International Stock Market Interdependence:
A South African Perspective
Owen Beelders∗
Department of Economics
Emory University
March 14, 2002
Abstract
The time-varying interdependence between South Africa and both
the UK and US is modeled using a latent variable approach. We find
little interdependence prior to March 1995 when exchange controls
and a dual exchange rate regime were in place. After the unification
of the exchange rates and the removal of exchange controls on nonresidents, the interdependence with the US increased considerably.
Despite the fact that many large South African companies have their
primary or secondary listing on the London Stock Exchange, there is
little interdependence with the UK after March 1995. The increase
in interdependence with the US is consistent with the increase in US
purchases of South African equities after March 1995.
JEL Classification Code: G15
∗
I thank Hisham Foad and Francisco Parodi for the comments and Daniel English
for his research assistance. All remaining errors are mine. Contact Information: Owen
Beelders, Department of Economics, Emory University, Atlanta Ga 30322-2240; tel.no.:
(404) 727-6650; fax: (404) 727-4639; e-mail: obeelde@emory.edu
1
1
Introduction
The South African financial markets have been through a tumultuous time
during the decade of the 1990’s. Following enormous political changes and an
easing of foreign sentiment towards the country in the first half of the decade,
it was reclassified as an emerging market and was subject to severely volatile
portfolio flows in the latter half of the decade. The objective of this paper
is to analyze the relationship between the South African (SA) stock market
and the stock markets of the United Kingdom (UK) and United States (US)
during this period.
In the decade of the 1990’s, the most important economic event was the
unification of the dual exchange rate on March 13, 1995. This was accompanied by the relaxation of exchange controls on residents and the removal
of exchange controls on non-residents. The dual exchange rate regime and
stringent exchange controls were originally introduced to insulate the local
economy from the severe capital outflow due to political risk, but with the
release of Nelson Mandela (the imprisoned leader of the African National
Congress) in 1990, the first democratic elections in April 1994, and an improvement in the level of foreign reserves, these measures could be removed.
Despite all these positive changes, the Economist classified South Africa as
an Emerging Market in its January 8, 1994 issue. This classification was
also adopted by the global financial community and as a result, the South
African stock market was severely affected by the emerging market crises in
the latter part of the 1990’s.
Ripley (1973) and Roll (1992) have documented that the strength of the
correlation between stock markets is affected by the following factors. First,
markets that are in the same times zone tend to be more strongly correlated.
Trading times on the London Stock Exchange run from 9am to 5pm, Greenwich Mean Time (GMT), 9:30am to 4pm (GMT-5) on the New York Stock
Exchange and 9am to 5pm (GMT+2) on the Johannesburg Stock Exchange
(JSE). We expect to find a stronger correlation between SA and the UK
because the trading times overlap by 6 hours as opposed to only 90 minutes
during daylight savings time in the US. Second, the strength of the correlation is positively related to the number of stocks in each national index. To
be consistent across the three countries, we choose the broadly based market
indexes for this study. We use the JSE all share index for South Africa,
the Standard and Poors 500 Index for the US and the Financial Times All
share index for the UK. Third, differences in the industrial composition of
2
each country reduces the measured correlation. The South African economy
has been resourced based for most of the past century and this has been
reflected in the stock market where precious metals such as gold have played
a very important role. To the extent that the US and UK have a greater
manufacturing component and more recently a greater service sector, this
may reduce the correlation with the US and UK. Fourth, the exchange rate
regime matters. From 1985 to 1995, South Africa had a dual exchange rate
regime: a commercial rate was used for trade flows and a financial rate for
capital flows. The financial rate traded at a discount to the commercial rate
and the discount was referred to as a political risk premium. Following the
removal of the dual exchange rate regime in South Africa and the move to
a freely floating exchange rate, we expect to find a stronger correlation with
the US and UK after March 1995.
Beside the research of Ripley (1973) and Roll (1992), Bekaert (1995) has
also documented that the cross-listing of stocks helps to increase the correlation between markets. The fact that many South African companies are
traded as American Depository Receipts (ADR’s) in the US and have secondary listings on the London Stock Exchange should increase the correlation
with both the US and UK. Finally, with the reduced cost of electronic trading, and the development of information media such as Bloomberg terminals
and CNN that have expedited the transmission of news, we expect to see
greater co-movement in the latter half of the decade.
