Discussion Papers In Economics
And Business
A Study on Market Efficiency Using Data from
Shanghai Stock Exchange and Shenzhen Stock
Exchange
Guoxi Duan
Hisashi Tanizaki

Discussion Paper 21-22

December 2021

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Study on Market Efficiency Using Data from Shanghai Stock Exchange and Shenzhen Stock
Exchange

Guoxi Duan†
Hisashi Tanizaki†

Abstract
This paper studies market efficiency from weak form aspect using data of Shanghai Stock Exchange
composite index (SSEC) and Shenzhen Stock Exchange composite index (SZSEC) under expected return
theory. Some classical methods are used to examine the features of stock returns and a little evidence against
mutually independency, random walk of returns, and sub-martingale of stock prices is found. A notion of a
new simple statistical test based on information set for judgement of market efficiency is proposed. Throughhypothesis tests, evidence indicating inefficient markets around 2008, 2011 and 2018 under expected return
theory is found. It is a new finding that SZSEC is more sensitive to information and therefore may be more
appealing to investors than SSEC. Moreover, there is an another new finding that when market extends insize the degree of whole market efficiency declines. From the relationship between market efficiency andvolatility, volatility is not a very good criterion for market efficiency but some rough rules can be concluded
to help investors make their decisions on what time to conduct their own strategies. Finally, the results
suggest that it is the time to think about strategies.
Keywords: stock market, market efficiency hypothesis, random walk, investment strategy, hypothesis test
JEL Classification: C12, G12, G14————————————————————†Graduate School of Economics, Osaka University, Osaka 560-0043, Japane-mail: u729096j@ecs.osaka-u.ac.jp†Graduate School of Economics, Osaka University, Osaka 560-0043, Japane-mail: tanizaki@econ.osaka-u.ac.jp

