Classifying Chinese Bull and Bear Markets: Indices and ... · By comparing the intervals of bull and bear markets between stocks and indices, this paper finds a high degree of overlapping

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Classifying Chinese Bull and Bear Markets: Indices and Individual Stocks

Wei Chia, Robert Brooks

b,1, Banita Bissoondoyal-Bheenick

c, Xueli Tang

d

a Department of Accounting and Finance, Monash University

b Department of Business Statistics and Econometrics, Monash University

c Department of Accounting and Finance, Monash University

d School of Accounting, Economics and Finance, Deakin University

Abstract: Using a Markov Regime Switching model, this paper discusses Chinese bull and

bear markets. A focus of the analysis is to compare classifications based on indices and

individual stocks. By comparing the intervals of bull and bear markets between stocks and

indices, this paper finds a high degree of overlapping of bear cycles between stocks and

indices. This helps to explain the long duration of Chinese bear market cycles. We also find a

high level of overlapping between the bear market and a fraction of stock with increasing

stock prices. This leads to the conclusion that the stock performance and trading behaviour

are widely diversified. Furthermore, we find that the same industry may have different

overlapping intervals of bull or bear cycles in the Shanghai and Shenzhen stock markets.

Firms with different sizes could have different overlapping intervals with bull or bear cycles.

JEL classification: C13; C32; G32;

Keywords: Markov Switching; Overlapping Intervals; Bull and Bear Markets; Emerging

Market.

1 Corresponding author. Tel.:+613 9903 1423.

E-mail addresses:[email protected], [email protected],

[email protected], [email protected]

mailto:[email protected]



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1. Introduction

Discussion of bull and bear market cycles attracts much attention in the literature, e.g., Pagan

and Sossounov (2003), Yan, et. al (2007), Rutledge, Zhang and Karim (2008), Zhou, et al

(2009), de Bondt, Peltonen and Santabarbara (2011), because cycles of bull and bear markets

not only reflects the economic development and investors‟ confidence but has a significant

impact on the whole economy and social welfare. This is important for all countries around

the world in particular for developing countries which have emerging financial markets and

are more vulnerable to global economic fluctuations. As found in Chen, Chong and Li (2011),

the Chinese stock market has experienced a long period bear cycle from early 2000 until

2006 and then it fluctuated greatly until 2010. However, the cyclical behaviour of stock

markets during this period is less well-established. We may ask why the Chinese stock

market experienced a long duration of bear market, and what industries would contribute to

this cyclical behaviour, and whether firm size can determine the relationship between the firm

stock cycles on the market cycles. By comparing the intervals of bull and bear markets

between stocks and indices, this paper will provide more explanation to the cycles of Chinese

stock markets, and will contribute to the literature regarding the development of emerging

markets.

Given that the Chinese stock market is one of the largest emerging markets in the world and

some of its unique characteristics, such as economic, institutional and microstructural

features, plus the existence of A- and B-share markets, provides a rich environment for the

investigation of bull and bear cycles in an emerging market. The Chinese stock market is

composed of two markets according to the traders, specifically, A- and B-share markets. Prior

to 2001, domestic investors could only trade in the A-share markets in RMB while foreign

investors could only trade in the B-share markets in U.S. dollars in Shanghai or in Hong

Kong dollars in the Shenzhen stock market. After 2001, the Chinese government allowed

domestic investors to freely trade B-shares. However, due to foreign currency control,

Chinese citizens cannot freely use RMB to buy foreign currencies and purchase B-shares.

Therefore, there still remains a certain degree of segmentation between A- and B-share

markets. After 2002, Qualified Foreign Institution Investment (QFII) are allowed to invest in

local currency and use specific accounts to invest in the A-share stock markets. As Chinese

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GDP has become the world number two in 2010 and stock market capitalization has

overtaken Japan as the world‟s second-largest stock market, any change in the Chinese

economy or stock market could potentially influence the world economy significantly.

In this paper, a Markov-switching model will be applied to investigate bull and bear markets.

Hamilton (1989) first introduces the Markov-switching model to replicate the recessions and

expansions of the U.S. economy as measured by the NBER. Subsequently, based on

Hamilton (1989), there are a number of articles to investigate bull and bear markets, such as

Durland and McCurdy (1994) and Maheu and McCurdy (2000).2 In this paper, rather than

focusing on macroeconomic shocks or policy issues, we explore the bull and bear cycles from

a new perspective, by studying the overlapping intervals of bull and bear cycles between

stock and index data.

This paper aims to identify and to account for cyclical regimes in the Shanghai and Shenzhen

stock markets. Specifically, the contribution of this study is three-fold. First, we find that the

overlapping of bear cycles between stocks and the index is quite high. It helps explain the

long period of bear cycle in the Chinese stock market. Second, by grouping the stocks

according to 13 industry categories and firm size, we find that stock performance is widely

diversified across the market. Firms with different size could have different overlapping

intervals with bull or bear cycles. Third, we find that in the Shanghai and Shenzhen stock

markets, even the same industry may have different overlapping intervals of bull or bear

cycles. This implies that a certain shock to one industry could have different impacts on these

two markets even though these two markets have strong correlations with each other.

There is some literature discussing Chinese bull and bear markets. For example, following

Pagan and Sossounov (2003), Girardin and Liu (2003) use a Markov-switching model to

investigate movements in capital gains and losses on the Chinese stock market from 1995

through 2002. Based on the index of the Shanghai A-share market, at a weekly frequency,

they found that in overall, the Chinese stock market is like a „Casino‟ because, most of the

2 Ryden, Terasvirta, and Asbrink (1998) have shown that the Markov-switching model is well suited to

explaining the temporal and distributional properties of stock returns as the information set to the

econometrician and agents are not necessarily assumed to coincide.

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time, an investor with a weekly horizon finds herself in the bear market and makes capital

losses but also makes substantial capital gains in very short periods of „luck‟ to compensate

her for the losses. Instead, using monthly stock index data from 1991 through 2006, Yan, et.

al (2007) identify and describe cyclical regimes in the Shanghai and Shenzhen stock markets

based on the algorithm developed by Bry and Boschan (1971). They identify bull and bear

market regime-turning points using five-month average returns and show non-identical cycles

for these two markets. In addition, they find that the return differences between bull and bear

market regimes decrease recently reflecting a maturing of the Chinese market.