Within the broader macroeconomic and political changes in South Africa,
there were also two positive changes on the JSE that may lead to an increase
in its the correlation with the US and UK. First, brokerage fees on the JSE
changed from fixed to flexible in November 1995 after the introduction of
the new Stock Exchange Control Act. Second, the Johannesburg electronic
trading (JET) system was phased in on the JSE from March to June of
1996. In addition, there has also been a positive change on the South African
futures exchange. In 1995, the JSE indices underlying the futures contracts
were redesigned to consist of a smaller basket of stocks. The All Share Index
that consisted of over 400 stocks was replaced by an index consisting of 40
stocks, the ALSI40. Similarly, the gold and industrial indexes were replaced
by the GLDI10 and INDI25 indexes, respectively, where the number at the
end of each index denotes the number of stocks in the index. Each of these
changes reduced the cost of trading and hedging, and made the markets more
accessible to foreign investors. In 2000, 40% of the trading on the SAFEX
was conducted by foreign investors.
3
However, despite all these positive changes, a number of large South
African companies such as Old Mutual, South African Breweries, etc. have
moved their primary listing to the London Stock Exchange due to the greater
access to global capital markets and possibly to avoid paying the sovereign
risk spread associated with South Africa’s status as an emerging market. As
of September 2001, eight South African companies had their primary listing
on the London Stock Exchange and 29 had a secondary listing.
Given the removal of the dual exchange rate system, the reduction in
exchange controls and the increase in the number of cross-listings of South
African companies on the LSE we expect to find greater interdependence
with both the US and the UK after March 1995. To test our hypothesis,
we use the methodology of Rockinger and Urga (2001) who develop a timevarying parameter approach that is flexible enough to allow the degree of
interdependence to change over time. We find that while South Africa’s
interdependence with the US has in fact increased over time, it has not increased with the UK. The latter result is surprising given the cross-listings
and 6-hour overlap in trading times. The result also stands in contrast to
Ripley (1973) who found that South Africa had a stronger relationship with
the UK than the US during the period 1960 to 1970. The greater interdependence with the US is consistent with the increase in purchases of South
African equities by US citizens after March 1995 and the fact that the US
has become the dominant capital market in the world.
The outline of the paper is as follows. In Section 2 we briefly document
the history of exchange controls and the dual exchange rate in South Africa.
In section 3 we outline the methodology of Rockinger and Urga (2001) and
our motivation for using it. We discuss the empirical implementation of our
model and the results in Section 4 and conclude with Section 5.
2
Dual exchange rates and Exchange Controls
The purpose of this section is to emphasize the importance of the dual exchange rate regime and exchange controls in protecting the capital account
from large capital outflows due to the episodes of political risk in South
Africa’s history.
Exchange controls on South African residents have been in place since the
4
outbreak of the Second World War (Garner (1994), Kahn (1991)). Following
the Sharpeville massacre in 1960, there was a sharp increase in the sale
of South African securities by non-residents due to the increase in political
uncertainty, and in December 1962, the rapid deterioration of South Africa’s
capital account led to the introduction of exchange controls on the sale of
securities by non-residents. Before February 1976, the proceeds from selling
capital assets and securities on the JSE by non-residents were designated as
the “blocked rand” when approval to purchase foreign exchange was denied
by the South African authorities. These funds were not directly transferable
among non-residents, but could be used to buy long-term government bonds
or quoted South African securities. The quoted Johannesburg securities could
be transferred to London and sold, generally at a discount. This discount
emerged due to the combination of a lack of demand from non-residents
for South African securities and upward pressure on security prices on the
JSE due to controls on residents’ capital outflows. In February 1976, the
government introduced the “securities rand” which allowed the direct transfer
between non-residents.
On January 24, 1979 the securities rand was replaced by the “financial
rand” and the dual exchange rate regime was put in place. The dual exchange
rate regime consisted of a “commercial rate” and a “financial rate”. The
financial rand served as the principal exchange control on non-resident equity
capital flows into and out of South Africa with the purpose of insulating the
South African current account from the volatility in the flow of non-resident
equity capital. The core role of the financial rand was to set a price at which
equity capital was traded among non-residents while ensuring that the total
stock of the non-resident investment in the South Africa remained constant.
The financial rand in general applied to portfolio investments or approved
direct investment by non-residents, while the commercial rand applied to
foreign trades as well as foreign loans and credits.
On February 7, 1983 the South African government decided that the abolition of the financial rand was feasible because foreign reserves had improved
substantially since mid-1982, the current account deficit had been reduced
and a surplus was expected for the year of 1984. However, after renewed
political turmoil, the imposition of economic sanctions by the UN and the
refusal of a number of international banks to roll over short-term loans to
South African borrowers, the South African government announced a state of
emergency and re-introduced the financial rand mechanism on September 1,
1985, in essentially the same form as it existed before February 1983 (Kahn
5
(1991)). Both the commercial rate and the financial rate were freely floated,
but with more government intervention in the commercial rate. During this
period, the financial rate traded at an average discount of 30% to the commercial rand: this discount reflected a political risk premium required by
foreign investors. After the first democratic elections in the country, the removal of sanctions and the stabilization of the South African economy, the
dual exchange rates were unified on March 13, 1995. Since then the rand has
been freely floating against foreign currencies.