1.Introduction
Up till now, there are a great number of studies on efficient capital markets. However, for people whostarted studying problems of efficient capital markets, the first problem they encountered was how to define
the word “efficient”. One famous paper, Fama (1970), which summarized important theory and empirical
work on efficient capital markets, has been playing a significant role in development of market efficiency.
This famous paper perfectly summarized studies before 1970 giving the other economists a detailedreference which was useful for keeping on doing deeper research. It said that “A market in which prices
always fully reflect available information is called efficient”. However, it was unable to make any progress if
the theory about efficient markets was stated only in simple words but not in mathematical or statisticalforms. Transforming the simple words into mathematical or statistical form, or more specifically, into
concrete and verifiable models is not only important but also quite difficult. It may have been the next
difficulty during that time after the definition of ‘efficient’. In order to do hypothesis tests in details, we needmore specific descriptions and have to make some rational, sometimes maybe irrational, assumptions on
efficient market theories in the process of modeling and optimization. Fortunately, it had already been solved
to some extent by economists. Fama (1970) summarized “Expected return theories” or called “Fair gamemodels”, which had been assumed in available work at that time, as the model describing that the expectedvalue of price of one security at time t+1 based on information at time t is equal to the value of price at time tmultiplying the expected return at time t+1 based on the information at time t plus 1. The details of thismodel will be reviewed in the methodology part. Under this theory, two aspects of assumption had beendeveloped. First, that is random walk hypothesis: assuming returns are mutually independent. Lots of studies
doing research with various stock return data form different countries tested random walk feature of stock
returns. Second, that is sub-martingale hypothesis. Researches on sub-martingale model are anotherimportant parts of empirical studies on market efficiency theories, which assumes that simply stock price isrising constantly.
In fact, the theories we talked about above can be classified into weak form tests. Literatures and studies onmarket efficiency theories can be divided into three categories in terms of what information set the tests are
based on: weak form tests, only using historical prices and returns as information set, semi-form tests, also
including available public information such as stock split, information from company monthly magazines,
and strong form tests, also including monopoly in information within some special investors or brokers.
What this paper concerns about is whether market is efficient only under historical information, that is, weakform tests.
A major work on semi-form tests of market efficiency is, Fama, Fisher, Jensen and Roll (1969). It examined
the reaction of stock price when new information reached at market. It solved two related questions as it saidat the beginning of the paper:(1)Is there normally some “unusual” behavior in the rates of return on a split security in the months
surrounding the split?
(2)If splits are associated with “unusual” behavior of security returns, to what extent can this be accounted
for by relationships between splits and changes in other more fundamental variables?
Fama, Fisher, Jensen and Roll (1969) first regressed return of individual stock returns on market portfolio to
get rid of influence of general market condition. Then they calculated average regression residual for monthm preceding split month, which was defined as month 0, and cumulative average residual in month m. They
divided the two kinds of residual to four based on increased dividends or decreased dividends after splits.
They considered that unusually high returns on splitting shares in the months immediately preceding a split
reflected the market’s anticipation of increases in dividends and concluded that when the information effects
of dividend changes were taken into account the apparent price effects of the split would vanish and on the
average the market’s judgments concerning the information implications of a split were fully reflected in the1price of a share at least by the end of the split month but most probably almost immediately after theannouncement date of split. Thus the result supported the idea that the market was efficient.
In the meanwhile, there is another type of definition on the word “efficient”, or more specific definition
than the word “fully reflect”. Malkiel (2003) treated the definition that such markets do not allow investors
to earn above-average returns without accepting above-average risks as the definition of an efficient market.
What was also new in this paper is that it said a believe about stock prices at least partially predictable was
gradually held by economists after the start of the twenty-first century. The efficient market hypothesis isassociated with the idea of random walk, which suggests new information is immediately reflected in stock
prices and therefore price changes are unpredictable. Anyone could do as well as the experts in the field ofstock. Before twenty-first century, the answer was yes. However, just as Malkiel (2003) summarized, future
stock prices were somewhat predictable on the basis of past stock price patterns. Many studies reviewed in
the next paragraph indeed confirm this view. Although positive serial correlations of stock returns overperiods of days, negative serial correlations of stock returns over longer holding periods, or any otherpredictable weekday patterns existed, Malkiel (2003) concluded there was no sufficient evidence forinefficiency that would enable investors to make excess returns. Except for Fama (1970) and Malkiel (2003),
Akintoye (2008) also reviewed efficient market hypothesis including theory of behavioral finance.
There are lots of findings on stock prices or returns. Early in Fama (1965), random walk theory in stock
prices was briefly discussed. Stevenson and Bear (1970) focused on random walk model on commodity
future prices and found that the random walk did held. Fama and French (1988) said that the autocorrelationin returns was weak for the daily and weekly holding periods but stronger for long-horizon returns. Liu andHe (1991) tested random walk hypothesis using five pairs of weekly nominal exchange rate series. The
hypothesis was rejected at five percent significance level. Ding, Granger and Engle (1993) investigated ‘long
memory’ property of stock market returns. They found that there was more correlation between absolute
returns than returns themselves and that the power transformation of the absolute return |rt|^d also had quite
high autocorrelation for long lags. They called this property ‘long memory’ and this property was strongest
when d was around 1. Solnik, Boucrelle and Fur (1996) found that international correlations increased inperiod of high market volatility. Pan, Chan and Fok (1997) found little evidence against random walk of four
currency futures prices except Japanese yen. Chen and Yeh (1997) confirmed short-term nonlinear
regularities existing in TAISE and S&P but the search costs of discovering them might have been so high thatthe market was still efficient. Porta, Lakonishok, Shleifer and Vishny (1997) confirmed the view that
expectational errors about earrings prospects influenced the superior to value stocks. Although increases in
portfolio returns existed from using technical rules, as Bessembinder and Chan (1998) studied, this could not
be seen as a single of market inefficiency because of elimination of these increases as costs were underconsideration. Ojah and Karemera (1999) found evidence supporting random walks and weak-form
efficiency in major American emerging equity markets and investors could not make profitable trading
schemes using historical information. In the same year, Karemera, Ojah and Cole (1999) also found the same
results as Ojah and Karemera (1999) in fifteen emerging markets.
Smith, Jefferis and Ryoo (2002) studies random walk model for four types of stock market in Africa. Only
the South African market followed the model. Worthington and Higgs (2004) tested random walks and weakform market efficiency for sixteen developed markets and four emerging markets. They found that the
emerging markets were not consistent with random walk model except Hungary while the results fordeveloped markets were mixed: some was consistent with random walk while some were not. Özdemir(2008) studied the efficient market hypothesis for Istanbul Stock Exchange National (ISEN) 100 price index.
They used ADF unit root test, runs test and variance-ratio test. The ISEN 100 index was characterized by aunit root with two structural breaks. They split the sample into three sub-periods according to the trend shifts
and tested efficient market hypothesis for different periods. They concluded that ISE was a weak form
efficient market. Magnus (2008) examined Databank Stock Index for test of weak-form efficient market
hypothesis of Ghana Stock Exchange and concluded that the market was inefficient because of rejection of2

