The Effect of B Share Market Reform on Volatility Spillovers and Changes in Correlation between Chinese A and B Shares

The Effect of B Share Market Reform on Volatility
Spillovers and Changes in Correlation between Chinese
A and B Shares
Bernardo da Veiga, Felix Chan and Michael McAleer
School of Economics and Commerce, University of Western Australia, E-Mail
Bernardo.Veiga@uwa.edu.au

Keywords: China A and B shares, multivariate conditional volatility, conditional correlations.

EXTENDED ABSTRACT



The aim of this paper is to investigate the effect

of the Chinese B share market reform on the

correlation and information transmission

between A and B Shares issued in the Shanghai

and Shenzen stock exchanges. Daily returns for

the Shanghai A share index (SHA), Shanghai B

share index (SHB), Shenzen A share index

(SZA) and Shenzen B share index (SZB) are

used for the period 6 October 1992 to 8 February

2005. The results suggest that the all pairs of

correlations increase dramatically over the period

analysed, but such increase begins well before

the reforms to the B Share market.





















































2210

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1 Introduction
led to an increase in jump intensity and

frequency and that the volatility transmission had

accelerated.
An important feature of the shares issued by the

typical People’s Republic of China (PRC) state-
All the studies mentioned above suggest that the
owned enterprises is that they are divided into
B share market reform had a significant impact
negotiable and non-negotiable blocks of scrip.
on the covariance matrix between A and B
The non-negotiable block is typically larger,
shares. The covariance matrix of a portfolio of
accounting for 60-70% of issued equity, and is
assets is one of the most important inputs in
controlled by the PRC. The negotiable portion of
almost all financial applications, from risk
issued equity can be traded in three forms A, B
management, asset and option pricing to
or H shares. H shares are listed in exchanges
portfolio construction and management to
outside of mainland China while A and B shares
mention but a few. The aim of this paper is to
can be listed in either the Shanghai or Shenzen
examine the impact of the recent B share market
exchanges, dual listing is not permitted.
reform on Value-at-Risk (VaR) thresholds
Furthermore, companies listed in the Shanghai
forecast. Following the B share market reform, it
stock exchanges have typically greater market
is likely that many Chinese investors would have
capitalization. than those listed in the Shenzen
expanded their portfolios to also include B
stock exchange. Prior to 28 February 2001
shares. Since the B share market reform has been
ownership of A shares was restricted to residents
shown in various papers to have led to a change
of the PRC while ownership of B shares was
in the volatility dynamics between A and B
restricted to foreign investors. However, starting
shares, a logical question is how to optimally
from 28 February 2001, Chinese residents were
accommodate these changes when modelling and
allowed to open foreign exchange accounts to
forecasting the covariance matrix.
trade in B shares.


The Vector Autoregressive Moving Average
As both classes of shares represent identical
Asymmetric Generalized Autoregressive
ownership in the same company, the Efficient
Conditional Heteroskedasticity (VARMA-
Market Hypothesis (EMH) would suggest that
AGARCH) model of Hoti et al. (2003), is used
both classes of shares should trade at the same
to estimate the covariance matrix and to test for a
price. Yet prior to the deregulation B shares
change in the correlation between A and B
tended to trade at a significant discount to their A
shares following the reforms in the B share
share counterparts. Various studies have
market. An attractive feature of the VARMA-
documented this observed market segmentation,
AGARCH model is its ability to capture the
including Bailey (1994) and Ma (1996).
asymmetric effects of positive and negative
Subsequent papers analysed the volatility in the
shocks on the conditional volatility, and to
Chinese stock markets. For example Su and
accommodate interdependencies (or spillovers)
Fleisher (1999) analyse daily data for a matched
in returns and volatilities, which allows the
sample of 24 firms issuing both A and B shares
existence of mean and volatility spillovers to be
and find that both types of shares exhibit time
tested jointly.
varying volatility and that A shares tend to be

more volatile. Poon and Fung (2000) use
Hence, the use of the VARMA-AGARCH model
threshold GARCH models to investigate the
allows us to explore several empirical side issues
asymmetric response of A and B share volatility
such as returns and volatility transmission and
to positive and negative shocks and find that A
spillovers, across the different classes of shares
and B shares react asymmetrically to good and
within markets and across markets, as well as
bad news. Brooks and Ragunathan (2003)
between the same class of shares within markets.
analyse the information transmission between A
By analysing the sample before and after the
and B shares prior to the B share market reform
reforms separately, this paper also investigates
and find evidence of returns spillovers but not
whether the transmission and spillover of
volatility spillovers. More recently Chiu et al.
volatility was affected by the reform.
(2005) use the Autoregressive Conditional Jump