Figure 1A contains a time series plot of the commercial and financial
exchange rates in dollars per rand from January 2, 1990 to December 29,
1999. Two features stand out in figure 1A: first, the financial rate always
trades at a discount to the commercial rate, and second, the commercial
rate has been depreciating against the dollar for the entire decade because of
the inflation differential between the US and SA. Figure 1B contains a time
series plot of the percentage discount of the financial exchange rate to the
commercial exchange rate. The discount was clearly highly variable prior
to the unification of the dual rates in March 1995 and was regarded as a
political risk premium that discouraged foreign investors from investing in
South Africa.
In summary, South Africa imposed a dual exchange rate regime on two
occasions: from January 24, 1979 to February 7, 1983, and from September
2, 1985 to March 10,1995. We are interested in the second regime because it
covers our sample period.
3
A Model of Time-Varying Integration
It has long been recognized that the interdependence between markets is not
constant, but varies over time. Cumby and Khanthavit (1998) and Bekaert
and Harvey (1995) have used switching models to capture the time-varying
nature of the interdependence, but the drawback to their approach is that
it only allows for two regimes. Recently, Rockinger and Urga (2001) introduced a model that allows for a time-varying relationship between a dominant
market and a satellite market. We prefer the model of Rockinger and Urga
because it can capture the time-varying nature of the South African political risk prior to March 1995 and the effect of the emerging market crises on
South Africa after March 1995.
Let the dominant country be indexed by D and denote the market returns
6
as rD,t = 100 · ln(SD,t /SD,t−1 ) where SD,t is the closing price of the market
index of country D at time t. We assume that the market returns evolve
according to the following model:
rD,t = αD,t xD,t + ²D,t
αD,t = ξ D αD,t−1 + η D,t
²D,t = σ D,t zD,t
(1)
(2)
(3)
with
2
σ 2D,t = β 0D + β +
D · ²D,t−1 1 (²D,t−1 > 0)
+β −
D
·
²2D,t−1 1 (²D,t−1
≤ 0) +
β 1D
(4)
·
σ 2D,t−1
and αD,t is a time-varying vector of parameters allowing for autoregressive
behavior in the conditional mean. We assume that zD,t and η D,t are random noise that have a normal distribution with mean zero and variances of
1 and QD,t , respectively. QD,t is a square matrix with dimension equal to
the number of rows of αD,t . The vector xD,t corresponds to variables that
are assumed to describe the conditional mean. These variables may include
lagged returns, seasonal dummies etc. or simply an element equal to 1 that
creates a latent factor. Finally, (4) allows for the presence of conditional
−
heteroskedasticity in the returns where β +
D and β D capture the different im1
pacts of positive and negative shocks and β D captures the serial dependence
in the conditional variance. This form of the conditional variance is known
as the threshold ARCH (TARCH) model where ARCH is an acronym for
autoregressive conditionally heteroskedasticity (Zakoïan (1994) and Glosten,
Jaganathan, and Runkle (1993)).
For a given satellite country i we assume that the return dynamics can
be modeled as follows:
(1)
ri,t = αi,t xi,t + ²i,t
(2)
²i,t = αi,t · ²D,t−1 + ei,t
ei,t = σ i,t zi,t
with
2
σ 2i,t = β 0i + β +
i · ²i,t−1 1 (²i,t−1 > 0)
1
2
2
+β −
i · ²i,t−1 1 (²i,t−1 ≤ 0) + β i · σ i,t−1 ,
7
αi,t
´0
³
(1)
(2)
= αi,t , αi,t ,
αi,t = ξ i αi,t + η i,t
where we also assume that zi,t and η i,t have a normal distribution with mean
zero and variances of 1 and Qi,t , respectively. The vector xi,t consists of
variables that describe the conditional mean of country i, the time-varying
(1)
(2)
parameter αi,t captures the degree of predictability in country i, αi,t captures
the time-varying degree of integration with the dominant country and we also
allow for conditional heteroskedasticity.
The advantage of this specification is that it demonstrates how foreign
shocks affect local volatility. If E[²D,t ei,t ] = 0, then the conditional variance
of country i is given by
£ 2 ¤ ³ (2) ´2 2
Et−1 ²i,t = αi,t · σ D,t + σ 2i,t ,
where the condition requires that foreign shocks are uncorrelated with domestic shocks. Following Bekaert and Harvey (1997), we can measure the proportion of the local variance accounted for by the dominant market through
the variance ratio,
´2
³
(2)
αi,t · σ 2D,t
(5)
V Rit = ³
´2
(2)
2
2
αi,t · σ D,t + σ i,t
(2)
and because Et−1 [²D,t ²i,t ] = αi,t · σ 2D,t , the correlation between country i and
the dominant country D is given by
σ D,t
(2)
.