Using monthly data from April 1999 to September 2009, de Bondt, Peltonen and

Santabarbara (2011) examined Shanghai A-share price misalignments in bull and bear

markets. They found that it can be reasonably well explained by some fundamentals, such as

corporate earnings and the risk-free interest rate. In addition, they found that stock prices in

booms and busts can be significantly influenced by some policy actions from the Chinese

authorities, either in the form of low deposit rates, loose liquidity conditions or stock market

liberalizations. This implies that bull or bear markets are not only closely related with

economic fundamentals but also with a wide spectrum of policy instruments.

Further, Yao and Luo (2009) argued that due to some government policies, such as

privatisation and strong state support for the state-owned commercial banks, investors can be

over-optimistic about the Chinese future economic performance. Moreover, besides the

change in interest rates, trade balances, exchange rates, employment and inflation, which

could affect share prices, the poor psychological factors, such as greed, envy and speculation,

could also help explain the Chinese stock market bubble and burst during 2005 and 2008.

There is some literature arguing that there exits bubbles in the Chinese stock market in bull

phases as the average daily return jumps become much higher than previous periods. For

example, using the Shanghai Composite Index obtained from the TX Investment Consulting

Co., Ltd. from January 3, 2004 to December 31, 2007, Nishimura and Men (2010) find that

the average daily return from December 2006 to October 2007 is much higher than that

during January 2004 to November 2006. This result shows that the Chinese stock market

entered a speculative bubble period after the second half of 2006. By comparing the abnormal

market returns of the Shanghai and Shenzhen A- and B-share markets, Lehkonen (2010) finds

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that the weekly data demonstrate bubbles but monthly data does not show bubbles for all of

the Mainland Chinese stock markets. This implies that the duration dependence, a

characteristic of the hazard function for duration times, is sensitive to the use of weekly

versus monthly data and should be taken into account for bubble analysis. This also indirectly

shows that there are no differences in terms of bubble existence between Chinese A- and B-

share stock markets even though the A-shares are dominated by individuals and B-shares by

more sophisticated institutional investors.

Rutledge, Zhang and Karim (2008) examine the relationship between firm size and excess

stock returns in the Chinese stock exchange (Shanghai and Shenzhen) bull and bear market

phases from 1998 to 2003. They found that small firms had greater positive excess returns

during the bull market period but greater negative returns or no significant difference in

returns (using float market value) during the bear market period. In contrast, large firms show

greater or similar portfolio returns as compared to small firms during the bearish time period.

This finding reflects that small stocks react stronger than large stocks to economic conditions

and events.

There are a number of articles discussing bull and bear markets for other emerging markets.

For example, Assoe (1998) investigates regime-switching behaviour of nine emerging

markets3 as these markets experienced significant changes in government policies and capital

market reforms from December 1975 to December 1997. He finds, based on Markov-

switching models, that these emerging market returns and volatilities change significantly

over time in response to government policies and capital market reforms. This implies that

booms and busts in emerging stock markets could be influenced by events such as monetary

shocks and productivity switches, as these events could have an impact on traders‟

confidence. Similarly, following Bry and Boschan‟s (1971) nonparametric approach, Biscarri

and Gracia (2004) identify the bull and bear phases of Spanish stock market and discuss its

characteristics. They find that the process of financial development, such as capital market

opening, financial liberalization or integration processes, affect the Spanish stock market

3 The nine emerging markets are Argentina, Brazil, Chile, Greece, India, Korea, Mexico, Thailand, and

Zimbabwe. The data is from the International Finance Corporation‟s Emerging Markets Data Base.

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behaviour significantly. As the financial liberalization process proceeded, the Spanish stock

market became more concordant with other developed markets.

The remainder of the paper is organized as follows. Section 2 describes the data and

methodology. Section 3 presents empirical results and discusses their implications, and

Section 4 concludes.

2. Data and Methodology

2.1 Data

The monthly returns for Shanghai and Shenzhen Stock Exchanges are calculated based on the

average daily return. The daily price is from the Thomson Reuters Tick History Server via the

Securities Industry Research Centre of Asia-Pacific (SIRCA). The dataset consists of all

ordinary common stocks listed on the Shanghai and Shenzhen Stock Exchanges from 1

January 2002 through 31 December 2010.4 Stock market capitalization is from Datastream

and industry category is from the Shanghai and Shenzhen Stock Exchange website. In both

the Shanghai and Shenzhen Stock Exchanges, there are two trading sessions, one is in the

morning from 09:30am to 11:30am, and another one is in the afternoon from 13:00pm to

15:00pm. There is a one-and-a-half-hour lunch break.

To deal with missing observations in time series data, the Spline Interpolation method is

applied as follows:5

))(()32())(2()132( 12

23

1

23

21

23

1

23

ttttttt DDDDDDD ,

where tD is the missing observation at time t that needs to be filled in, is the relative

position of the missing observation divided by the total number of missing observations in the

4 The stocks listed less than five months are not included as we consider five lags in the Markov Switching

model.

5 This method has been used extensively in the literature, e.g., Norbert (1949); Friedman (1962); Damsleth

(1980) and Pavlov and Vladimir (2004).

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series. The 1tD and 2tD are the next two non-missing observations. The 1tD and 2tD are

the previous two non-missing observations.

A-shares (B-shares) are identified by a stock code commencing with “600” (“900”) in the

Shanghai stock market, and in Shenzhen stock market, A-shares (B-shares) are identified by a

stock code commencing with “000” or “001” (“200”). The summary characteristics of the

Chinese stock market are presented in Table I.

<Insert Table I here>

Clearly, Table I shows that the number of B-shares and their market capitalization are much

smaller than A-shares because the number of domestic traders is much more than foreign

traders. The market capitalization increases steadily in both A- and B-share markets except

for a drop in 2008 due to the subprime crisis. The number of companies listed in the

Shenzhen Stock Exchange was lower than in the Shanghai Stock Exchange before 2009 but

greater after as the Shenzhen Stock Exchange introduced Chinext, a second board market, in

which small high-technology companies with high growth rates are listed.