Intensity model of Chan and Maheu (2002) to

investigates the impact of the B share market
2 Data
reform on the volatility dynamics between A and

B shares. Their results suggest that deregulation

2211

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The data used in this paper are daily returns for
restrictions, which allows the various special
the Shanghai A share index (SHA), Shanghai B
cases of the VARMA-AGARCH model to be
share index (SHB), Shenzen A share index
tested. An alternative multivariate model for
(SZA) and Shenzen B share index (SZB) for the
which asymptotic theory has been considered is
period 6 October 1992 to 8 February 2005. All
the BEKK model of Engle and Kroner (1995).
data was gathered from Datastream and
Comte and Lieberman (2003) showed
converted to a single currency, namely the US
consistency of the QMLE of BEKK using the
dollar. Table 1 gives the descriptive statistics for
conditions established in Jeantheau (1998), and
the daily returns. As can be seen all series
asymptotic normality of the QMLE by assuming
display similar means and median close to zero.
the existence of eighth moments. However, as
The A shares consistently display greater range
the moment conditions have been assumed rather
than their B share counterparts, with
than derived, it is not possible to verify the
significantly higher maxima and significantly
conditions in practice.
lower minima. All series display excess kurtosis,

with the distribution of A shares displaying
The general multivariate model is given by:
significantly thicker tails than B shares. Finally,

all series are found to be highly non-normal


according to the Jarque-Bera statistic.
Y = E(Y | F ) +
−
ε (3.1)
t
t
t 1
t



Φ(L)(Y − μ) = Ψ(L)ε (3.2)
t
t
Table 1:Descriptive Statistics for Returns


SHA
SHB
SZA
SZB
ε = Dη (3.3)
t
t
t
Mean

0.007 0.007 -0.008 0.017

Median
0.000 0.000 0.000 0.000
r
r
→
→
H = W + ∑ A ε
∑
t −l +
C I (η )
−
ε −

Maximum
30.886 12.184 29.608 13.597
t l
t
l
l
t l
l 1
=
l 1
=
Minimum -38.790 -13.085
-40.332 -16.670
s
+∑
SD
2.708 2.146 2.484 2.201

B H

(3.4)
l
t −l
l 1
=
Skewness
0.616 0.435 -0.484 0.373
Kurtosis
37.014 8.373 39.772 10.967


Jarque-Bera 155479
3976 181598
8593
where
H = (h ,..., h ) ' ,
W = (ω ,...,ω ) ' ,

t
1t
mt
1
m
1/ 2

D = diag(h ) ,
η = (η ,...,η )' ,
t
it
t
1t
mt
3 Model
→
2
2
ε t = (ε ,...,ε ) , ,
A C and
B are
m × m

1t
mt
l
l
l
Equation Chapter 3 Section 3
matrices with typical elements α , γ and β ,
ij
ij
ij
This paper uses the vector autoregressive moving
respectively, for i, j = 1,..., m ,
average asymmetric generalised autoregressive
I (η ) = diag(I (η )) is an m × m matrix,
conditional heteroskedasticity (or VARMA-
t
it
AGARCH) model of Hoti et al. (2003) to model
Φ(L) = I − Φ L −...
p
− Φ L and
m
1
p
the time varying volatility and test for the
Ψ(L) = I − Ψ L −...
q
− Ψ L are polynomials in
existence of volatility spillovers and asymmetric
m
1
q
effects. Hoti et al. (2003) derived the necessary
L, the lag operator, F is the past information
t
and sufficient conditions for strict stationarity
available to time t, I is the m × m identity
and ergodicity, sufficient conditions for the
m
existence of the log-moment and all moments,
matrix, and I (η ) is an indicator function,
it
and sufficient conditions for consistency and
given as:
asymptotic normality of the quasi-maximum

likelihood estimator (QMLE) under non-
⎧1, ε ≤ 0
it
normality of the standardized shocks to returns.
I (η ) = ⎨
(3.5)
it
0,
⎩ ε > 0.
Their proofs are based on the derivation of the
it
causal expansions, which do not require the

existence of moments. The structural and
The time subscripts in the model correspond to
asymptotic properties of all nested special cases
calendar time. The coefficients αij and βij , i ≠ j ,
follow by the imposition of appropriate
measure the extent to which the lagged
2212

---

unconditional shock and lagged conditional
(ρ − ρ )
1
2
variance in market j, respectively, influence the
Z =
(4.1)
SE
conditional variance in market i.