ρi,t = αi,t · r³
´2
(2)
αi,t · σ 2D,t + σ 2i,t
(6)
The correlation coefficient drives home two important points: first, when
foreign volatility increases with respect to local volatility, then correlation
increases across markets (Longin and Solnik (1995)), and second, the stronger
(2)
the impact of the dominant market on the local market through αi,t , the
higher the correlation.
To implement this model in the context of emerging markets we can allow
xi,t to capture the macroeconomic variables. However, in the case of emerging
8
markets these variables are not very well measured so they may cause more
problems than they resolve. In addition, it is difficult to measure political
events and expectations (Cutler, Poterba and Summers (1989)). Thus we
rely on a latent variable specification for the constant, time-varying serial
correlation and time-varying market integration.
Following these remarks we reformulate the system for country i as follows:
(0)
(1)
(2)
ri,t = αi,t + αi,t ri,t−1 + αi,t · ²D,t−1 + ei,t
ei,t = σ i,t zi,t
(7)
(8)
with
2
σ 2i,t = β 0i + β +
i · ²i,t−1 1 (²i,t−1 > 0)
+β −
i
·
²2i,t−1 1 (²i,t−1
(j)
(j)
≤ 0) +
β 1i
(j)
αi,t = αi,t−1 + η i,t ,
(1)
(9)
·
σ 2i,t−1 ,
(10)
(2)
where αi,t is the measure of predictability and αit is the measure of timevarying integration.
4
4.1
Empirical Implementation
Data
We use the Standard and Poors 500 index (S&P500) and the Financial Times
All Share Index (FTAS) to represent the two dominant markets of the US and
UK, respectively, and the JSE All Share Index represents the satellite market. Daily data for the three indexes were obtained from Datastream for the
period January 2, 1990 to December 29, 1999. The commercial and financial
rand-dollar and rand-pound exchange rates were also obtained from Datastream for the sample period so that we can convert the FTAS and S&P500
indexes into rand equivalents, i.e. we are considering interdependence from
a South African investor’s perspective.
9
4.2
Estimation
We assume that Qt , the covariance matrix of the time-varying parameters,
is diagonal, i.e. the changes in the parameters occur independently of each
other. To implement the Kalman filter we assume that the errors have a
normal distribution and correct for non-normality following Bollerslev and
Wooldridge (1992). We follow the same two-step method of Rockinger and
Urga (2001): first, we estimate univariate asymmetric GARCH models for
the US and UK and save the standardized residuals as, ²US,t−1 and ²U K,t−1 ,
i.e. we estimate (1), (2), (3) and (4) where we assume that αD is constant
and xt equals 1 for all t. In the second step we use the Kalman filter to
estimate the model in (7), (8), (9) and (10). (We provide an outline of the
Kalman filter in the next subsection.) To obtain starting values, we proceed
step-wise, starting from a reduced model and adding subsequent variables.
4.3
The Kalman Filter
The general form of the state space model (Harvey (1989), p. 100-105) can
be written as follows: the measurement equation is
yt = ct + zt αt + ζ t
where E[ζ t ] = 0 and V ar(ζ t ) = Ht , and the transition equation is
αt = dt + Tt αt−1 + Rt η t
where E[η t ] = 0 and V ar(η t ) = Qt . We further assume that both ζ t and η t
have a normal distribution. Let at−1 denote the optimal estimator of αt−1
based on the observations up to and including yt−1 . Let Pt−1 denote the
m × m covariance matrix of the estimation error, i.e.
£
¤
Pt−1 = E (αt−1 − at−1 ) (αt−1 − at−1 )0 .
Given at−1 and Pt−1 , the optimal estimator of αt is given by
at|t−1 = Tt at−1 + ct ,
while the covariance matrix of the estimation error is
Pt|t−1 = Tt Pt−1 Tt0 + Rt Qt Rt0 , for t = 1, ..., n.
10
These two equations are known as the prediction equations. Once the new
observation yt becomes available, the estimator of αt , at|t−1 , can be updated.
The updating equations are
¡
¢
at = at|t−1 + Pt|t−1 Zt0 Ft−1 yt − Zt at|t−1 − dt
Pt = Pt|t−1 − Pt|t−1 Zt0 Ft−1 Zt Pt|t−1 ,
where
Ft = Zt Pt|t−1 Zt0 + Ht ,
for t = 1, ..., n. We can use the fact that the condition distribution of the
prediction errors,
vt = yt − Zt at|t−1 − dt
is Gaussian with mean zero and variance Ft to construct a likelihood
¢
1 X¡
ln (2π) + ln kFt k + vt0 Ft−1 vt .