<Insert Figure 1 here>

Figure 1 plots the raw data series of Shanghai and Shenzhen A-, B- and composite index

from 2002 to 2010. The data in Figure 1 shows that from 2002 to mid 2006, the Chinese

stock market was in a bearish period. After that, the Chinese stock market went up and

experienced a bullish period. The Shanghai A-index and Shanghai Composite index, and

Shenzhen A-index and Shenzhen Composite index move closely while the Shanghai B-index

and Shenzhen B-index are much lower than A- or Composite index. This is because most of

the composite index is drawn from the A-index while the B-index is just composed by a small

number of stocks as shown in Table I.

<Insert Table II here>

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Table II shows that the B-index has higher mean returns and kurtosis than the A- and

Composite index. The standard deviation of the Shanghai B-index is higher than the Shanghai

A- and Composite index while the Shenzhen B-index has a lower standard deviation than the

Shenzhen A- and Composite index. This means that the Shanghai B-index is more volatile

and has thinner tails while the Shenzhen B-index is less volatile but has fatter tails than other

indices.

<Insert Table III here>

Table III shows the unconditional cross-correlations for all of the indices. It can be seen that

the highest degree of correlation for Shanghai and Shenzhen Stock Exchanges is between

Shanghai A and Shanghai Composite, and Shenzhen A and Shenzhen Composite. This is

because most of the composite index is composed of A-shares. The correlation between

Shanghai A and Shenzhen A is 0.921 and between Shanghai-B and Shenzhen-B is 0.869. The

correlations among other indices are also quite high. This means that these indices would

have similar bull and bear cycles. These results are consistent with Lin, Menkveld and Yang

(2009) in which they find increased correlation between Shanghai and Shenzhen Stock

markets.

2.2 Research Methodology

Following Hamilton (1989) and subsequently Hamilton and Gang (1996), the Markov regime

switching model of stock returns is as follows

t

j

i

titititt vSSrSr

1

,

where the unobserved state is governed by a state variable tS ( tS =1 or tS =2) that accords

with the regime either labelled bull or bear market, j is the number of lags, tS and tS

are the conditional mean and variance, tv ~ i.i.d (0,1).

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By maximizing the log likelihood of the observed data,6

we estimate the transition

probabilities. Let 1,1P denote the probability of being in a bull market next period if in a bull

market this period, 2,1P the probability of moving out of a bull market, 2,2P the probability of

staying in a bear market and 1,2P the probability of moving out of a bear market. Thus, the

probability transition matrix can be written as follows,

2,21,2

2,11,1

PP

PPP .

The conditional mean and variance tS and tS can be either state dependent or not.

This implies that if the mean return switches while the variance does not, we have tS and

. It is denoted as S=[1,0]. Similarly, we can have S=[0,1] or S=[1,1] for the case with

variance switching or both the mean and variance are switching with state.

If there are three states, i.e., tS can be 1, 2 or 3, then the probability transition matrix will be

in a 33 format. In this paper, we use the Bayesian Information Criterion (BIC) to determine

the optimum number of regimes, and to compare different competing Markov switching

models with the mean of return switching or the variance of error term switching or both.

BIC is designed to penalize models with more parameters. Thus, lower BIC implies better fit.

After choosing the number of regimes and mean or variance switching, we follow Ang and

Bekaert (2002) to use the Regime Classification Measure (RCM) to assess whether the

regime switching model can be used to discriminate regimes well or not. The explicit formula

for the 2-state RCM is following Chan et al (2011) is:

,11

4001

T

t

TtTt jSPjSPT

RCM

6 The log likelihood function can be found from Hamilton (1989, page 370-371) or Hamilton and Gang (1996,

page 580).

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where Tt jSP denotes the smoothed regime probability conditioned on the full

information set T . The statistic is normalized to be between 0 and 100 by the constant term

400. If the regime switching model is able to discriminate between regimes, the statistic

should be below 50.

3. Empirical Results

The smoothed probability determines if and when the regime switches. Following Hamilton

(1989), we define the bull and bear market as below:7

Definition 1: A bull market is said to occur in month t+1 if the market was in an expansion in

month t and P( 1tS =1) > 0.5.

Definition 2: A bear market is said to occur in month t+1 if the market was in a recession in

month t and P( 1tS =1) 0.5.

3.1 Selection of Regime Switching Model

In order to determine the number of regimes, we estimate BIC values for two- and three-state

univariate Markov Switching models for the monthly returns of Shanghai and Shenzhen A-,

B- and composite index (stock). Then, we estimate the RCM to check whether the regime

switching models is appropriate. In addition, by the high negative values of skewness of

Shanghai A- and composite index, and Shenzhen A-, B- and composite index from Table II,

we choose Student‟s t-distribution, which is like the normal distribution but has fatter tails,

for tv . In contrast, the skewness of Shanghai B-index is close to zero. Thus, we choose

normal distribution for its tv .

<Insert Table IV here>

7 In contrast, Pagan and Sossounov (2003) and Yan, et. al (2007) take the absolute return as an important

indicator such that the market is identified as bull or bear market if the stock market price is higher or lower than

five-month average returns.

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Table IV shows that by the value of BIC, 2-state regime switching model with the mean

return switching, i.e., S=[1,0], is the most appropriate model for estimating Shanghai and

Shenzhen index.8 This implies that the Chinese stock market has two regimes, bull and bear

regimes, with the mean returns switching while the variance is constant across regimes.

Correspondingly, the RCM values are all less than 50. It implies that this 2-state regime

switching model can be used to discriminate between regimes. This regime classification is

identical to Yan, et al (2007) which is based on the algorithm developed by Bry and Boschan

(1971).

3.2 Maximum Likelihood Estimates and Smoothed Probability

After choosing the number of regimes and switching variables, in this subsection, we present

the Maximum likelihood estimates of the parameters for the Shanghai and Shenzhen A-, B-

and composite index.

<Insert Table V here>

The first and second columns of Table V show the mean return for the six indices. It can be

seen that: 1) the mean returns are positive in bull markets but negative in bear markets.

Moreover, the absolute values of the mean returns in bull markets are higher than the bear

markets; 2) the mean return for the A-index is higher than the mean return for the B-index in

both Shanghai and Shenzhen markets. This result is comparable to Chen, Chong and Li (2011)

and Yan, et al (2007) in which they also found that the difference of return between the bull

and bear markets could be more than double and highly significant compared to those of

traditional markets, e.g., Schaller and Van Norden (2002) and Gonzalez et al (2005); 3) most

of the mean returns are significant; 4) the mean return of the A-index is equal to the mean

return of composite index. This is because most of composite index overlaps the A-index as

compared to the B-index.