An attractive feature of the VARMA-AGARCH
model is its ability to capture multivariate
1
1
SE =
+
(4.2)
asymmetries concerning the impact of positive
(n − 3)
(n − 3)
1
2
and negative shocks to market i on the

conditional variance in market i through the
where n1 and n2 are sample sizes used to
coefficient γi. If γi is positive, it implies that
calculate ρ and ρ respectively.
negative shocks increase the conditional
1
2

volatility in market i to a larger extent than do
positive shocks.
Table 2:Conditional Mean Equation 6

October 1992 - 8 February 2005
Bollerslev (1990) proposed the Constant
Coefficient SHA
SHB SZA SZB
Conditional Correlation (CCC) GARCH model.
Constant
-0.019 -0.017 -0.054 -0.003
The CCC model calculates the conditional

-0.152 -0.203 -1.093 -0.031
correlations as E(η η′) = Γ , where Γ is the
t
t

-0.487 -1.586 -1.847 -0.099
constant conditional correlation matrix of the
SHA(-1)
-0.007 0.016 0.107 0.002
conditional shocks which is, by definition,
equivalent to the constant conditional correlation

-0.004 0.378 2.616 0.044
matrix of the unconditional shocks. This
-0.003 -1.115
1.656
0.166
procedure can be applied to the VARMA-
SHB(-1) -0.033 0.016 -0.054 0.120
AGARCH model and all its special cases to
-0.546 0.019
-2.219
2.608
estimate the conditional correlation matrix and in
-0.964 5.388
-1.779
4.048
turn the covariance matrix.
SZA(-1)
0.024 -0.014 -0.323 -0.002

4
Return and Volatility Spillovers and

0.388 -0.287 -0.973 -0.036
Change in Conditional Correlation

0.460 -0.193 -0.961 -0.168
Equation Chapter (Next) Section 4
SZB(-1) 0.046
0.105 0.066 0.011


0.894 3.158 3.121 0.007
The first issue we explore in this paper is

1.585 2.595 3.509 0.009
whether the reform to the B share market
MA(1) -0.007 0.017 0.256 0.011
substantially changed the conditional correlation
between A and B shares. In order to answer this,

-0.004 0.020 0.729 0.007
three estimated conditional correlation matrices

-0.003 -5.332 0.696 0.009
between A and B shares are obtained by
Notes:
1.
The three entries for each parameter are their
estimating the VARMA-AGRACH model for
respective estimate
the entire sample, the sub-sample before the
Asymptotic and Bollerslev-Wooldridge (1992) robust t-
reform (6/10/1992 to 28/2/2001) and the sub-
ratio.
2.
SHA(-1), SHB (-1), SZA (-1), SZB (-1) denote the
sample after the reform (28/02/2001 to
lagged returns
8/2/2005). All estimation was undertaken using
for each index.
3.
Entries in bold are significant at the 5% level using
EViews 5 and full convergence was achieved.
the robust t-ratios.
Both the asymptotic t-ratios of Weiss (1986) and

the Bollerslev and Wooldridge (1992) robust t-
Tables 2 and 3 give the parameter estimates of
ratios are reported, inference is based on the
the VARMA-AGARCH model for the entire
robust t-ratios as these are robust to the presence
sample. Evidence of returns spillover is found
of outliers and non-normality.
from SZB to both SHB and SZA, indicating that

past returns of SZB affect future returns from
Let ρ and ρ be the correlations from the first
SHB and SZA; and from SHB to SZB, indicating
1
2
that past returns of SHB affect future returns to
and second period, respectively. The test statistic
SZB. Evidence of positive volatility spillover is
for testing differences in correlations is then
found from SHA to SZA. While evidence of
given by:
negative spillovers is found from SZB to SZA.

Positive (negative) volatility spillover suggests


2213

---

that a shock to one index would increase
-3.704 -1.855
-5.051
5.983
(reduce) the volatility of other indices.