2 t=1
n
L=−
We maximize the likelihood with respect to the parameter vector to obtain
the maximum likelihood estimates. Based on our specification in (7) through
(10) we set
yt = ri,t , zt = (1, ri,t−1 , ²D,t−1 ), ζ t = ei,t
Ht = σ 2i,t
´0
³
(0)
(1)
(2)
αt = αi,t , αi,t , αi,t , Tt = Rt = I3 .
³
´
(0)
(1)
(2)
−
1
The parameter vector for country i is αo , αo , αo , q1 , q2 , q3 , β 0i , β +
,
β
,
β
i
i
i
(j)
(j)
where α0 denotes the starting value for αit for j = 0, 1, 2.
4.4
Descriptive Statistics
We report the descriptive statistics of the three indexes for the sample period
January 2, 1990 to December 29, 1999 in Table 1. We use the GMM estimator to obtain the test statistics for skewness and kurtosis because its standard
11
errors are robust to conditional heteroskedasticity (Pagan (1996)). The common characteristics of the US and UK in their own currency are the small
average returns, variances of less than 1% per day, no skewness, and excess
kurtosis. When we convert these indices into rands, we find that the variance
triples for the UK and doubles for the US, there is still no skewness and the
excess kurtosis increases and remains statistically significant. The JSE is also
characterized by a small average return, a variance of approximately 1% per
day and both excess skewness and kurtosis. The excess kurtosis in the JSE
returns can be attributed to conditional heteroskedasticity, political risk and
the many emerging market crises at the end of the decade, e.g. the Asian
crisis in October 1997 and the Russian crisis in October 1998.
It is interesting to note that the variance of SA is smaller than the variance
of the US and UK when denominated in rands. Based on the time series plot
of the returns of the three indexes in rands in Figure 2, we notice that the
US and UK indexes are a lot more variable before the unification of the dual
exchange rate regime in March 1995. This observation is consistent with the
dual rate serving as a mechanism for insulating the domestic market from
foreign shocks due to political risk. To test this hypothesis we report the
variance ratios of the indexes and the financial exchange rate in Table 1.
For the own-currency returns, we find that the variance ratio of the pre- to
post-March 1995 returns are less than one and statistically significant for
all three indexes, i.e. SA, the US and UK were less volatile before March
1995 than after March 1995. When denominated in rands, we find that the
variance ratios are greater than one and statistically significant for both the
US and UK. Finally, the variance ratio for the exchange rates is 3.6 for the
UK and greater than 4 for the US. These results confirm that the exchange
rate was more variable in the pre-1995 period and served as buffer for the
South African financial markets.
In the last two panels of Table 1 we report tests for serial correlation
and conditional heteroskedasticity. We find significant serial correlation for
SA and the UK at the first lag in their own currency, and greater serial
dependence for the UK when it is denominated in rands. For the US we find
significant serial correlation at the third and fourth lags when denominated
in dollars, and at the first lag when denominated in rands. Finally, using an
LM test, we find significant evidence of conditional heteroskedasticity for all
three indexes in their own currency and in rands.
12
4.5
Extreme Returns
In Tables 2A and B we report the five largest positive and negative returns
for SA, the UK and the US. In Table 2A we report the extreme returns when
the indexes are denominated in their own currency. First, it is interesting to
note that all the extreme events for South Africa occur after March 13, 1995,
after the dual exchange rates were unified. Four of the negative returns of
SA occur at the end of August and end of October 1998 and correspond to
two events on the same dates in the US returns. These dates coincide with
the Russian crisis that affected many of the emerging markets. The UK also
has a large negative return at the end of August, but beside that date, there
is no common event for SA and the UK.
For the positive returns, the end of October 1997 (Asian crisis) and middle
of October 1998 (Russian Crisis) are associated with positive returns in both
the US and SA, but there is no common event with the UK. Based on the
own currency returns, we can draw three conclusions: first, co-movement in
extreme events is greater after the March 1995; second, the US is the more
important link for extreme events; finally, the extreme returns occur during
crisis periods in other emerging markets.
Turning to Table 2B, where we report the extreme events in rands, we find
very little overlap between the three countries. All the large negative events
in the UK returns occur before or during 1995, and there is no common event
for SA and the US. The only common event for the US and SA occurs at the
end of August 1998 (Russian Crisis). For the positive events, the US and
the UK both experience the largest positive return on April 11, 1994: this
event is associated with the first democratic elections in South Africa and is
driven by an appreciation in the exchange rate and not by a movement on
any of the three stock markets. There is no common event for SA and the
UK and the only common event for SA and the US is at the end of October
1997 (Asian Crisis).
We can conclude that in terms of extreme events, South Africa appears
to have stronger ties with the US, especially after 1995. In addition, we
notice that the dual exchange rate insulates the JSE from extreme movements
during the pre-1995 period and makes the US and UK appear a lot more risky
from the South African investor’s perspective.
