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This article was downloaded by: [University of Bristol]On: 10 November 2014, At: 01:27Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Journal of Chinese Economic andBusiness StudiesPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/rcea20
Time-varying Informational Efficiencyin China's A-Share and B-Share MarketsXiao-Ming Li aa Department of Commerce, Massey University (Albany), PrivateBag 102904, Auckland, New ZealandPublished online: 18 Oct 2010.
To cite this article: Xiao-Ming Li (2003) Time-varying Informational Efficiency in China's A-Share and B-Share Markets, Journal of Chinese Economic and Business Studies, 1:1, 33-56, DOI:10.1080/1476528032000039730
To link to this article: http://dx.doi.org/10.1080/1476528032000039730
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Journal of Chinese Economic and Business Studies, Vol. 1, No. 1, 2003, pp. 33–56
Time-varying Informational Efficiency in China’s
A-Share and B-Share Markets
XIAO-MING LI
ABSTRACT This paper employs a time-varying framework to examine the informational
efficiency of China’s A-share and B-share markets, with a focus placed on the following
issues: changing weak-form efficiency, the leverage effect, and information transmission
in return volatility. We find that the A-share markets perform better than the B-share
markets in terms of efficiency-improving; significant leverage effects exist in three of four
markets but with different signs; and no weak and strong volatility transmissions
characterise different pairs of markets. Market segmentation is also documented, as
evidenced by no co-movements in the long-run behaviour of the four Chinese share markets.
Key words: A shares; B shares; Weak-form efficiency; Return volatility; China.
JEL classifications: G14, C22.
1. Introduction
Informational efficiency is one of the three types of efficiency of financial markets,
the other two being operational efficiency and allocative efficiency. Concerned with
the availability and use of information, informational efficiency can be further clas-
sified as weak-form, semi-strong-form, and strong-form efficiencies. Weak-form
efficiency (WFE) is the easiest type of efficiency for quantitative analysis, and
thus has been extensively studied for developed and emerging financial markets.
There is growing evidence that emerging share markets in transition economies
are characterised by time-varying WFE.1 In the Chinese context, Li (2003) uses
a time-varying AR framework combined with the GARCH-type models to assess
the evolution of the Chinese share markets in terms of WFE. That study considers
two aggregate share markets: the Shanghai Stock Exchange (SHSE) and the
Shenzhen Stock Exchange (SZSE), and finds gradually improved WFE for both
of them over the period 1991–2001. While Li’s findings are interesting, it is of
further interest to probe into the time series properties of A and B shares, the two
sub-markets of the SHSE and of the SZSE, for the similar informational efficiency
Xiaoming Li, Department of Commerce, Massey University (Albany), Private Bag 102904, Auckland,
New Zealand; e-mail: [email protected]
Journal of Chinese Economic and Business StudiesISSN 1476-5284 print: ISSN 1476-5292 online � 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journalsDOI: 10.1080/1476528032000039730
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issues, if only because the results may reveal which one, the A-share market or the
B-share market, has contributed more to overall efficiency improving in the aggre-
gate stock market.
Before starting formal statistical investigations, an account of different classes of
the Chinese shares, especially of A and B shares, may be in order. The account is
necessarily brief, however, to converse space, and more details can be found in
the existing literature.2 The shares of China’s listed companies are presently
categorised into six classes: A, B, H, red-chip, N and S, mainly in accordance
with different listing locations and the investors faced. Among them, A and B
shares are traded on the SHSE and the SZSE, both types of shares being denomi-
nated in the renminbi (RMB), but the former are traded in RMB whereas the latter
are in US dollars (Shanghai) or HK dollars (Shenzhen).3 A shares are restricted
to Chinese nationals domiciled in mainland China. B shares were available only
to foreigners, Hong Kong, Macao and Taiwan investors, as well as overseas
Chinese citizens until 31 May 2001. The original idea of devising B shares in addi-
tion to A shares for the same listed company was mainly for overseas investors to
circumvent foreign-exchange controls while making security investments in
China. However, due to problems such as isolations between Chinese and foreign
currencies, information asymmetry between domestic and foreign investors, clien-
tele bias against B shares and so on, the two share markets moved independently
most of the time, as illustrated in Figure 1. While the A-share markets grew rapidly,
the B-share markets sometimes were so faltering that the listed companies’ market
values became even lower than their net capital values. In other words, B shares
failed to play an expected role of raising capital for the listed companies, and
even became a burden on China’s security markets.
It is apparently out of tune with the workings of modern financial markets that
the same company in the same country and same market issues different classes of
shares just according to different currencies and/or investors with different residen-
cies/nationalities. Although aware of this bizarre practice, the Chinese authorities,
such as the China Securities Regulatory Commission (CSRC), were perplexed
for effective remedies. Obviously, the ultimate way out is for the two markets to
merge, but the main problem afflicting them is the restricted convertibility of the
RMB. In 2000–2001, China’s impending entry into the WTO speeded up its pre-
parations for further financial liberalisation, including an ultimately complete lift
of the ban on currency convertibility. Since then, a series of measures regarding
B shares have been initiated. They included the following. (1) As of 1 June 2001,
domestic Chinese nationals are allowed to trade B shares using ‘lawfully-acquired’
foreign exchanges. Since then, the shares have virtually become available to all
investors, albeit with US or HK dollars. (2) Those B-share-only companies are
allowed to issue A shares. (3) No newly-listed companies are permitted to issue B
shares only. The first measure can be seen as the prelude of opening the A-share
markets to all investors, domestic and foreign. The second and third measure
seem to be aimed at ultimately phasing out the B-share-only companies.