8 Note that the Shanghai B-index has the lowest BIC for 2-state regime model with S=[0,1]. To be consistent

with other indices, however, we chose S=[1,0], instead of S=[0,1], for the Shanghai B-index.

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The third and fourth columns of Table V show the probability of staying in a bull or bear

market from this period to the next period. It can be noted that if the market is in a bear

market, it is more likely the market will stay in a bear market next period compared to the

case in which a bull market stays in a bull market from one period to the next period, i.e.,

2,21,1 pp .

The fifth column of Table V shows the standard deviation of the market. It can be seen that: 1)

the variance of the A-index is equal to the variance of composite index; 2) The variance of

Shanghai B index is higher than the variance of the Shanghai A index. In contrast, the

variance of the Shenzhen B index is lower than the variance of Shenzhen A index. This is

consistent with Table II.

The sixth and seventh columns of Table V show the duration of regime 1 and 2, i.e., bull and

bear markets. It can be seen that the bear market has a longer duration than the bull market.

This has been indicated by 2,21,1 pp . This result is consistent with Girardin and Liu (2003)

and Chen, Chong and Li (2011) in which they find that the mean duration of the contraction

period is greater than the expansion period for the Chinese market.

Figure 2 shows the smoothed regime probability conditioned on the full information set T ,

Tt jSP , for the markets of Shanghai and Shenzhen A-, B- and composite index from

Jan 2002 to Dec 2010. It highlights that, except for a short bull period from the end of 2003

to the March of 2004 for the Shanghai A- and composite index, these two markets were in

bear markets from 2002 to the end of 2005, and then stayed in the bull markets until the

September of 2007, and went out from bear markets from Nov 2008. This result is highly

consistent with Yan, et al (2007, Table 1) in which they show the bull and bear cycles of the

Shanghai and Shenzhen Stock Exchanges from 1991 to 2006 based on the algorithm

developed by Bry and Boschan (1971).9 Furthermore, the big jump of the stock market in

2006 implicitly supports the conclusion made in Nishimura and Men (2010) that the Chinese

stock market would enter a speculative bubble period after the second half of 2006.

9 The Shenzhen B index shows a slightly different path due to its low trading and small number of stocks listed.

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The A- and composite index are very consistent with each other relative to the B-index. This

is because A-index and composite index, which is mostly composed of A-index, are

determined by A-shares which are traded by domestic traders. In contrast, the B-index is

determined by B-shares which are traded by foreign traders. To explain why the B index has

different bull and bear cycles from the A and composite index, we need to know what factors

could affect them. We know that the B index is determined by the B share trading while the

A index is determined by A share trading and the composite index is determined by both A

and B share trading. The difference between A- and B-share trading has been discussed in the

literature, such as Chan, Menkveld and Yang (2007, 2008) and Ahlgren, Sjo and Zhang

(2009). By studying A- and B-share trading, and comparing the price discovery role of the

two segmented markets, they find that there exists information asymmetry between A-share

traders and B-share traders. The domestic investors either have more private information or

trade on the information faster than do foreign investors. Due to information asymmetry,

therefore, they may have different trading behaviours even though they trade the share which

is issued by the same company but traded in different markets.

From mid 2005 after a few favourable policies announced, such as the Lawsuit System of

Shareholder Representatives, Non-tradable Share Reform, and adopting a certain degree of

flexible exchange rate, etc, the Chinese stock market soared. In 2008, however, due to the

subprime crisis, Chinese stock market suffered a sharp down turn as shown in Figure 2. To

overcome the crisis, the Chinese Ministry of Finance and Administration of Taxation decided

to adjust the stamp duty rate of the stock market from April 24, from 0.3% to 0.1%. This

favourable policy stimulates both the Shanghai and Shenzhen stock markets. It can be seen

from Figure 2 that both the Shanghai and Shenzhen index went up from late 2008. This result

is consistent with Lin, Menkveld and Yang (2009) and de Bondt, Peltonen and Santabarbara

(2011) in which they find that Chinese bull or bear markets can be influenced by a wide

spectrum of policy instruments. Similarly, Assoe (1998) by investigating other emerging

markets, finds that government policies and capital market reforms can significantly affect

booms and busts in the stock markets.

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In summary, our results clearly show two regimes during this period, which is consistent with

our choice of 2-state regime switching model. In the next subsection, based on the 2-state

regime model, we will discuss the cyclical behaviour of the bull and bear market.

3.3 Overlapping of Bull and Bear Cycles between Stocks and Index

In this subsection, we discuss the overlapping intervals of bull and bear cycles between the

index and individual stocks to assess consistency between index and its corresponding stocks.

This will explain the properties of bull and bear cycles, and the diversification of stock

performance in the market and their reactions to macroeconomic shocks.10

<Insert Table VI here>

The first column of Table VI, “Bull – Bull”, shows the percentage of stocks‟ bull cycles that

overlap the market‟s bull cycles. For example, the first result in the first column, 18.89%,

means that 18.89% of Shanghai A-share bull cycles overlap with the Shanghai A index bull

cycles.

Comparing the results of “Bear – Bear” with “Bull – Bull”, it can be noted that the

overlapping of bear markets between stocks and the market index is much higher than the

overlapping of bull markets except for the overlapping between the Shanghai B-index and B-

shares which have close values. This implies that in the bear market cycles, a large fraction of

shares are in the bearish cycles concurrently. These results are consistent with Table V which

shows that the duration of the bear market is longer than the duration of the bull market, and

2,21,1 pp . This result can be explained by the herding effect as discussed in Tan, et al (2008)

in which they find stronger herding effects of A-share investors in the Shanghai market. In

contrast, in the bull market cycles, a smaller fraction of shares concurrently have price

increases. The Shanghai B-index and B-share have a higher value of “Bull – Bull” because as

shown in Table V the Shanghai B-index has a longer duration of bull cycles. 10

For example, Zhang et al (2011) find that monetary policy could affect the volatility of Chinese stock market

significantly based on a Markov regime switching GARCH model.