13
4.6
Interdependence with the UK
We report the parameter estimates of (7), (8), (9) and (10) for SA and the
UK in column 1 of Table 3. First, we find that the starting values of the
(j)
time-varying parameters αit are indistinguishable from zero. Second, the
TARCH effects and asymmetry are significant. Finally, each of the variances
of the time varying parameters is statistically significant thus confirming the
importance of time-varying component of the parameters.
The best way to analyze the model is to interpret Figures 3 and 4. In
Figures 3A, B and C we plot the smoothed values of the time varying parameters and their 95% confidence intervals across the full sample period
(January 1990 to December 1999) and in Figures 4A and B we plot the time
varying correlation coefficient (6) and variance ratio (5). Based on Figure
3A, we can conclude that the conditional mean return of the JSE All Share
Index is not statistically different from zero because the confidence interval
(0)
of αt straddles zero for the entire sample period. This result is consistent
with market efficiency where (excess) returns should be a martingale difference sequence (Harrison and Kreps (1979)). Turning to Figure 3B, where we
(1)
plot the time varying coefficient of the lagged returns, αit , we notice that
the confidence interval does not straddle zero for most of the sample except
in 1996 and at the end of the sample period. In addition, the coefficient
fluctuates between 0.1 and 0.2 which is consistent with the first order serial
correlation coefficient of 0.15 in Table 1. Finally, in Figure 3C we plot the
time-varying parameter that is the measure of interdependence with the UK,
(2)
αit : it is surprising to see that the confidence interval straddles zero for the
entire sample period. There is a small upward movement in April 1994 after the South African elections that was caused by an appreciation in the
exchange rate, but the general conclusion is that the UK has little effect on
the South African financial markets. This is surprising given the number of
cross listings between South Africa and the UK, and the 6-hour overlap in
their trading hours.
In Figure 4A we plot the time-varying correlation between SA and the
UK. It is interesting to note there are a number of episodes where the correlation between the two countries is negative. For example, in 1997 the JSE
was severely affected by the Asian crisis, but the UK was largely unaffected,
hence the negative correlation. Following the 1994 elections, the correlation
increases dramatically, but this increase does not persist beyond 1996. In
fact, from 1997 onward the correlation has been negative. One caveat to
14
note is that the correlation is based on the time-varying parameter in Figure
3C, so it is unlikely to be statistically significant. Turning to the variance
ratio in Figure 4B, we find that the largest percentage of variation explained
by the UK is 12% in 1993 and thereafter the percentage is less than 6%.
Once again this confirms the fact that the JSE and FTAS indexes are not
closely linked at all despite the overlap in trading time, the cross-listing of
companies and the improvements in the trading systems on the JSE and
SAFEX.
4.7
Interdependence with the US
We report the parameters estimates of (7), (8), (9) and (10) for SA and the
US in column 2 of Table 3. First, we find that the starting values of the
(j)
time-varying parameters αit are indistinguishable from zero. Second, the
TARCH effects and asymmetry are significant. Finally, each of the variances
of the time-varying parameters is statistically significant thus confirming the
importance of the time-varying parameters.
The best way to analyze the results of the model is to consider Figures
(j)
5A, B and C where we plot the smoothed values of the αit and their 95%
confidence intervals. In Figures 5A and 5B we can draw similar conclusions
to those obtained when considering interdependence with the UK. In Figure
5A we notice that the intercept of the conditional mean return is never statistically different from zero and is consistent with the results with the UK.
In Figure 5B, the first order autocorrelation coefficient fluctuates between
0.1 and 0.2, which is consistent with the first order serial correlation coefficient of 0.15 in Table 1 and the confidence interval does not straddle zero
except during the volatile periods of 1996 and 1997. Finally, in Figure 5C
we plot the time-varying parameter that measures interdependence between
(2)
SA and the US, αit . The confidence interval straddles zero from 1990 to the
end of 1993. From 1994 onwards, interdependence between SA and the US
increases, briefly dips in the first half of 1997, reaches a maximum in 1998
and then it begins to decline. The greater degree of interdependence at the
end of 1997 and in 1998 can be associated with the Asian and Russian crises
that made this period very turbulent. This is even clearer in the next set of
figures.
In Figures 6A and B we plot the correlation and variance ratio of the
JSE all share index and the S&P500. There is small increase in correlation
between the S&P500 and the JSE index at the end of 1992 and then continues
15
to fluctuate between negative and positive values until 1994. In 1994, the
correlation jumps up after the first free election in South Africa and increases
from 0.1 to 0.5 at the end of 1997 and re-attains this value at the end of
1999. It is interesting to note that the spike in 1994 after the South African
elections is followed by a period in which the correlation averages around
0.3 for the post-March 1995 period. In Figure 6B we see that the S&P 500
exlains less than 10% of the percentage of variation in the JSE up until 1994.