These new policies taken by the CSRC were perceived by the markets as a signal
that the merger between A and B shares seems to be underway. What immediately
followed was a buying spree of B shares in both the Shanghai and Shenzhen stock
markets. Figure 1 shows that the prices of B shares rocketed in March–July 2001. It
also shows the price discounts on B shares relative to A shares for both the SHSE
and the SZSE throughout the entire sample period. Investors went on a panic
purchase of B shares in the hope that they could make enormous profits from
34 X.-M. Li
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such huge price differentials between A and B shares today, should the two markets
merge tomorrow. But the expected merger did not actually happen. Then, from
August 2001, the prices of both types of shares started to fall all the way down,
according to Figure 1.
Having set up a brief background of the A- and B-share markets, we are now in a
position to pose several questions regarding their informational efficiency, which the
rest of the paper will address. How does weak-form efficiency in each of the markets
change over time? How do they react to the arrivals of good and bad news? How
seriously are they segmented in terms of the short-run interdependence of return
volatility between them and in terms of co-movements in their long-run trends?
As far as China’s A- and B-share markets are concerned, the WFE question has
been addressed in Laurence et al. (1997) and Long et al. (1999), while the
second and third questions have not yet been addressed in previous studies, to
the best of our knowledge.4 However, the statistical techniques, such as random
Figure 1. (a) The price indexes of Shanghai’s A and B shares; (b) the price indexes ofShenzhen’s A and B shares. — A share; - - - B share.
Time-varying Informational Efficiency 35
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walk and Granger causality tests, employed by the authors are, in our opinion, inap-
propriate. To show the reasons why, Section 2 presents the statistical profiles of the
data and their discussions. Section 3 describes and explains the models and estima-
tion methods we employ in this paper. Empirical results are given and interpreted in
Section 4, and concluding remarks are made in Section 5.
2. Statistical Profiles of Daily Returns on A and B Shares
In this section, we present the statistical profiles of the A- and B-share data. The
data are the daily closing price indexes of the Shanghai SE A Share (SHA), the
Shanghai SE B Share (SHB), the Shenzhen SE A Share (SZA) and the Shenzhen
SE B Share (SZB), obtained from Datastream. The A-share price indexes are in
the Chinese currency. Although B shares are traded in US/HK dollars, their
RMB-denominated price indexes are also readily available and thus were directly
used in our study for the sake of comparability. The sample covers the period
from 5 October 1992 to 24 May 2002 (with a total of 2515 observations), for
which the data on SZA and SZB are available, but for which the data on SHA
and SHB are truncated. The truncation on the SHA and SHB data seems to be
inevitable, because the relationships between the Shanghai and Shenzhen markets
for A and B shares can only be examined over the same sample period.
Table 1 reports some descriptive statistics. All of the four return series exhibit
severe leptokurtosis and are characterised by positive skewness. Not surprisingly,
the Jarque–Bera normality test statistic suggests that they are non-normal, as
evidenced by the highly significant test statistic generated in each case. The four
return series are also found to possess heteroscedasticity and autocorrelation,
given the significant ARCH test statistics and Ljung–Box statistics.
The ADF statistics indicate that there is a unit root in each of the four logarith-
mic price indexes, but not in their first differences. In other words, they all follow a
random walk process. It is tempting to take the acceptance of the random walk
Table 1. Summary statistics
Share Skewness Kurtosis J-B L-B(26) ARCH ADF CUSQ
(r) (r) (r) (r) (r) (p) (r) (p) (r)
SHA 1.661 21.12 2865.7** 120.4** 47.54** � 2.33 � 11.4** 0.408** 0.413**
(18) (17)
SHB 2.145 33.71 4390.2** 79.88** 4.179* � 1.14 � 27.0** 0.117** 0.116**
(3) (2)
SZA 0.980 16.55 3468.1** 52.43** 26.56** � 1.19 � 11.6** 0.316** 0.315**
(19) (19)
SZB 1.996 33.48 5091.6** 124.7** 10.67** � 1.63 � 15.3** 0.153** 0.153**
(8) (7)
Note: ‘p’ denotes the logarithmic price level. ‘r’ denotes the rate of return (i.e. �p). J-B denotes the
Jarque–Bera normality test statistic. L-B(26) denotes the Ljung–Box test statistic of the 26th order.
ARCH denotes the ARCH test statistic of order 1. ADF denotes the augmented Dicky–Fuller test
statistic. CUSQ denotes the CUSUMSQ test statistic. *Significant at the 5% level. **Significant at the
1% level. The figure in parenthesis are the lag lengths chosen according to the ‘t-sig’ method (see Perron,
1997).
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hypothesis for a market price index to suggest that the market is weak-form efficient.
However, this overlooks the fact that the presence of some significant autoregressive
terms in the ADF-test equation still implies the predictability of market returns. In
addition, the computation of the t-type ADF statistic is based on the OLS regres-
sion, which requires the residual also to be normal and homoscedastic, but these
two assumptions are violated in each case, according to the results of diagnostic
checks on the regression equation for the ADF test (not reported).
A further problem that has been largely ignored pertains to the possible struc-
tural change in the behaviour of the data. The last column of Table 1 provides
the CUSUMSQ statistic for each of the ADF-test regression models. One can see
that the null hypothesis of stable parameters is decisively rejected in all four
cases. Hendry and Neale (1991) and Perron (1989) showed that inference on
unit roots is affected by structural change; that is, the unit root tests tend to
under-reject the null of a unit root. If a structural change is abrupt in nature and
takes place at a certain point of time, unit root tests may still be conducted after
taking such a break into account. However, many studies on Chinese stock
market efficiency (including Laurence et al., 1997, as mentioned in Section 1)
have failed to do so when applying unit root tests. Worse still, in the cases where
structural changes take place gradually over time and where they occur at every
point of time, performing unit root tests to examine market efficiency, which is
now time-varying, would be simply out of the question.
To summarise the above discussion, unit root tests such as the ADF test do not
lend a helping hand in studying the efficient market hypothesis (EMH) for the
Chinese stock markets. We need to find an alternative framework for this purpose.
