returns on the GOLD index over the full sample: (1) 20/3/86 to 23/2/96.GOLD φ1 α0 α1 α2 α3 α4 α5 α6 α7 α8 α9 α10 α11 α12 β1 β2 β3

Σ(αi +βi)

PAGAN-SCHWERT R2

AR (1) 0.072*(2.820)

ARCH (1) 0.081*(3.763)

0.459*(42.622)

0.083*(4.681)

0.083 0.005443

ARCH (2) 0.095*(4.385)

0.416*(32.195)

0.086*(4.984)

0.091*(4.131)

0.177 0.009085

ARCH (3) 0.081*(4.004)

0.372*(27.906)

0.087*(5.289)

0.075*(3.482)

0.107*(5.889)

0.269 0.012167

ARCH (4) 0.095*(4.550)

0.333*(26.080)

0.068*(4.530)

0.072*(3.534)

0.109*(6.307)

0.092*(6.307)

0.341 0.032557

ARCH (5) 0.094*(4.514)

0.321*(24.579)

0.063*(4.245)

0.071*(3.581)

0.109*(6.343)

0.901*(6.263)

0.032(1.796)

0.366 0.032507

ARCH (6) 0.100*(4.750)

0.295*(21.385)

0.071*(4.673)

0.066*(3.529)

0.105*(6.308)

0.086*(5.785)

0.027(1.630)

0.066*(3.720)

0.421 0.033815

ARCH (7) 0.101*(4.746)

0.274*(19.017)

0.071*(4.650)

0.072*(3.790)

0.098*(6.120)

0.085*(5.661)

0.027(1.667)

0.070*(3.873)

0.045*(3.318)

0.468 0.032086

ARCH (8) 0.091*(4.310)

0.249*(16.173)

0.069*(4.622)

0.056*(2.856)

0.084*(4.686)

0.090*(5.890)

0.022(1.364)

0.042*(2.150)

0.043*(3.368)

0.107*(6.088)

0.513 0.039997

ARCH (9) 0.092*(4.295)

0.244*(15.248)

0.065*(4.447)

0.055*(2.736)

0.084*(4.684)

0.092*(5.918)

0.022(1.340)

0.043*(2.147)

0.043*(3.353)

0.107*(5.890)

0.018(1.295)

0.529 0.039931

ARCH (10) 0.095*(4.364)

0.208*(13.879)

0.073*(4.845)

0.046*(2.459)

0.088*(4.867)

0.089*(6.010)

0.023(1.384)

0.047*(2.392)

0.041*(3.475)

0.077*(4.315)

0.019(0.806)

0.112*(6.506)

0.615 0.039262

ARCH (11) 0.094*(4.390)

0.195*(12.443)

0.070*(4.934)

0.046*(2.391)

0.083*(4.479)

0.087*(6.078)

0.015(0.905)

0.043*(2.230)

0.041*(3.476)

0.060*(3.274)

0.007(0.647)

0.111*(6.717)

0.068*(3.847)

0.631 0.04066

ARCH (12) 0.096*(4.455)

0.189*(11.463)

0.071*(4.994)

0.046*(2.428)

0.084*(4.505)

0.086*(5.838)

0.015(0.908)

0.040*(2.097)

0.041*(3.465)

0.054*(2.781)

0.007(0.568)

0.110*(6.390)

0.067*(3.750)

0.021(1.257)

0.642 0.041758

GARCH(1,1)

0.091*(4.238)

0.009*(4.887)

0.058*(9.413)

0.926*(124.242)

0.984 0.044295

GARCH(1,2)

0.091*(4.162)

0.009*(4.396)

0.064*(5.744)

0.790*(3.725)

0.129(0.639)

0.983 0.044079

GARCH(1,3)

0.089*(4.018)

0.010(4.353)

0.074*(5.919)

0.606*(2.732)

0.285(0.859)

0.016(0.084)

0.981 0.042956

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 9: ARCH/GARCH MODELS FOR GOLD RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the GOLD index over the pre-announcement sample: (2) 20/3/86 to 1/2/90.