-1.621 0.419 -2.707 4.280

Notes:
Tables 4-6 give the conditional correlation
1.
The three entries for each parameter are their
matrix for the entire sample, the pre-reform
respective estimate
and Bollerslev-Wooldridge (1992) robust t-ratio.
sample and the post-reform sample respectively.
2.
The parameters in the conditional variance
As can be seen the calculated conditional
equation associated
with SHA, SHB, SZA and SZB index returns are
correlations for all index pairs are significantly
denoted by α and β.
higher following the reform than prior to the
3.
Entries in bold are significant at the 5% level
reform. For example, the correlation between

SHA and SHB prior to the reform is 0.344 while
The results reported in Table 4 show that the
the correlation for the period following the
existence of structural change has significant
reform is 0.704, similar results are found for all
impact on the conditional correlation and the
index pairs. Table 7 uses the testing procedure
assumption of static conditional correlation may
described above to test for differences in
not hold. In this case, failing to accommodate the
correlation between samples and finds all the
structural change can cause downwards bias in
differences in all correlations to be statistically
the conditional correlation. Such downward bias
significant at the 99% level.
can have serious implications for many financial

applications. For example, this downwards bias
Table 3: Conditional Variance Equation 6
indicating a greater diversification in a portfolio
October 1992 - 8 February 2005
is detrimental as the risk of a portfolio is
underestimated by the low conditional
Coefficient SHA SHB SZA SZB
ω
correlation between the returns of different
6.933 3.933 2.321 4.317
assets. This can then lead to suboptimal hedge

6.171 5.268 8.543 4.614
ratios, poor asset allocation decisions and

2.957 3.833 3.170 3.275
excessively aggressive VaR thresholds.
γ
0.043 -0.040 0.123 0.019


1.298 -1.329 2.890 0.406
Table 4: Conditional Correlation 6 October
1992 - 8 February 2005

0.262 1.523 1.457 0.264
SHAα
0.145 -0.002 -0.013 -0.003

SHA
SHB
SZA
SZB

5.139 -1.169 -8.952 -0.541
SHA
1.000 0.344 0.785 0.327

1.484 -1.324 -0.197 -0.926
SHB 1.000
0.390
0.671
SHAβ
0.582 -0.009 0.331 -0.010
SZA 1.000
0.414

9.212 -0.786 6.507 -0.757
SZB



1.000

3.775 0.173 2.936 -1.287

SHBα
-0.029 0.125 0.000 -0.015
Table 5: Conditional Correlation 6 October
1992 - 28 February 2001

-1.451 4.277 0.084 -0.448

SHA
SHB
SZA
SZB

-1.310 2.770 0.046 -0.716
SHA
1.000 0.277 0.763 0.256
SHBβ
-0.034 0.549 -0.015 -0.026
SHB 1.000
0.290
0.598
-0.829 6.511
-1.373
-0.651
SZA 1.000
0.313
-0.861 3.045
-0.706
-0.776
SZB 1.000
SZAα
-0.018 -0.003 0.114 -0.003

-0.476 -1.799
5.092
-0.608
Table 6: Conditional Correlation 28 February

-0.411 1.017 1.521 -1.060
2001- 8 February 2005
SZAβ
-0.019 -0.015 0.261 -0.016

SHA
SHB
SZA
SZB
-0.732 -1.101
2.944
-1.027
SHA 1.000 0.704 0.964 0.693
-0.925 -0.553
1.313
-1.677
SHB
1.000
0.706
0.859
SZBα
-0.025 -0.018 -0.007 0.140
SZA

1.000
0.711

-2.428 -1.806 -1.280 4.366
SZB



1.000

-1.335 -0.154 -1.348 2.236

SZBβ
-0.064 -0.026 -0.047 0.566
Table 7: Test for Differences in Correlation
2214

---

Between Samples
model is estimated for a restricted sample, then
re-estimated by adding one observation to the

SHA
SHB
SZA
SZB
end of the sample and deleting one observation
SHA
11.272 5.309 11.555
from the beginning of the sample. The process is
SHB