3. Research Framework
Let us start with the definition of weak-form efficiency in searching for such a frame-
work. Fama (1970) defines weak-form efficiency as follows. Security prices fully
reflect the information contained in past price movements, i.e. they do not follow
patterns that repeat and it is not possible to trade profitably purely on the basis of
historical price information. The essence of weak-form efficiency is that past returns
on a market cannot be used to predict current returns on the same market.
Mathematically, this can be formulated as:
rt ¼ b0 þXp
i¼1
birt�i þ et, et � Nð0, �2e Þ ð1Þ
where rt denotes the continuously compounded percentage returns on a share
market. If bi¼ 0 (i¼ 1, 2, . . . , p), then rt¼ b0þ et. That is, current returns rtdepend only on a constant b0 and a white-noise error term et. Since b0 and et do
not contain any information on past returns, we may say that current returns rtcannot be predicted based on past returns rt�i (i¼ 1, 2, . . . , p) and so the market
is weak-form efficient. If bi 6¼ 0, they measure the predictability of current returns
using past returns or the degree to which the market is weak-form inefficient,
according to Fama’s definition.
Equation (1) is a familiar AR( p) model, and provides a useful framework to
test the weak-form EMH (i.e. to test bi¼ 0 against bi 6¼ 0). An advantage of this
framework over the unit-root-test one is that the former can easily accommodate
Time-varying Informational Efficiency 37
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the possibility of gradual structural change – that is, the former can be used to study
time-varying WFE, whereas the latter cannot. Taking into account possible struc-
tural change over time, equation (1) may be modified to become:
rt ¼ b0t þXp
i¼1
bitrt�i þ et, et � Nð0, �2e Þ ð2Þ
and
bit ¼ �ibit�1 þ uit uit � Nð0, �2i Þ and i ¼ 0, 1, . . . , p ð3Þ
Equation (2) is known as the measurement equation, and equation (3) as the transi-
tion equation. In the measurement equation, all model parameters, bit (i¼ 0, 1,
2, . . . , p), are allowed to change at each point of time t. The transition equation
then describes the way these parameters evolve. We term it as general auto-
regression of order 1 (GAR(1)). The GAR(1) specification embraces several likely
outcomes. If �i¼ 0 and �i¼ 1, then bit are constant; if �i 6¼ 0 and �i¼ 1, then bitbecome a random walk; if �i 6¼ 0 and � 1 <�i < 1, then bit follows an AR(1) process;
and so on. Which outcome it will turn out to be, can be – and should be –
determined by the data. The assumption that bit are constant, as implicitly made
in previous studies on China’s share markets, is just one of the likely outcomes
of the transition equation (3), and is too restrictive to be able to capture the true
behaviour of market efficiency in China’s share markets.
A further advantage of employing the AR model over employing the unit-root-
test strategy is that the former can address the problem of heteroscedasticity whereas
the latter, again, cannot. Such a problem does exist in China’s share markets as
confirmed in the preceding section. In finance, heteroscedasticity, in the form of
a time-varying variance, represents time-varying volatility (risk) of the associated
market. The literature has suggested a variety of GARCH-type models from
which we can choose an appropriate one to combine with the AR model for a
particular purpose. More specifically, when considering the possible existence of
return volatility, we need to split equation (2) into two as follows:
rt ¼ b0t þXp
i¼1
bitrt�i þ et, et � Nð0, htÞ ð4Þ
ht ¼ a0 þXm
j¼1
aje2t�j þ
Xm
j¼1
aþj ðeþt�jÞ
2þXn
j¼1
cjht�j , eþt�j ¼ maxfet�j , 0g ð5Þ
with conditional variance ht replacing unconditional variance �2e . Here, the transi-
tion equation (3) is retained. Equation (5), termed the threshold GARCH (or
TGARCH) model, describes the behaviour of conditional variance ht. It also
embraces the possible leverage effect, i.e. asymmetries in the return-volatility reac-
tion to information shocks (see, for example, Campbell and Hentschel, 1992): if
aþj < 0 ð> 0Þ, past bad news (et�j < 0) has a greater (smaller) impact on the current
volatility of returns than past good news (et�j>0).
The time-varying AR model (i.e. equations (4) and (3)) can also be combined
with the TGARCH-spillover model to investigate the transmission of information
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on return volatility across different share markets. The TGARCH-spillover model is
specified as:
ht ¼ a0 þXm
j¼1
aje2t�j þ
Xm
j¼1
aþj ðeþt�jÞ
2þXn
j¼1
cjht�j þXq
j
dje20t�j ð6Þ
where e0t�j may be interpreted as past information shocks to markets other than
the own one. Statistically insignificant values of dj would imply that past information
shocks to other markets are not utilised by, or available to, participants in the own
market, as the return volatility of the own market is not affected by the shocks. In a
sense, this reflects a certain degree of market segmentation.
The above discussion arrives at a conclusion that the AR model is a superior
framework to the unit-root-test one in studying the EMH. This is especially so if
WFE is time-varying. In the case of the AR-model parameters being time-varying,
however, the Kalman Filter algorithm must be applied. For the technical details of
the algorithm, readers are referred to Harvey (1989). Very briefly here, this techni-
ques gives the minimummean-squared-error linear estimator of bit (i¼ 0, 1, 2, . . . , p)based on the observations up to and including time t, even if the disturbances are
not normal (see Maddala and Kim, 1998, p. 473). In other words, it allows learning
to occur with each additional observation. The Kalman Filter technique may be
implemented in an econometrics package TSP with the initial values bi0 and the
starting values of �i and �i (i¼ 0, 1, 2, . . . , p) provided by the user. The final esti-
mates of these values will be determined at convergence by the TSP program.
4. Empirical Results
We first estimated equation (1) for each return series, ignoring the possible insta-
bility of bi and possible non-normality and heteroscedasticity of et. In the estimation
process, the order of the AR terms, p, was determined as such a minimum value that
the associated Ljung–Box Q statistics of et up to the 26th order show no evidence of
autocorrelation (see Table 2). This was to ensure that et are not contaminated with
any information on past returns, and so such information will be embodied only in
the predictable components �bi r t�i in equation (1).