random walk model. Chen (2009) examined random walks for Pacific Basin foreign exchange markets andfound some markets were not weak-form efficient. Onali and Goddard (2009) confirmed serial correlationand non-Normality in the Mibtel, the principal Italian stock market index, and that the markets had longmemory.
Borges (2010) tested the weak-form market efficiency of indexes of France, Germany, UK, Greece,
Portugal and Spain with serial correlation test, runs test, augmented Dicket-Fuller test and multiple varianceration test. They found convincing evidence that monthly prices and returns followed random walks but daily
returns were not normally distributed with negatively skewness and kurtosis over three. Hamid, Suleman,
Shah and Akash (2010) also conducted a test on weak-form market efficiency and found that monthly prices
did not follow random walks in all countries of the Asian-Pacific region. Enowbi, Guidi and Mlambo (2010)
tested several emerging African stock markets and found week effects with negative Monday and positive
Friday effects. AI-Jafari (2011) focused on Kuwait stock exchange and found evidence against efficient
market and therefore they thought investors could make profitable returns by using historical information.
NWOSA and OSENI (2011) found evidence revealing the Nigeria stock market inefficiency as well. Sewell(2012) made a specific study on Dow Jones Industrial Average log returns by using daily, weekly, monthly
and annual data. He found that first-order autocorrelation was small but positive for all time periods.
However, autocorrection close to 0 was consistent with an efficient market for daily and weekly returns
while standard runs test was rejected for daily returns but not rejected for the others. He also concluded thatno evidence supporting long memory in returns was found. Nisar and Hanif (2012) examined the weak-form
market efficiency on four major stock exchanges of South Asia including, India, Pakistan, Bangladesh and
Sri Lanka with four statistical tests, runs test, serial correlation, unit root and variance ratio test. They
concluded that none of the four major stock markets of South-Asia followed random walk. Therefore they
thought all these markets were not weak-form efficient markets. Afego (2012) found evidence indicating
inefficient Nigerian stock market as well. Mbululu, Auret and Chiliba (2013) rejected random walkhypothesis using data of daily nominal United States dollar/Zambian kwacha. Degutis and Novickyte (2014)
thinks that investors could not earn an excess profits although stock market anomalies exist. Titan (2015)
reviewed the growing body of empirical research on efficient market hypothesis. It said there were many
opposite views regarding efficient market hypothesis: some of them rejecting it while other supporting it. It
stressed the truth that testing for market efficiency was difficult and new theoretical model had to be
developed. Rossi (2015) summarized studies on calendar anomalies of markets, such as January effect, Dayof-the-week effect and Turn-of-the-month effect and said that the evidence against efficient market
hypothesis had grown. Malafeyev, Awashi and S.Kambekar (2017) studied Bombay Stock Exchange andShanghai Stock Exchange Composite Index. They found evidence against weak-form market efficiency as
well.
Many papers have focused on the weak form test of an market. They tried to study different stock markets
in the world with statistical tests. But just as Titan (2015) said, some found evidence against market
efficiency while some did not found strong evidence against it.
This paper utilizes some classical methods to examine market efficiency hypotheses but also provides anotion of new simple statistical test for judgement of market efficiency. Moreover, this paper also works on a
new question: how does market efficiency change when market extends in size.
The rest parts of this paper are arranged as follow. Part two sketches out the theory under which theresearches are done and states what and how this paper does to study the market efficiency. Briefly, examine
random walk hypothesis, sub-martingale hypothesis and fair game models in three situations (or based on
three different information sets). Draw a comparison between market efficiency and market volatility. Part
three introduces the data and analyzes summary statistics of the data. Part four shows empirical results oftests and draws some conclusions. Part five summarizes all the paper and raises some questions.