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From the high values of “Bear – Bull”, we can conclude that the performance of each stock is

widely diversified across the market especially when the market is in a bearish cycle. This

diversification is more obvious in the emerging markets due to low levels of management

skills and investment strategies of firms or higher heterogeneous behaviours of traders as

discussed in Yao and Luo (2009). This can also indirectly help understand why the Chinese

stock market experienced a long period of bear market and shorter period of bull market even

though the values of “Bull – Bear” are low.

Among the eight combinations, we can see that the overlapping between the B-index and B-

share, in particular the “Shanghai B index – B share”, have the highest values of “Bull –

Bull”. This can be explained by the finding from Chiang, et al (2008) in which they find that

B-shares react quickly to good news. Even though domestic investors were allowed to trade

B shares after 2001, there is still some degree of segmentation between the A- and B-share

markets in China. This is consistent with Ahlgren, Sjo and Zhang (2009) in which they find

that firms’ A and B shares are cointegrated, but not for all firms.

<Insert Table VII.I here>

Table VII.I shows the percentage of the overlapping between A-shares and Shanghai and

Shenzhen A-index, by industry and firm size, from January 2002 through December 2010. It

can be seen that “Bear – Bear” has very high percentage in all the industries except industry

L (Communication and cultural industries), which is just 0.65% of the total firms in Shenzhen

market. A high percentage from “Bear – Bear” implies that there would be strong herding

effects among investors in the bearish period as discussed in Tan, et al (2008). This result is

consistent with Welch (2000) in which he finds that when the stock market has fallen due to

bad news, traders would revise their forecasts and follow the prevailing consensus. Almost

50% of industry I, i.e., Finance and Insurance, stocks overlap its bear cycles with the

Shanghai A index. In contrast, 30.51% of industry I stocks overlaps its bear cycles with the

index in the Shenzhen market. This big difference implies that the rise or fall of stock price in

a certain industry could have different effects on these two markets even though these two

markets have strong correlations as shown in Table III. This can be due to the composition of

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stocks between these two markets, as shown in Table VII.I that industry I is just 1.32% of the

total firms in Shanghai while 0.86% of the total firms in Shenzhen market. This difference

also reflects the non-identical property of cycle between these two markets as found in Yan,

et. al (2007).

Industries K (Social services), L (communication and cultural industries) and M (General

field) in the Shanghai stock market, and industries C (manufacturing), G

(telecommunications) and L (communication and cultural industries) in the Shenzhen stock

market, have a very high result of “Bear – Bull” overlapping. This can be explained as when

the market is in a bear cycle, stocks in certain industries go up. This could be due to risk

avoidance from other industries or the diversification of firm performance. Especially,

industries C and G compose a large fraction of the Shenzhen stock market. The high

inconsistency between stock performance and the market leads to a short duration in both bull

and bear markets as compared to the Shanghai stock market, as shown in Table V.

Industry C, i.e., manufacturing, is the largest industry. It comprises of more than 50% of the

whole market. The results for this industry in Table VII.I are consistent with Table VI. This

implies that any policy which affects the manufacturing industry would affect the whole

market directly and significantly. Next to the manufacturing industry, industries G

(telecommunications), H (wholesale and retail trade), and J (real Estate) are relatively large

compared to the rest. Policies relevant to these industries also have a significant impact on the

market. In contrast, industry L, communication and cultural industries, is just composed of

0.65% of the Shenzhen stock market. It would not affect the market much even thought its

“Bear – Bear” result is far from other industries.

The results of “Bull – Bull” overlapping decrease with firm size while the results of “Bear –

Bear” overlapping increase with firm size in both the Shanghai and Shenzhen stock markets.

This implies that larger firm stocks tend to have different bull cycles but consistent bear

cycles with the market. Large firms would have greater impact on the whole market. This

also explains why the bear cycles of the market are longer than the bull cycles.

<Insert Table VII.II here>

17

Table VII.II shows the overlapping of bull and bear cycles between B-shares and Shanghai

and Shenzhen B-index from January 2002 through December 2010. It can be seen that there

are some industries missing in either Shanghai or Shenzhen B-share markets because of a

small number of firms listed in these two markets and also some requirements for listing B-

shares in the market.11

The results in Table VII.II are different from Table VII.I. 12

For

example, industry H, i.e., wholesale and retail trade, stocks have high overlapping of “Bull –

Bull” cycles in the Shanghai stock market but high overlapping in “Bear – Bear” cycles in the

Shenzhen stock market. The bull or bear cycles of industry D, i.e., Electricity & Coal &

Water Supplies, have few overlapping intervals in the Shanghai stock market but many

overlapping intervals in the Shenzhen market. The bull or bear cycle overlapping differs

significantly according to the firm size especially in the Shanghai stock market. For example,

the results of “Bull – Bull” overlapping and “Bear – Bear” overlapping for large-size firm are

22.12% and 23.27%, respectively. They increase to 33.42% and 30.41% respectively for

small-size firms. This means that the smaller the firm size is, the more consistent the firm‟s

stock can be with the market index. However, this result is not as strong in the Shenzhen

stock market. All of these differences reflect the heterogeneity between these two markets as

argued in Wang and Firth (2004) in which they find the Chinese A-stock market is more

comparable to a developed market than an emerging market while Chinese B-shares are

better categorized as being emerging than developed.

<Insert Table VII.III here>

Table VII.III gives similar results as Table V.I because most of the composite index is

composed of A-shares.

11

See the following website for the detailed requirements for issuing B shares:

http://www.sipf.com.cn/en/chinassecuritiesmarketoverview/introtobshare/index.shtml

12Some extreme results in Table VII.II could be due to the low number of firms of each industry listed in the B-

share market. See the total number of stocks listed in B-share market from Table I.

http://www.sipf.com.cn/en/chinassecuritiesmarketoverview/introtobshare/index.shtml

18

<Insert Table VII.IV here>

Table VII.IV shows the overlapping intervals of bull and bear cycles between the Shanghai

and Shenzhen composite index and B-share stocks from January 2002 through December

2010. Comparing Table VII.IV with Table VII.II, it can be seen that the overlapping intervals

of bear cycles between stocks and the index is quite high while the overlapping intervals of

bull cycles is relatively low. This is consistent with the results in Table VII.I. In addition, it

can be noted that both the “Bull – Bull” and “Bear – Bear” overlapping decrease significantly

with the firm size as shown in Table VII.II.