Although not reported in Table 2, some or all of the estimated parameters bi are
highly significant. Because they are assumed to be constant, this would suggest that
the four share markets are not weak-form efficient throughout the entire estimation
Table 2. Some statistics of the estimated equation (1)
Statistics RSHA (12) RSHB (1) RSZA(4) RSZB (4)
L-B (26) 26.76[0.422] 24.83[0.529] 35.71[0.097] 31.21[0.221]
CUSQ 0.418[0.000] 0.117[0.000] 0.314[0.000] 0.153[0.000]
ARCH 30.14[0.000] 7.304[0.0007] 23.36[0.000] 11.01[0.001]
J-B 3222.1[0.000] 4575.4[0.000] 3629.2[0.000] 6089.1[0.000]
Note: RSHA, RSHB, RSZA and RSZB are respectively the rate of returns on Shanghai’s A and B shares,
and Shenzhen’s A and B shares. L-B(26) is the Ljung–Box test statistic of the 26th order. CUSQ is the
CUSUMSQ test statistic. ARCH is the ARCH test statistic of order 1. J-B is the Jarque–Bera normality
test statistic. Figures beside the four return variables are their AR orders of equation (1).
Time-varying Informational Efficiency 39
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period. However, this result is doubtful as the non-normality and heteroscedasticity
problems are not properly dealt with, rendering invalid the t-statistics of bi computed
by the OLS method. Moreover, the highly significant CUSUMSQ statistics suggest
that the model parameters are not stable. To confirm this Figure 2 presents graphical
results of the CUSUMSQ test for the Shanghai A and B shares in (a) and (b), and for
the Shenzhen A and B shares in (c) and (d). That the recursive residuals exceed the
5% bound of significance indicates instability of the AR parameters bi, and one can
observe that this is true in each case. Instability appears to be more serious for the
two A-share markets than for their two B-share counterparts, according to Figure 2.
The useful messages conveyed by the ARCH and CUSUMSQ test results are
that return volatility and weak-form efficiency must have changed over the sample
period in all four share markets. Now, an immediate question of how arises. To
address this question, we next estimated the system consisting of equations (4),
(3) and (5), assuming TGARCH errors for all four return series. To make it
easier for the program to reach convergence, the smallest order p of the time-varying
AR model (i.e. equation (4)) and the smallest orders m and n of the TGARCH
Figure 2. The CUSUMSQ tests of parameter stability in equation (1) for SHA (a); SHB (b);SZA (c); SZB (d).
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model (i.e. equation (5)) were chosen, provided that the Ljung–Box test statistic
of the 26th order shows no autocorrelation, and the ARCH statistic also shows
no heteroscedasticity, in the standardised residuals eSTDt ¼ et=ffiffiffiffiht
p. The Kalman
Filter method then yielded the estimation results in Table 3.
Several messages emerge from Table 3. First, regarding the time-varying AR
model, its order turns out to be 1 for all four shares, quite different from the time-
invariant AR model considered in Table 2. As a result, there are two b
estimates, two � estimates and two � estimates for each of the four share markets.
That the time-varying AR model is of order 1 suggests that the values of returns in
the immediate previous period only can be used to infer current returns if the
AR(1) parameter is statistically significant. The estimates of bb00 reveal that
Shanghai’s B shares enjoyed a positive mean rate of daily returns (0.3996%), while
Shanghai’s A shares, Shenzhen’s A and B shares suffered negative mean rates of
daily returns (�0.0999%, �0.7739% and �0.0321%), on the starting date of our
sample (i.e. 7 October 1992, due to two observations lost). The estimated initial con-
ditions of the four AR(1) parameters ðbb10Þ including their t-values seem to suggest
that returns on Shanghai’s A- and B-share markets were predictable while those on
Shenzhens’ were not, on this starting date. These results need to be confirmed
later on, however, as the standard errors (underlying the reported t-values of bb10)
of the initial state vector (e.g. b0¼ [b00, b10]T) are computed from numeric second
derivatives of the model by the TSP program, but the standard errors used for com-
puting the confidence intervals of the AR-model coefficients (b0t and b1t) should be
the ones associated with the vector’s covariance matrix Var(b0) (see Rockinger and
Urga, 2000). So at this stage we can only roughly judge the significance of the
start-up values of the AR parameters on the t-values given in Table 3.
Table 3. Estimation results of equations (4), (3) and (5)
Share bb00 bb10 ��0 ��1 ��0 ��1 LLF
SHA � 0.0999 0.2534 1.0000 1.0000 0.0026 0.0019 � 6195.18
(� 0.657) (2.887)* (677.64)** (483.52)**
SHB 0.3996 0.2327 0.9750 0.9989 0.0215 0.0032 � 5816.67
(0.614) (2.319)* (41.74)** (750.98)**
SZA � 0.7739 0.1886 0.9650 1.0000 0.0235 0.0097 � 5950.83
(� 0.762) (1.276) (33.493)** (286.88)**
SZB � 0.0321 0.2619 1.0000 1.0000 0.0030 0.0155 � 5848.00
(� 0.239) (1.227) (669.16)** (305.05)**
Share aa0 aa1 aaþ1 cc1 L-B(26) ARCH LRT
SHA 0.0243 0.1102 � 0.0608 0.9277 38.152 0.1531 29.88**
(3.159)** (9.764)** (� 5.280)** (155.13)** [0.059] [0.696]
SHB 0.1338 0.1599 0.1185 0.8081 33.289 0.0133 23.80**
(5.651)** (8.858)** (4.646)** (64.23)** [0.154] [0.908]
SZA 0.0286 0.0996 � 0.0541 0.9321 31.177 0.0012 46.50**
(3.016)** (9.287)** (� 5.029)** (150.59)** [0.222] [0.972]
SZB 0.9248 0.2670 0.0067 0.6171 23.602 0.0270 0.040
(10.84)** (6.788)** (0.136) (22.99)** [0.599] [0.869]
Note: The effective estimation period is from October 7, 1992 to May 24, 2002. LLF is the log-likelihood
function. L-B(26) is the Ljung–Box test statistic of the 26th order. ARCH is the ARCH test statistic of
order 1. LRT is the likelihood ratio test statistic for no asymmetry between positive and negative shocks.