GOLD φ1 α0 α1 α2 α3 α4 α5 α6 α7 α8 α9 β1 β2 Σ(αi +βi)

PAGAN-SCHWERT

R2

AR(1) 0.071*(2.214)

ARCH (1) 0.111*(3.250)

0.330*(22.885)

0.222*(6.234)

0.222 0.049187

ARCH (2) 0.109*(2.878)

0.293*(19.250)

0.199*(6.248)

0.116*(3.225)

0.315 0.047738

ARCH (3) 0.765*(2.307)

0.262*(15.874)

0.190*(6.614)

0.113*(3.399)

0.089*(3.478)

0.392 0.051185

ARCH (4) 0.097*(2.760)

0.230*(14.190)

0.152*(5.703)

0.112*(3.685)

0.064*(2.726)

0.123*(5.165)

0.451 0.088320

ARCH (5) 0.097*(2.742)

0.224*(12.876)

0.153*(5.637)

0.109*(3.689)

0.065*(2.775)

0.125)*(5.187)

0.011(0.499)

0.463 0.086800

ARCH (6) 0.101*(2.805)

0.214*(11.424)

0.158*(5.713)

0.110*(3.713)

0.065*(2.829)

0.120*(0.561)

0.024(1.079)

0.023(1.080)

0.500 0.085900

ARCH (7) 0.099*(2.697)

0.208*(10.619)

0.155*(5.542)

0.114*(3.784)

0.064*(2.753)

0.118*(4.797)

0.014(0.605)

0.024(1.097)

0.174(0.717)

0.663 0.084800

ARCH (8) 0.091*(4.467)

0.181*(9.771)

0.158*(5.636)

0.101*(3.098)

0.079*(3.289)

0.116*(4.767)

0.019(0.801)

0.002(0.083)

0.011(0.442)

0.091*(3.122)

0.577 0.085414

ARCH (9) 0.089*(2.363)

0.178*(9.132)

0.153*(5.606)

0.098*(3.079)

0.081*(3.330)

0.118*(4.815)

0.015(0.642)

0.001(0.040)

0.012(0.475)

0.090*(3.068)

0.017(0.617)

0.568 0.085313

GARCH (1,1) 0.078*(2.209)

0.019*(3.954)

0.105*(7.132)

0.851*(42.802)

0.956 0.078311

GARCH (1,2) 0.076*(2.122)

0.021*(3.671)

0.126*(7.211)

0.371*(2.112)

0.454*(2.655)

0.951 0.082268

Note: All parameter estimates in the α0 column should be multiplied by 10-4.

TABLE 10: ARCH/GARCH MODELS FOR GOLD RETURNS

This table presents estimated ARCH and GARCH models for daily returns on the GOLD index over the post-announcement sample: (3) 5/2/90 to 23/2/96.

GOLD φ1 α0 α1 α2 α3 α4 β1 Σ(αi + βi)PAGAN-

SCHWERTR2

AR(1) 0.072*(2.820)

ARCH (1) 0.072*(2.809)

0.550*(35.370)

0.004(0.281)

0.004 0.000131

ARCH (2) 0.081*(3.120)

0.520*(27.730)

0.010(0.561)

0.052(1.870)

0.062 0.020665

ARCH (3) 0.080*(3.203)

0.470*(24.823)

0.009(0.512)

0.046(1.701)

0.100*(4.290)

0.155 0.035515

ARCH (4) 0.090*(5.559)

0.423*(22.135)

0.162(0.099)

0.039(1.673)

0.124*(4.898)

0.072*(4.083)

0.397 0.015363

GARCH (1,1) 0.097(3.356)

0.006*(2.745)

0.040*(5.391)

0.949*(94.836)

0.989 0.030719

Note: All parameter estimates in the α0 column should be multiplied by 10-4.