Overall, from Tables VII.I-VII.IV, we can see that result of “Bear – Bear” overlapping and

“Bear – Bull” overlapping are high across different industries. That could help us

understanding why China has a long duration of bear market. The results of “Bull – Bull”

overlapping decrease while the results of “Bear – Bear” overlapping increase with the firm

size in both the Shanghai and Shenzhen stock markets. This implies that larger firm stocks

tend to have different bull cycles but consistent bear cycles with the market. Large firms

would have greater impact on the whole market. This result indirectly supports the

observation of the longer duration of bear markets. In addition, among 13 industries, the

Manufacturing industry composes more than 50% of the total listed firms. Next to it are

Telecommunications, Wholesale and Retail Trade and Real Estate. This implies that any

policy relevant to these industries could have a significant impact on the market.

4. Conclusion

In this paper, following Hamilton (1989) and Hamilton and Gang (1996), we use a Markov

regime switching model to analyse the bull and bear cycles in the Chinese stock market. We

find the 2-state regime Markov switching model with the mean return switching and variance

constant gives us a good fit to the data. We then find that the Chinese stock market

experienced a long period of a bear cycle. By grouping the stocks according to 13 industry

categories and firm size to explain the bull and bear cycles, we find that: 1) the overlapping

19

of bear cycles between stocks and the index is quite high. This implies that there would be

strong herding effects among investors in the bearish period as discussed in Welch (2000)

and Tan, et al (2008). In addition, the high value of “Bear – Bull” overlapping leads to the

conclusion that stock performance is widely diversified across the market. This feature is

consistent with the other emerging markets in which management skills and investment

strategies of firms are relatively low and trader behaviours are highly heterogeneous. This can

also indirectly help in understanding why Chinese stock market experienced a long period of

a bear market cycle; 2) in the Shanghai and Shenzhen stock markets, the same industry may

have different overlapping intervals of bull or bear cycles. This implies that a certain shock to

one industry could have different impacts on these two markets even though these two

markets have strong correlations with each other; 3) firms with different size could have

different overlapping intervals with bull or bear cycles. Specifically, we find that firms with

larger size have more overlappings with bear market cycles. It means that bear market would

have greater impact on large firms relative to small firms.

Our result, through discussing overlapping intervals of bull and bear cycles between stock

and index, provides implications for portfolio diversification and hedging. For example, in a

bearish period, there exists certain industries which may have an increasing stock price, such

as social services, communication and cultural industries in the Shanghai stock market or

manufacturing, telecommunications and communication and cultural industries in the

Shenzhen stock market. In a bullish period, investors may find small size firms to earn high

returns. Overall, our finding may help investor to hedge the risk or diversify their portfolio in

bull and bear markets.

Acknowledgement: We use Perlin, M. (2010) MS Regress - The MATLAB Package for

Markov Regime Switching Models. It is available at SSRN:

http://ssrn.com/abstract=1714016. We also thank Professor Perlin for his useful suggestions

regarding the Matlab code.

http://ssrn.com/abstract=1714016

20

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http://www.sciencedirect.com/science?_ob=RedirectURL&_method=outwardLink&_partnerName=27983&_origin=article&_zone=art_page&_linkType=scopusAuthorDocuments&_targetURL=http%3A%2F%2Fwww.scopus.com%2Fscopus%2Finward%2Fauthor.url%3FpartnerID%3D10%26rel%3D3.0.0%26sortField%3Dcited%26sortOrder%3Dasc%26author%3DFirth,%2520Michael%26authorID%3D7006574464%26md5%3Df5a20ca6c2f997d607455d648b140be8&_acct=C000004058&_version=1&_userid=32381&md5=7930fbbff17b6288c8562d702a692379

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Table I: Summary of Chinese Stock Market.

2002 2003 2004 2005 2006 2007 2008 2009 2010

No. of Companies listed

Shanghai Stock Exchange 715 780 837 834 842 860 864 870 894

Shenzhen Stock Exchange 508 505 536 544 579 670 740 830 1169

No. of Share listed

Shanghai Stock Exchange 759 824 881 878 886 904 908 914 938

A share 705 770 827 824 832 850 854 860 884

B share 54 54 54 54 54 54 54 54 54

Shenzhen Stock Exchange 551 548 578 586 621 712 782 872 1211

A share 494 491 522 531 566 657 727 818 1157

B share 57 57 56 55 55 55 55 54 54

Marekt Capitaliztion (100 m)

Shanghai Stock Exchange 25363.72 29804.92 26014.34 23096.13 71612.38 269838.9 97251.91 184655.2 179007.2

A share 24921.42 29400.65 25714.07 22856.07 71117.95 268497.3 96875.31 183799.9 17800.02

B share 442.3 404.27 300.27 240.06 494.43 1341.6 376.59 855.35 1007.22

Shenzhen Stock Exchange 12965.41 12652.79 11041.23 9334.15 17791.52 57302.02 24114.53 59283.89 86415.35

A share 12605.14 12119.83 10595.28 8954.48 16996.01 56090.47 23691.24 58327.14 85220.52

B share 360.27 532.96 445.95 379.67 795.51 1211.55 423.29 956.75 1194.83

Table II: The Mean, Standard Deviation, Skewness, and Kurtosis for All of the Returns for

the Entire Sample Period. The monthly return of the index is the average of daily return, tr ,

which is defined as 1lnln*100 ttt ppr , where tp denotes the daily share or index price.

The sample period runs from Jan 2002 to Dec 2010.

Mean Standard Deviation Skewness Kurtosis

SHH A index 0.00031 0.00452 -0.62109 0.95614

SHH B index 0.00036 0.00589 -0.17254 2.54899

SHH Composite index 0.00030 0.00453 -0.62210 0.94604

SHZ A index 0.00054 0.00496 -0.51363 0.63253

SHZ B index 0.00060 0.00485 -0.58742 1.35348

SHZ Composite index 0.00054 0.00493 -0.52595 0.62382

25

Table III: Unconditional Cross-correlations For All of the Returns.