The figure in parentheses are t-ratios. The figures in square parentheses are p-values. *Significant at the
5% level. **Significant at the 1% level.
Time-varying Informational Efficiency 41
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Second, regarding the transition equation (3), two markets (SHA and SZB) have
their AR-model coefficients following a random walk process, given that their ��0
and ��1 estimates are unity and extremely significant. SHB’s AR-model coefficients
evolve according to an AR(1) process, as ��0 ¼ 0:9750 < 1, ��1 ¼ 0:9989 < 1 with
extremely high t-values. As for SZA, its intercept is an AR sequence
ð��0 ¼ 0:9650 < 1Þ but its first-order autocorrelation coefficient is characterised as
a random walk ð��1 ¼ 1Þ, given again huge t-values. The estimated standard errors
of uit in the transition equation, ��i ði ¼ 0, 1Þ are also reported in Table 3, but ��isstandard errors are not. This is because, in the estimation process, constraints
��i > 0 were imposed to prevent them from taking negative values; that is, they
were forced to follow non-standard distributions. Therefore, their own estimated
standard errors do not have the usual meaning and it is pointless to report them.
Each ��i determines the variability of the corresponding AR-model coefficient bbit:
the greater is ��i, the larger swing bbit will have. For example, SZA’s ��0 has the highest
value (0.0235), and so the mean rate of returns on Shenzhen’s A shares (bb0t of SZA)
must have the largest range of change among all markets’ mean rates of returns.
Another example is that SZB’s ��1 (0.0155) is the largest among the standard
errors of all markets’ AR(1) parameters, and so SZB’s AR(1) parameter bb1t (predict-
ability) is expected to have the greatest magnitude of fluctuations. In addition,
non-zero ��i make the variances of the parameters, Vit¼Var(bit) (and the resultant
confidence intervals ½bit þ 1:96ffiffiffiffiffiffiVit
p�� ½bit � 1:96
ffiffiffiffiffiffiVit
p� ¼ 2 1:96
ffiffiffiffiffiffiVit
pÞ, vary across
different points in time (these results can be confirmed by examining the time
plots of bbit in Figures 3–10).
The third group of messages pertains to the estimated TGARCH model whose
orders (m and n) determined in the above-described way are all 1 for the four
markets. The component et of the measurement equation (4) contains other sets
of information than on past returns per se that hit the market. One such set of
information includes the volatility (risk) of past returns, since the conditional var-
iance ht is found to be dependent on e2t�1 and ht�1, as evidenced by the highly sig-
nificant estimates of aa1 and cc1 in Table 3 for all four shares. Note that we did not
impose restrictions on the TGARCH-model coefficients in the estimation process,
which means that the distribution of the t-statistics is standard and so the
computed t-values are reportable. Thus, even if the AR(1) parameter bb10 is
zero, that is, even if past reruns can no longer be used to predict currency returns,
past return risks ht�1 may still be useful information in predicting current return
risks or the ‘amplification’ of current returns (i.e. ht in rt ¼ b0t þffiffiffiffiht
peSTDt ). In this
case, one may say that, even if the market has become weak-form efficient (as
bb1t ¼ 0), it is not yet semi-strong-form efficient (as ht¼ f(ht�1)).5 Put differently,
the genuine unpredictable component of the AR model is not et but eSTDt , as
the latter is purified of the ARCH effect in each case (see the seventh column
in the lower panel of Table 3).6
The last results to be observed from Table 3 are the leverage-effect results. aaþ1 ’s
t-values are statistically significant at the higher than 1% level for SHA (� 5.280),
SHB (4.646) and SZA (� 5.029), and the likelihood ratio test statistic LRT is
also significant at the higher than 1% level for each of these three markets (29.88,
23.80 and 46.50), implying that they possess asymmetries in the return-volatility
reaction to different information shocks. A noticeable difference, however, is that
the two A-share markets react to bad news more strongly than to good news
ðaaþ1 < 0Þ, whereas good news dominates bad news in affecting the volatility of
the Shanghai B-share returns ðaaþ1 > 0Þ. For the Shenzhen B-share market, no
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asymmetry between negative and positive shocks is found to exist, according to both
the insignificant t statistic (0.136) and LRT statistic (0.040).