Thereafter, the interdependence increases and the percentage of variation
explained reaches a maximum of 35% in 1997 and 40% in 1998.
The main conclusion of this analysis is that the strength of the interdependence between SA and the US has increased significantly following the
positive macroeconomic and political changes in 1994 and 1995. This result
is consistent with the increase in purchases of South African equities by US
citizens in Figure 7.1 From 1990 to 1994, the average monthly purchases
(sales) of South African equities by US residents was $14.5 million ($6.95)
and from the 1995 through 1999 the corresponding amount was $109 ($54).
Figure 7 also provides a nice contrast with the financial rand discount in
Figure 1B, i.e. after the unification of the exchange rates and the removal
of the discount, US purchases and sales of South African securities increased
dramatically.
5
Conclusion
The objective of this paper was to analyze the interdependence between
South Africa’s stock market and those of the US and UK. Given the tremendous positive economic and political changes that have taken place in South
Africa during the first half of the 1990’s, we expect to find greater integration
with the US and UK in the latter half. This is indeed the case for the US:
following the unification of the dual exchange rate regime and the removal
of exchange controls on foreign investors in March 1995, the correlation with
the US averages around 0.35 as opposed to fluctuating between -0.2 and 0.2
before March 1995. However, there is little increase in the interdependence
with the UK despite the fact that many large South African companies are
cross-listed on the LSE or have the LSE as their primary listing. These results contrast very strongly with those of Ripley (1973) who found that South
1
These data were obtained
http://www.treas.gov/tic/.
from
16
the
website
of
the
US
treasury,
Africa had a stronger relationship with the UK during the period 1960 to
1970. The strong correlation with the US may be due to the fact that the US
has become the dominant capital market in the world. The interdependence
with the US is also consistent with the increase in purchases of South African
equities by US investors; unfortunately, we were unable to get similar data
for the UK.
References
[1] Bekaert, G. (1995) “Market Integration and Investment Barriers in
Emerging Equity Markets,” World Bank Economic Review, 9, 75-107.
[2] Bekaert, G. and C. Harvey (1997) “Emerging Equity Market Volatility,”
Journal of Financial Economics, 43, 1, 29-77.
[3] Bollerslev, T. and J. Wooldridge (1992) “Quasi-Maximum Likelihood
Estimation and Inference in Dynamic Models with Time Varying Covariances,” Econometric Reviews, 11, 143-172.
[4] Cutler, David M., James M. Poterba and Lawrence H. Summers (1989)
“What moves stock prices?” The Journal of Portfolio Management, 15,
3, 4-12.
[5] Cumby, R. E. and A. Khanthavit (1998) “A Markov Switching model
of Market Integration,” in Emerging Market Capital Flows, ed: Richard
M. Levich, p. 237-257.
[6] Harrison and Kreps (1979) “Martingales and Arbitrage in Multiperiod
Securities Markets,” Journal of Economic Theory, 2, 3, 381-408.
[7] Garner, Jonathan (1994) “An analysis of the Financial Rand Mechanism,” Centre for Research into Economics and Finance in South Africa,
Research Paper no. 9.
[8] Harvey, Andrew C. (1989), Forecasting, Structural Time Series Models
and the Kalman Filter, Cambridge University Press.
[9] Khan, Brian (1991) “Capital Flight and Exchange Controls in South
Africa,” Centre for the Study of the South African Economy and International Finance, Research Paper No. 4.
17
[10] Longin, F. and B. Solnik (1995) “Is the Correlation in International
Equity Returns Constant: 1960-1990?,” Journal of International Money
and Finance, 14, 1, 3-26.
[11] Pagan, Adrian R. (1996) “The Econometrics of Financial Markets,”
Journal of Empirical Finance, 3, 15-102.
[12] Ripley, Duncan M. (1973) “Systematic Elements in the Linkage of National Stock Market Indices,” Review of Economics and Statistics, 55,
3, p. 356-361.
[13] Roll, R. (1992) “The Industrial Structure and the Comparative Behavior
of International Stock Market Indices,” Journal of Finance, 47, 3-41.
[14] Rockinger, Michael and Giovanni Urga (2001), “A Time-Varying Parameter Model to Test for Predictability and Integration in the Stock
Markets of Transition Economies,” Journal of Business and Economic
Statistics, 19, 1, 73-84.
18
Table 1: Descriptive Statistics of the Returns of the Three Indexes
JSE All Share
Rands
FT All Share
Rands Pounds
S&P500
Rands Dollars
Mean
0.0401
0.0619
0.0419
0.0828
0.0605
Variance
1.0670
1.7909
0.6511
1.8057
0.7929
Skewness
-1.1784
(0.004)
11.180
(0.027)
0.2256
(0.706)
7.1924
(0.001)
0.0372
(0.629)
3.1266
(0.000)
0.2248
(0.482)
8.5647
(0.002)
-0.3296
(0.284)
5.6975
(0.001)
Kurtosis
Variance Ratios: Pre-March 13, 1995 to Post-March 13, 1995
Returns
Foreign
Exchange
0.809
(0.000)
1.666
(0.000)
3.646
(0.000)
0.911
(0.051)
1.285
(0.000)
0.715
(0.000)
4.082
(0.000)
The p-values are in parentheses below each statistic.