Shanghai A Shanghai B Shanghai Composite Shenzhen A Shenzhen B

Shanghai A

Shanghai B 0.788

Shanghai Composite 1.000 0.792

Shenzhen A 0.921 0.847 0.922

Shenzhen B 0.796 0.869 0.799 0.792

Shenzhen Composite 0.923 0.853 0.925 1.000 0.804

Table IV: Panel A reports Bayesian Information Criteria (BIC) values for two- and three-

state univariate Markov Switching models for the monthly returns of the Chinese Shanghai

and Shenzhen A-, B- and composite index (stock). Panel B reports the RCM statistics for the

2-state regime model as determined by the lowest BIC value reported in Panel A. S=[1 1],

S=[1,0] and S=[0,1] mean that both the mean return and variance of the error term are

switching or just the mean return switching or just the variance switching.

2-state

regime

3-state

regime

2-state

regime

3-state

regime

2-state

regime

3-state

regime

Shanghai A index -824.04 -798.17 -827.83 -811.09 -823.14 -790.86

Shanghai B index -778.20 -742.45 -769.54 -750.02 -782.68 -742.98

Shanghai composite -824.13 -806.16 -827.94 -820.17 -827.86 -794.03

Shenzhen A index -804.79 -790.97 -809.01 -797.54 -806.52 -784.29

Shenzhen B index -815.98 -795.57 -817.99 -801.35 -808.45 -785.90

Shenzhen composite -804.54 -789.51 -808.32 -788.26 -804.79 -774.68

Shanghai A index 30.54 14.50 31.92 14.44 25.13 24.27

Shanghai B index 30.46 4.05 36.85 0.49 29.83 24.48

Shanghai composite 30.14 15.03 31.46 1.23 24.88 21.56

Shenzhen A index 32.57 10.07 33.69 14.76 23.53 53.72

Shenzhen B index 22.98 16.59 36.02 45.09 18.96 77.82

Shenzhen composite 33.30 11.23 35.64 48.14 24.47 26.09

S=[1,1] S=[1,0] S=[0,1]

Panel B: RCM values

Panel A: BIC values

26

Table V: Maximum Likelihood Estimates of Parameters and Duration of Regime 1 and 2

Based on Data for Shanghai and Shenzhen A-, B- and composite Index from January 2002

through December 2010. *, ** and *** denote significance at 10%, 5% and 1% levels,

respectively.

1 2 p1,1 p2,2

Duration of Regime 1

(months)

Duration of Regime 2

(months)

Shanghai A index 0.0033*** -0.0008** 0.9*** 0.94*** 0.000008*** 10.24 17.61

Shanghai B index 0.0031*** -0.0016** 0.94*** 0.95*** 0.000028*** 17.94 19.17

Shanghai composite 0.0033*** -0.0008** 0.9*** 0.94*** 0.000008*** 10.34 17.95

Shenzhen A index 0.0041*** -0.0008* 0.89*** 0.94*** 0.000011*** 8.81 17.01

Shenzhen B index 0.004*** -0.0002 0.86*** 0.94*** 0.000008*** 6.97 15.87

Shenzhen composite 0.0041*** -0.0008* 0.88*** 0.94*** 0.000011*** 8.50 15.71

Table VI: The Percentage of the Overlapping Interval of Bull and Bear Cycles in Shanghai

and Shenzhen Stock Exchange from January 2002 through December 2010. “Shanghai A

index – A share” means the match of bull and bear cycles between A-share and Shanghai A

index. This shows the percentage of the bull or bear cycles of each A-share can match or

mismatch with the Shanghai A-index. The same explanation applies to other combinations,

such as “Shanghai B index – B share”, etc. “Bull – Bull” means the case when both the index

and stock are in the bull markets. Similarly, “Bear – Bull” means the case when the index is

in the bear market while the stock is in the bull market.

Bull - Bull Bear - Bear Bear - Bull Bull - Bear

Shanghai A index - A share 18.89% 31.04% 32.95% 17.12%

Shanghai B index - B share 26.83% 25.66% 17.89% 29.62%

Shanghai composite index - A share 18.53% 31.35% 33.31% 16.81%

Shanghai composite index - B share 12.52% 40.43% 32.20% 14.85%

Shenzhen A index - A share 18.77% 31.03% 34.48% 15.73%

Shenzhen B index - B share 18.35% 39.07% 27.22% 15.36%

Shenzhen composite index - A share 18.77% 31.03% 34.48% 15.73%

Shenzhen composite index - B share 18.12% 38.48% 27.45% 15.95%

27

Table VII: The Percentage of the Overlapping Interval of Bull and Bear Cycles in Shanghai

and Shenzhen Stock Exchange, by Industry and firm size, from January 2002 through

December 2010. It contains four sub-Tables, from Table VII.I – VII.IV. It shows that for each

industry, from Category A to M, the percentage of A and B-share‟s bull or bear cycles

overlapping with the Shanghai and Shenzhen A-, B- and Composite index. Each industry,

categorized from A to M, are: A: Agriculture; B: Mining; C: Manufacturing; D: Electricity &

Coal & Water Supplies; E: Construction; F: Transportation & Logistic; G:

Telecommunications; H: Wholesale and Retail Trade; I: Finance and Insurance; J: Real

Estate; K: Social Services; L: Communication and cultural industries; M: General Field.

“Bull – Bull” means the case when both the index and each stock are in the bull markets.

Similarly, “Bear – Bull” means the case when the index is in the bear market while the stock

is in the bull market. “% of the Total Firms” shows the fraction of the firm in each industry to

the whole market. Small-Size firm, Medium-Size firm and Large-Size firm are categorized

according to the market capitalization, bottom 30%, middle 40%, and top 30%.