The spillover effect of volatility in one market into the other can be understood
as information transmission in volatility across different markets. We investigated
it on a pair-wise basis for the four share markets, and the results are reported in
Table 4. Based on both the magnitude and significance of the parameter dd1, there
groups of results may be identified. In group 1, of no information transmission,
Shenzhen’s A shares do not demonstrate any spillover effect of volatility
on Shanghai’s A shares and Shenzhen’s B shares, nor do Shanghai’s A shares on
Shanghai’s B shares and Shenzhen’s B shares, since t-values in these cases are
highly insignificant. This is also true for Shenzhen’s B shares on Shanghai’s B
shares. In group 2, weak information transmission is found from SHB to SHA
and SZA, from SZB to SHA and SZA, and from SZA to SHB, according to the
very small magnitudes ðjddij < 0:01Þ, but significant t-ratios, of the corresponding
dd1. The third group shows strong information transmission that runs from SHA
to SZA (0:01 < jdd1j < 0:1 with t-statistic¼ 3.878), and from SHB to SZB
(0:1 < jdd1j with t-statistic¼ 10.77). In this last group, the spillover effects are all
positive, in contrast to group 2 where they are all negative, albeit with negligible
magnitudes. It may therefore be claimed that, in terms of volatility transmission,
the two A-share markets are, relatively speaking, less segmented from each other,
Table 4. Estimation results of equation (6)
ht of e20t�1 of aa0 aa1 aaþ1 cc1 dd1 ARCH L-B(26)
SHA SHB 0.0682 0.1174 �0.0666 0.9189 � 0.0044 0.2145 38.316
(5.333)** (9.279)** (� 5.457)** (122.96)** (� 6.258)** [0.643] [0.057]
SHA SZA 0.0243 0.1096 � 0.0613 0.9276 0.0010 0.1526 38.087
(3.156)** (9.310)** (� 5.173)** (154.73)** (0.179) [0.696] [0.059]
SHA SZB 0.0457 0.1139 � 0.0636 0.9232 � 0.0025 0.1805 38.615
(4.203)** (9.529)** (� 5.346)** (135.64)** (� 5.282)** [0.671] [0.053]
SHB SHA 0.3580 0.2431 0.2336 0.6819 � 0.0004 0.1511 31.784
(3.817)** (7.755)** (4.649)** (18.08)** (� 0.090) [0.697] [0.200]
SHB SZA 0.1395 0.1569 0.1367 0.8099 � 0.0042 0.0054 33.013
(6.346)** (8.788)** (5.195)** (65.81)** (� 8.719)** [0.941] [0.162]
SHB SZB 0.1260 0.1586 0.1213 0.8069 0.0052 0.0143 33.311
(5.315)** (8.750)** (4.709)** (64.23)** (1.270) [0.905] [0.153]
SZA SHA 0.2722 0.1558 � 0.0758 0.7894 0.0586 0.1339 37.016
(4.856)** (5.699)** (� 3.048)** (25.72)** (3.878)** [0.714] [0.075]
SZA SHB 0.0371 0.1006 � 0.0561 0.9322 � 0.0016 0.0038 31.199
(4.283)** (9.443)** (� 5.211)** (158.99)** (� 3.737)** [0.951] [0.221]
SZA SZB 0.0367 0.1028 � 0.0577 0.9311 � 0.0016 0.0033 31.348
(4.145)** (9.446)** (�5.248)** (157.07)** (� 3.979)** [0.954] [0.216]
SZB SHA 0.9051 0.2620 0.0076 0.6236 � 0.0005 0.0269 23.832
(10.43)** (6.546)** (0.153) (21.87)** (� 0.147) [0.870] [0.586]
SZB SHB 0.1657 0.0581 0.0116 0.7945 0.1532 0.0049 24.786
(5.546)** (3.761)** (0.525) (55.76)** (10.77)** [0.944] [0.531]
SZB SZA 0.9161 0.2640 0.0097 0.6215 � 0.0024 0.0270 23.676
(10.89)** (6.698)** (0.197) (23.21)** (0.000) [0.869] [0.594]
Note: This effective estimation period is from 7 October 1992 to 24 May 2002. ARCH is the ARCH test
statistic of order 1. L-B(26) is the Ljung–Box test statistic of the 26th order. The figures in parentheses
are t-ratios. The figures in square parentheses are p-values. *Significant at the 5% level. **Significant at
the 1% level.
Time-varying Informational Efficiency 43
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and so are the two B-share markets, with unidirectional spillover effects from
Shanghai to Shenzhen in both cases. A higher degree of segmentation is found to
exist between the markets in each of other pairs, as evidenced by no or very weak
information transmission. Note that the ARCH and Ljung–Box statistics are all
insignificant at the 5% or lower level, exhibiting the fact that the standardised
errors eSTDt resulting from the TGARCH-spillover specification for conditional
variance are free of the ARCH and autocorrelation problems. Thus, we have
a certain degree of confidence in the above inference. Comparing Table 4 with
Table 3, we also find that the conclusions here regarding the leverage effect
do not change qualitatively: it is still significantly negative for both SHA and
SZA, significantly positive for SHB, and not significant at all for SZB.
Since all parameters of the AR models are non-constant over time, we need to
conduct a graphical analysis of their smoothed estimates. Figures 3–6 depict the
smoothed estimates of the time-varying intercept b0t in equation (4) for the four
shares respectively. b0t, the long-run mean rate of returns on the market, may be
interpreted as appropriately capturing the long-run trend of the market. If two or
more markets are integrated, one would expect to observe some co-movements in
their long-run trends or some similar patterns of their long-run mean returns.
What we observe from the four figures, however, is that the four b0ts evolve along
utterly different time paths. For example, SHA’s long-run mean returns underwent
four discernibly different phases: rising (10.1992–02. 1997), declining slowly
(02.1997––06.1999), declining sharply (06.1999–08.2001) and declining slowly
(08.2002–05.2002), but SHB’s went through indiscernible changing phases. This
suggests that there do not exist co-movements in the two markets’ long-run mean
returns. The similar result also applies to other pairs of such returns, if the same gra-
phical inspection is conducted. Therefore, we may conclude that the four share
markets are highly segmented from each other. Restrictions such as those on the
dual listing of shares on the Shanghai and Shenzhen Stock Exchanges and those
on investing in A shares by domestic investors only and in B shares by foreign inves-
tors only have clearly contributed to these acute market segmentations. Even if a
major policy change or a big shock can alter a market’s long-run behaviour, it
cannot alter others’, at least in the same direction. As a result, the degree of diffi-
culty in regulating all share markets is increased for policy-makers. However, one
upside of the market segmentations is perhaps that, because of low correlation
between the four shares, including more than one of them in a portfolio will enhance
the effectiveness of risk reduction through diversification. Figures 4 and 5 also dis-
play that Shanghai’s B shares and Shenzhen’s A shares brought investors no returns
most times since the confidence intervals of their bb0t include zero during these
times. Figures 3 and 6 then show that investors of Shanghai’s A shares and
Shenzhen’s B shares experienced alternate periods of bullish and bearish markets,
again according to the time paths of the respective confidence intervals.