10.998 6.894
then repeated until the end of the sample. If the
SZA


10.510
rolling conditional correlations are found to vary
SZB




substantially over time, the assumption of
constant conditional correlations may be too
The figures given are the z scores given by equation 4.1.
Figures in bold are significant at the 1% level. using the
restrictive. Such a result may be used to motivate
robust t-ratio.
the estimation of dynamic conditional correlation

models, and may also question the existing
5
Correlation Dynamics
results based on constant conditional correlation

models. In order to strike a balance between

efficiency in estimation and a viable number of
The VARMA-AGARCH model, like all its
rolling regressions, the rolling window size is set
nested variations, imposes the assumption of
at 1000.
constant conditional correlations. Engle (2002)

and Tse and Tsui (2002) have recently proposed

closely related multivariate GARCH models
Figure 1: Rolling Conditional Correlation Between SHA & SHB
with time-varying conditional correlations.
.8
McAleer et al. (2004) provide a theoretical
motivation for these models in terms of a vector
.7
of serially correlated standardized residuals,
.6
develop the generalized autoregressive
conditional correlation (GARCC) model, and
.5
derive the theoretical and statistical properties of
a wide range of dynamic conditional correlation
.4
models.
.3

In the constant conditional correlation
.2
framework, Γ is the constant conditional
.1
correlation matrix of the standardised shocks,
1997 1998 1999 2000 2001 2002 2003 2004
η

, which are assumed to be either a vector of
t

independently and identically distributed (iid)

random variables, or a martingale difference
Figure 2: Rolling Conditional Correlation Between SHA & SZA
process. However, in the dynamic conditional
1.00
correlation framework, the conditional
correlation matrix, Γ , is no longer constant but
0.95
follows a restricted multivariate GARCH(1,1)
0.90
specification. If Γ is assumed to be time
varying, a more general multivariate GARCH
0.85
structure would be required to generalize the iid
0.80
assumption for η . This difficulty would render
t
0.75
the existing proofs of consistency and asymptotic
normality of the QMLE for the constant
0.70
conditional correlation GARCH model invalid
for its time-varying counterpart. Such
0.65
1997 1998 1999 2000 2001 2002 2003 2004
deficiencies would also prevent the models from

testing for the presence of volatility spillovers.



Using rolling windows approach, we can
examine the time-varying nature of the
conditional correlations using the VARMA-
AGARCH model. Rolling windows are a
recursive estimation procedure whereby the
2215

---

Figure 3: Rolling Conditional Correlation Between SHA & SZB
Figure 6: Rolling Conditional Correlation Between SHB & SZA
.8
.8
.7
.7
.6
.6
.5
.5
.4
.4
.3
.3
.2
.1
.2
.0
.1
1997 1998 1999 2000 2001 2002 2003 2004
1997 1998 1999 2000 2001 2002 2003 2004




Figure 4: Rolling Conditional Correlation Between SHB & SZB
Figures 1-6 plot the dynamic paths of the

.9
constant conditional correlation matrices for the
VARMA-AGARCH model using rolling
.8
windows. All the conditional correlations display
.7
significant variability. More specifically, all pairs
of conditional correlations appear to increase
.6

.5
over time. These results suggest that the
.4
assumption of constant conditional correlations
may not be valid, and hence may lead to biased
.3
inferences. It is interesting to note that all pairs
.2
of conditional correlations appear to strengthen
.1
from the beginning of the period, with all A and
1997 1998 1999 2000 2001 2002 2003 2004
B share pairs displaying similar patterns where

there appears to be an initial increase in the

conditional correlations in 1997, which could be

due to the handover of Hong Kong, a further
Figure 5: Rolling Conditional Correlation Between SZA & SZB
spike in 1999 which could correspond to the
.8
hand over of Macaw and finally a spike in 2001
.7
which is likely to be due to the reform to the B
share market.
.6


.5
6 Conclusion
.4


.3
This paper examined the effect of the B share
.2
market reform on the information transmission
and correlations dynamics between A and B
.1
shares listed in mainland China. The results
1997 1998 1999 2000 2001 2002 2003 2004

showed that the correlation between A and B

shares has increased dramatically over time, but

this increase began well before the B share
market reforms. The empirical results also
indicated the presence of both returns and
volatility spillovers between the four indices.


Acknowledgements

2216

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The first author acknowledges a University

Postgraduate Award and an International
Jeantheau, T. (1998), “Strong Consistency of
Postgraduate Research Scholarship at the
Estimators for Multivariate ARCH
University of Western Australia. The second and
Models”, Econometric Theory, 14, 70-86
third authors are grateful for the financial support

of the Australian Research Council.
Ma, X. (1996), “Capital Controls, Market

Segmentation and Stock Prices: Evidence

from the Chinese Stock Market”, Pacific
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