The mean, standard deviation, skewness and kurtosis and their standard errors
are estimated using the GMM estimator because it is robust to the presence of
conditional heteroskedasticity.
The sample period is January 2, 1990 to December 29, 1999.
The variance ratio equals the variance of the returns prior to March 13, 1995
divided by the variance of the returns after March 13, 1995.
There are 1274 (1206) returns before (after) March 13, 1995.
19
Table 1 (continued): Descriptive Statistics of the Returns of the Three Indexes.
JSE All Share
Rands
Lag
1
2
3
4
5
FT All Share
Rands Pounds
S&P500
Rands Dollars
Serial Correlation in Returns
0.151c
0.057
0.018
-0.024
0.015
0.013
-0.080c
-0.043b
-0.013
-0.04a
0.096c
-0.001
-0.010
0.023
-0.030
0.047a
-0.025
-0.017
-0.024
0.014
0.019
-0.010
-0.042a
-0.045a
-0.009
Serial Correlation in Squared Returns (5 lags)
LM test (χ2 )
392.277c
85.006c
168.019c
149.571c
157.186c
We use the Newey-West estimator to compute the standard errors for each
serial correlation coefficient so that it is robust to neglected heteroskedasticity
and serial correlation. A superscript a, b, and c denotes significance at the
10%, 5% and 1% level, respectively.
20
Table 2 A: The Five Largest and Smallest Returns in the Three Indexes
South Africa
Own Currency
UK
US
Negative Returns
10/28/97 -11.851us
11/21/98
-6.804
08/26/98 -6.400us
08/27/98 -5.830us
10/27/97 -5.823us
08/11/98
-3.933
10/05/92
-3.664
12/01/98
-3.228
08/19/91
-3.135
08/27/98 -3.103us,sa
10/27/97
08/31/98
03/22/99
08/27/98
11/15/91
-7.112sa
-7.043
-4.220
-3.912sa
-3.727
Positive Returns
6.695us
04/10/92
5.697
10/28/97
4.988sa
5.040us
09/17/92
4.329
09/08/98
4.964
4.601
10/12/98
3.756
10/15/98
4.088sa
us
4.568
10/06/98
3.658
12/30/91
3.883
4.332
09/18/92
3.327
09/11/98
3.790
The superscript sa, uk and us denotes the country that has an extreme return on
10/29/97
10/16/98
01/06/99
10/31/97
06/17/98
the same date.
21
Table 2 B: The Five Largest and Five Smallest Returns of the Indexes
South Africa
South African Rands
UK
US
Negative Returns
10/28/97 -11.851
11/21/98 -6.804
08/26/98 -6.400us
08/27/98 -5.837us
10/27/97 -5.823
04/19/94
03/11/95
10/07/92
10/09/90
11/19/90
-8.122
-7.605
-7.463
-7.178
-6.943
04/20/93
08/31/98
04/19/98
04/12/93
10/06/92
-9.044
-8.010sa
-7.434
-7.115
-6.833
Positive Returns
6.695
04/11/94 12.350us
04/11/94
12.113uk
5.040
10/08/90
7.208
10/05/92
9.497
4.601
04/10/92
6.941
08/27/90
7.242
4.568us
12/17/91
6.388
06/22/92
6.401
4.332
11/19/90
6.309
10/28/97
6.334sa
The superscript sa, uk and us denotes the country that has an extreme return on
10/29/98
10/05/97
01/06/99
10/31/97
06/17/98
the same date.
22
Table 3: The Parameter Estimates of the Model
where the Indexes are denominate in South African Rands
Dominant Market
Parameters
FT All Share
S&P 500
(0)
α0
(1)
α0
(2)
α0
q1
q2
q3
β0
β+
β−
β1
Sample Size
Mean Log-likelihood
0.004
(0.482)
0.010
(0.463)
0.019
(0.413)
0.005
(0.482)
0.010
(0.462)
0.020
(0.421)
0.001
(0.013)
0.0009
(0.053)
0.001
(0.004)
0.001
(0.011)
0.001
(0.047)
0.001
(0.000)
0.001
(0.192)
0.110
(0.000)
0.129
(0.000)
0.870
(0.000)
0.001
(0.179)
0.111
(0.000)
0.128
(0.000)
0.872
(0.000)
2481
-1.3422
2481
-1.3308
The p-values are in parentheses under the estimate of each parameter.
23