We now turn to examining the time-varying weak-form efficiency of the four
share markets. Relevant to this purpose are the four non-constant AR(1) parameters
b1t, and so the time plots of their smoothed estimates are displayed in Figures 7–10.
It was mentioned earlier that Shanghai’s A- and B-share markets might have
started up with significant return predictability. This is now confirmed by Figures 7
and 8: the initial values of their bb10 were both around 0.25 on 7 October 1992 with
high statistical significance (their lower bounds of the confidence intervals are all far
greater than zero). But the later development of the two markets witnessed an
increasing contrast between them in terms of return predictability. SHA’s bb1t
44 X.-M. Li
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Figure3.Smoothed
estimates
andco
nfiden
ceintervalsofb 0
tfortheShan
ghai
A-shareindex
.—
b 0t;---b 0
t�
1:96
ffiffiffiffiffiffiffi
V0t
p.
Time-varying Informational Efficiency 45
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Figure4.Smoothed
estimates
andco
nfiden
ceintervalsofb 0
tfortheShan
ghai
B-shareindex
.—
b0t;---b0t�
1:96
ffiffiffiffiffiffiffi
V0t
p:
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Figure5.Smoothed
estimates
andco
nfiden
ceintervalsofb0tfortheShen
zhen
A-shareindex
.—
b 0t;---b 0
t�
1:96
ffiffiffiffiffiffiffi
V0t
p.
Time-varying Informational Efficiency 47
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Figure6.Smoothed
estimates
andco
nfiden
ceintervalsofb 0
tfortheShen
zhen
B-shareindex
.—
b 0t;---b 0
t�
1:96
ffiffiffiffiffiffiffi
V0t
p:
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Figure7.Smoothed
estimates
andco
nfiden
ceintervalsofb1tfortheShan
ghai
A-shareindex
.—
b 1t;---b 1
t�
1:96
ffiffiffiffiffiffiffi
V1t
p:
Time-varying Informational Efficiency 49
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Figure8.Smoothed
estimates
andco
nfiden
ceintervalsofb 1
tfortheShan
ghai
B-shareindex
.—
b 1t;---b 1
t�
1:96
ffiffiffiffiffiffiffi
V1t
p:
50 X.-M. Li
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Figure9.Smoothed
estimates
andco
nfiden
ceintervalsofb 1
tfortheShen
zhen
A-shareindex
.—
b 1t;---b 1
t�
1:96
ffiffiffiffiffiffiffi
V1t
p:
Time-varying Informational Efficiency 51
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Figure10.Smoothed
estimates
andco
nfiden
ceintervalsofb 1
tfortheShen
zhen
B-shareindex
.—
b 1t;---b1t�
1:96
ffiffiffiffiffiffiffi
V1t
p:
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moved rapidly towards zero and crossed the horizontal axis for the first time in mid-
1993. Thereafter, it fluctuated but with the confidence interval basically covering
this axis, which can be interpreted as non-predictability. SHB’s bb1t, however,
stayed far above the horizontal axis almost throughout the past 10 years or so
with exceptions occurring only very recently in 2002, when it first touched the
axis. Closer inspection of its time plot reveals that the return predictability of
Shanghai’s B shares kept rising between January 1994 and December 1996, and
since then had declined all the way down. These observations suggest that SHA’s
returns became unpredictable much earlier than SHB’s, the latter experiencing
rising and then falling predictability.
Unlike the messages conveyed in Table 3, Figures 9 and 10 show that the SZA
and SZB markets started with significant return predictability, because their
bb1t were distinguishable from zero until 12 December 1992 and 2 April 1993
respectively. For SZA, the subsequent periods were mostly characterised as non-
predictablity, during which its AR(1) parameter had a zero value included in the
confidence interval. This is not the case for SZB, however. From Figure 10, it can
be seen that the AR(1) parameter was significantly different from zero during
seven periods covering 1244 of 2513 days, approximately 50% of the sample size.
But it is also true that since 4 April 2001, non-predictability has again featured the
SZB market.
It is of particular interest to compare the impacts of the 1994 RMB devaluation on
the two B-share markets where share trading takes place in non-Chinese currencies.
Starting from 7 January 1994, SHB’s autocorrelation coefficient went all the way
up (see Figure 8) until 9 December 1996 when it peaked at 0.35. We know that the
Chinese currency devalued sharply from 5.76 ¥/$ to 8.7 ¥/$ from 1 January 1994
onwards. Since Shanghai’s B shares are traded in US dollars this sharp devaluation
of the RMB meant a sudden drop in SHB’s US-dollar prices relative to SHA’s RMB
prices. Given that A and B shares for each listed company enjoy equal rights and
dividends, it would presumably trigger a buying spree for Shanghai’s B shares
among (mostly) the US investors, although such responses from them were delayed
4 days. During a panic buy, one expects investors to purchase even more if they
observe a large rise in prices. The soaring of the market then became self-sustaining
and, as a result, high or increasing autocorrelation is expected. This runs counter to
a fully weak-form efficient market where we expect complete and instantaneous
adjustments upon receiving good news. Interestingly, the devaluation of the RMB
did not have a similar significant impact on the correlation structure of
Shenzhen’s B shares. The AR(1) coefficient also started rising from 7 January
1994 but the rising trend ended shortly on 21 April 1994 when it reached
0.10495. Moreover, the associated confidence interval included zero throughout
this period (see Figure 10). This suggests that, although a RMB devaluation against
the US dollar would mean an equal devaluation against the HK dollar (as the latter
is pegged to the former), the HK investors were not as terribly interested as the US
investors. One possible reason might be because the ongoing intense
disputes between Chris Patton and the Chinese government over reforming
Hong Kong’s political systems had already increased political uncertainty about
Hong Kong’s future, and hence the risk in holding Shenzhen’s B shares.
Consequently, it is not surprising that no massive purchases of SZB and hence
no significant rising autocorrelation in SZB’s returns occurred.