28

Table VII.I

Shanghai A index -

A share Bull - Bull Bear - Bear Bear - Bull Bull - Bear % of the Total Firms

Shenzhen A index -


A 20.89% 26.24% 36.83% 16.03% 2.51% A 17.92% 38.29% 27.89% 15.90% 1.61%

B 16.12% 36.57% 24.79% 22.53% 2.28% B 15.07% 44.58% 26.37% 13.97% 1.94%

C 18.98% 31.84% 32.20% 16.98% 53.53% C 19.63% 29.61% 35.39% 15.36% 63.66%

D 19.42% 33.11% 30.56% 16.91% 4.91% D 16.96% 31.54% 34.15% 17.35% 2.69%

E 18.21% 35.60% 27.56% 18.62% 2.40% E 18.98% 42.88% 22.54% 15.59% 1.61%

F 18.46% 29.19% 35.22% 17.13% 4.91% F 18.49% 33.11% 33.33% 15.07% 1.94%

G 22.20% 28.70% 34.81% 14.28% 5.15% G 17.65% 29.75% 37.73% 14.87% 7.74%

H 16.19% 33.00% 30.34% 20.47% 7.43% H 17.18% 30.82% 34.94% 17.06% 5.48%

I 13.55% 47.66% 15.89% 22.91% 1.32% I 19.40% 30.51% 35.80% 14.29% 0.86%

J 19.24% 28.43% 35.79% 16.54% 7.78% J 15.85% 35.57% 30.88% 17.70% 6.02%

K 20.56% 19.84% 44.97% 14.63% 1.92% K 17.90% 34.28% 30.25% 17.56% 3.44%

L 20.20% 27.44% 39.23% 13.13% 1.32% L 29.08% 9.80% 55.23% 5.88% 0.65%

M 19.23% 22.99% 42.72% 15.06% 4.55% M 17.61% 32.35% 33.24% 16.80% 2.37%

Small-Size Firm 19.41% 29.09% 35.74% 15.76% 30.02% Small-Size Firm 19.09% 30.28% 35.37% 15.26% 29.50%

Medium-Size Firm 19.29% 30.76% 33.20% 16.75% 40.07% Medium-Size Firm 18.80% 30.84% 34.68% 15.69% 40.27%

Large-Size Firm 17.94% 33.19% 30.04% 18.82% 29.91% Large-Size Firm 18.39% 32.08% 33.26% 16.27% 30.24%

29

Table VII.II

Shanghai B index -

B share Bull - Bull Bear - Bear Bear - Bull Bull - Bear % of the Total Firms

Shenzhen B index -


A A 54.84% 16.13% 29.03% 0.00% 1.79%

B 9.26% 53.70% 0.00% 37.04% 1.85% B 0.00% 29.03% 16.13% 54.84% 1.79%

C 27.44% 22.86% 24.12% 25.57% 51.85% C 18.31% 41.34% 25.82% 14.53% 64.29%

D 2.13% 13.83% 5.32% 78.72% 3.70% D 30.65% 11.29% 33.87% 24.19% 3.57%

E 0.71% 41.43% 4.29% 53.57% 3.70% E

F 23.04% 10.29% 26.96% 39.71% 7.41% F 26.32% 36.84% 24.81% 12.03% 7.14%

G 54.17% 9.38% 9.38% 27.08% 5.56% G 3.70% 0.93% 73.15% 22.22% 1.79%

H 60.94% 12.50% 6.25% 20.31% 3.70% H 27.07% 46.29% 19.21% 7.42% 8.93%

I I

J 39.10% 38.14% 4.81% 17.95% 11.11% J 8.17% 33.66% 31.37% 26.80% 8.93%

K 23.18% 35.47% 5.31% 36.03% 11.11% K 22.22% 54.63% 19.44% 3.70% 1.79%

L L

M M




30

Table VII.III

Shanghai

composite index -


Shenzhen

composite index -


A 20.60% 26.34% 37.12% 15.94% 2.51% A 17.92% 38.29% 27.89% 15.90% 1.61%

B 15.93% 36.85% 24.98% 22.24% 2.28% B 15.07% 44.58% 26.37% 13.97% 1.94%

C 18.62% 32.15% 32.56% 16.67% 53.53% C 19.63% 29.61% 35.39% 15.36% 63.66%

D 19.13% 33.44% 30.85% 16.57% 4.91% D 16.96% 31.54% 34.15% 17.35% 2.69%

E 17.97% 35.93% 27.81% 18.29% 2.40% E 18.98% 42.88% 22.54% 15.59% 1.61%

F 18.03% 29.52% 35.65% 16.80% 4.91% F 18.49% 33.11% 33.33% 15.07% 1.94%

G 21.88% 29.09% 35.13% 13.89% 5.15% G 17.65% 29.75% 37.73% 14.87% 7.74%

H 15.91% 33.36% 30.62% 20.11% 7.43% H 17.18% 30.82% 34.94% 17.06% 5.48%

I 13.18% 48.15% 16.26% 22.41% 1.32% I 19.40% 30.51% 35.80% 14.29% 0.86%

J 18.82% 28.69% 36.21% 16.28% 7.78% J 15.85% 35.57% 30.88% 17.70% 6.02%

K 20.02% 20.02% 45.51% 14.45% 1.92% K 17.90% 34.28% 30.25% 17.56% 3.44%

L 19.53% 27.61% 39.90% 12.96% 1.32% L 29.08% 9.80% 55.23% 5.88% 0.65%

M 18.65% 23.17% 43.30% 14.88% 4.55% M 17.61% 32.35% 33.24% 16.80% 2.37%




31

Table VII.IV

Shanghai

composite index -


Shenzhen

composite index -


A A 41.94% 16.13% 41.94% 0.00% 1.79%

B 9.26% 72.22% 0.00% 18.52% 1.85% B 0.00% 41.94% 16.13% 41.94% 1.79%

C 14.54% 35.58% 37.03% 12.86% 51.85% C 18.06% 39.68% 26.07% 16.19% 64.29%

D 0.00% 53.19% 7.45% 39.36% 3.70% D 24.19% 17.74% 40.32% 17.74% 3.57%

E 0.71% 69.29% 4.29% 25.71% 3.70% E

F 5.88% 30.88% 44.12% 19.12% 7.41% F 20.30% 39.85% 30.83% 9.02% 7.14%

G 14.58% 29.17% 48.96% 7.29% 5.56% G 12.96% 4.63% 63.89% 18.52% 1.79%

H 17.19% 28.13% 50.00% 4.69% 3.70% H 26.20% 48.03% 20.09% 5.68% 8.93%

I I

J 14.10% 44.23% 29.81% 11.86% 11.11% J 7.19% 32.68% 32.35% 27.78% 8.93%

K 10.34% 52.51% 18.16% 18.99% 11.11% K 30.56% 57.41% 11.11% 0.93% 1.79%

L L

M M




32

Figure 1: Shanghai and Shenzhen A-, B- and Composite Index from 2002 to 2010.

33

Figure 2: Smoothed Probability of Regime 1 for Univariate Markov Switching Model. This Figure shows the smoothed regime probability

conditioned on the full information set T , Tt jSP , for the bull markets of Shanghai and Shenzhen A and B index from Jan 2002 to Dec

2010.