It has been argued by Fama (1991) and Malkiel (1992) that a market may be
efficient yet predictable. In other words, if non-predictability exists, the market
Time-varying Informational Efficiency 53
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must be weak-form efficient; but if the market is predictable, this does not necessa-
rily imply that the market is weak-form inefficient. In this case, predictability may be
caused by factors other than informational inefficiency. One such important factor is
the illiquidity of the market (Lo and MacKinlay, l990). It is certainly true that the
four markets under our investigation were illiquid at their earlier stages of develop-
ment, judging from their relatively small market values then (see Exhibit 1 in
Johnson, 2002). However, it is also true that when China’s four share markets
first started trading, investors were not familiar with the price discovery mechanism,
the information-releasing systems were incomplete or not established, regulations
were not normalised or enforced effectively, and so on. All these factors would
make it unlikely for the share prices fully to reflect relevant information.
Consequently, just relying on the fact of market illiquidity would lead to an erro-
neous conclusion that the markets were efficient albeit predictable. As their
market values grew, the market illiquidity became less and less – while informational
inefficiency became more and more – relevant in causing predictability if detected.
The point here is that the presence of predictability can be at least partly attributed
to information inefficiency in the Chinese context.
Based on the above consideration, we make inference on weak-form efficiency
for China’s four share markets as follows. First, the level of weak-form efficiency
has been improving through time in at least three markets: SHA, SHB and SZA.
The Shanghai A-share market is the first to have become efficient since 3
November 1997, followed by the Shenzhen A-share market (since 3 July 1998).
The Shanghai B-share market has shown a convergence (albeit very slow) towards
efficiency since 9 December 1996. A similar trend is, however, not observed for the
Shenzhen B-share market whose AR(1) parameter jumped to the highest level
(0.51978) recently on 1 March 2001, following the official announcement that
domestic investors would be allowed to trade in B shares from 1 June 2001 (this
announcement also resulted in a pulse in SHB’s AR(1) parameter on the same
day but only to a value of 0.12912). Second, compared with the A-share markets,
the B-share markets have been relatively inefficient and slow in moving towards
efficiency. Within a time-invariant framework, Laurence et al. (1997) find the
existence of weak-form efficiency in the A-share markets but not the B-share
markets. Using a time-varying framework, we have obtained similar but more
accurate and detailed results in the sense that our results shed some light on the
evolution behaviour of WFE of the A- and B-share markets in China. The differ-
ences in WFE between the A-share and the B-share markets reveal that overseas
investors have had less information available than domestic investors about the
listed companies, the relevant policies and the economy as a whole.
5. Concluding Remarks
In this concluding section, we summarise the main findings as follows. Within a
time-varying framework, we have been able to observe how, in the past 10 years
or so, the levels of informational efficiency changed in China’s two A-share and
two B-share markets. The A-share markets have been found to perform better
than the B-share markets in that the former were quicker and earlier in becoming
weak-form efficient than the latter. Therefore, it is the A-share markets that have
contributed to what Li (2002) finds as a steady convergence of the aggregate
Shanghai and Shenzhen stock markets towards efficiency. Despite this, however,
the two A-share markets are not semi-strong-form efficient, let alone the two
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B-share markets (weak-form inefficiency automatically implies semi-strong-form
inefficiency but not vice versa), given the presence of TGARCH errors in the AR
models of all four shares.
Asymmetrical market reactions to different information shocks have been found
in the SHA, SZA and SHB markets. For the former two, bad news has a larger
impact on volatility than good news, while for the latter the opposite applies.
No leverage effect has been detected for the SZB market.
We have provided evidence in support of the common belief that China’s share
markets are highly segmented. Part of the evidence comes from the estimation
results of the TGARCH-spillover models, which indicate the existence of three
groups of, respectively, no information transmission (SHA(SZA, SHB(SHA,
SHB(SZB, SZB(SHA and SZB(SZA), weak information transmission
(SHA(SHB, SHA(SZB, SHB(SZA, SZA(SHB and SZA(SZB), and strong
information transmission (SZA(SHA and SZB(SHB). So the degree of market
segmentation in terms of information transmission in return risks varies across
different groups of share markets in pairs. Another part of the evidence stems
from the Kalman–Filter estimates of the intercepts of the AR models. We have
found that the four markers do not share a common trend in their long-run behav-
iour, suggesting that they are not integrated. Although investors could reduce risk
by holding a diversified portfolio, policy-makers may prefer more integration
between share markets in the near future to enhance the effectiveness of financial
regulations.
Notes
1. These studies include Rockinger and Urga (2000), Zalewska-Mitura and Hall (1999), and Emerson
et al. (1997).
2. See, for example, Chiao (1998), Yao (1998), Bergstrom and Tang (2001), and the website of the
China Securities Regulatory Commission at http://www.csrc.gov.cn.
3. Companies that are listed on the Hong Kong Stock Exchange, the New York Stock Exchange and the
Singapore Stock Exchange issue the so-called H, red-chip, N and S shares traded in the HK, US and
Singapore dollars respectively.
4. Bergstrom and Tang (2001) focus on why B shares have shown a substantial discount against A shares.
Heaney et al. (1999) examine share return seasonalities and price linkages of A and B shares.
5. Semi-strong form efficiency is defined as follows: security prices fully reflect all publicly available infor-
mation, i.e. market participants cannot make superior returns by ‘searching out’ information from
publicly available sources, since the information will already be incorporated into security prices
(Fama, 1970).
6. If share prices fully incorporate information on past prices and on the volatility of their changes, then
current returns may be expressed as r0
t � ðrt � b01 � b1t rt�1Þ=ffiffiffiffiht
p� �¼ eSTDt , where rt represents current
returns that do not incorporate such information. Thus only ‘pure news’ eSTDt can determine the values
of r0
t . If a market’s returns behave like r0
t as defined here, we may say that the market is not only weak-
form efficient but also satisfies at least one criterion of semi-strong-form efficiency in that current
returns r0
t fully incorporate all the other-than-past-price information as contained in ht.
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