32.Methodology
The theory of market efficiency mainly means ‘expected return models’ or ‘fair gamemodels’ (Fama(1970)), which can be described as:(1)
That is to say: the expected price of security j at time t+1 based on information set
fully reflected in theprice at time t, is equal to one plus the expected return of security j in one period also based on theinformation set, multiplying price of security j at time t. The points above p and r mean that they are
random variables.
The most important implication under this theory is that it rules out the possibility of trading system having
expected returns in excess of equilibrium return. Therefore :(2)(3)
Of cause :(4)(5): the difference between real price and the expected price: the excess return
What we will do is all under this theory (1)~(5) and we will especially test (4) to verify something we wantto know.
The main purpose of this paper is to examine: first, whether stock markets are weakly efficient in China.
Second, whether the degree of market efficiency changes over time and how it changes. Third, what
investors can do to make profits when the degree of market efficiency fluctuates over time. The specificresearch processes are stated as follow.
First, examine random walk hypothesis. If random walk model stands up, the return series of one certain
security should be mutually independent and the results of statistical tests should not be significant.
Specifically, first step, calculate stock return autocorrelations. Then calculate Ljung-Box test statistics (Ljung
and Box(1978)) to confirm whether they are significant. Second step, check sign change of return series withruns tests. In order to check the sign change, three important values of a return series should be figured out:
the number of positive returns, the number of negative returns and the run of the series, which is the maximal
non-empty segment of the series consisting of adjacent equal elements. The former two are called plus andminus in this paper. Under random walk hypothesis, the true run value of a return series should not muchhigher or lower than the mean run value. If it is, the hypothesis of statistical independency is rejected. Well,
this is exactly the essence of runs test. For deeper perception and cognition, four other values of a returnseries will also be calculated: the number of positives returns following by positive returns, the number ofnegative returns following by negative returns, the number of positive returns following by negative returns
and the number of negative returns following by positive returns. They are called pplus, mminus, plusminus
and minusplus in this paper for convenience. If random walk model is the true model, plus and minus should
not have big difference. This also works for pplus, mminus, plusminus and minusplus.

4Second, examine sub-martingale hypothesis. The implication contained in this hypothesis is that stock priceis getting higher over time, so holding stock during a certain period is better than doing a “buy-and-sell”
strategy during the same period. No one will be willing to lose profits from persistent rise of stock price. We
construct concrete strategies and calculate strategy returns to confirm sub-martingale hypothesis. If theperiods in which strategy returns are higher than holding returns indeed exist, sub-martingale hypothesis
breaks down. In the meanwhile, it may be good news for investors because they can do more on their own
wisdom and intelligence during those periods to obtain higher returns. It should be noted that transaction cost
is not considered in this paper when calculate strategy returns. From existing documents the returns ofstrategies would be smaller even neutralized because of frequent trades although the transaction cost is verysmall. We use information set in the past to create strategies. The method for constructing strategies will beelaborated in the empirical part. It should be emphasized that in this part of research process, the information
set used to construct strategies of one certain market is the information contained in the target market itself.
For example, we use the return change of Shanghai Stock Exchange composite index as a benchmark toconstruct strategies targeted with Shanghai Stock Exchange composite index. This type of information set iscalled ‘itself’ in this paper.
Third, examine expected return theories in one market. That is analyzing market efficiency of every market
respectively, individually and independently. It has been discussed in the last part that some implications are
involved in the theories. The one considered here is that profitable strategies can not exist under these
theories. Strategies generated above will be tested to see if they are profitable. On other words, (4) and (5)will be tested. In a certain example, the first item of (4) can be substituted by the return of a particular
strategy, the second item, the expected return of a particular strategy based on past information,
unfortunately, can not be calculated correctly and precisely. We can not get the distributions of any strategies
if we do not have enough strategy returns and actually only one strategy return will be gathered for one
certain strategy during one certain period. Therefore, finding a proper substitute for expected strategy returnis crucial. Here we use the mean value of historical daily returns of one year’ interval, whose interval is thesame as the interval of the strategy being considered, to substitute expected strategy return. We also assume
that the returns of one year’ interval are distributed as normal distribution whose mean value is the sample
mean value and variance is the sample variance of daily returns of one year’s interval. Actually this can beverified to be proper through drawing a plot. Then testing of (4) and (5) of single strategy can be converted
to the following hypothesis test with null hypothesis H0 and alternative hypothesis H1.
H0: mean return_year = strategy mean returnH1: mean return_year < strategy mean return.
Therefore, expected return theories of market efficiency are checked in the way that calculate all the valuesof hypothesis tests over time per strategy. If results of hypothesis tests of most strategies are consistent with
H1 during some certain periods, it can be concluded that in those periods strategy mean returns are higher
than mean return of one year’s interval, profitable strategies exist and therefore the market is inefficientunder expected return theory. Using historical return change to make the decision of buying or selling stockand than construct a strategy means that the information available is only from past. That is exactly one typeof weak form test.
Fourth, examine expected return theories in whole market. That is analyzing market efficiency of wholemarket or regard all separated markets as a whole. Here, we also test (4) and (5). But, the substitutes foritems in (4) have to be changed a little: one market to whole market. The first item of (4) can be substitutedby the return of a particular strategy. It is the same here but we use new return values. Change theinformation set to create new strategies and calculate new returns. In above part, information set is theinformation contained in target market itself, well simply ‘itself’. Here, two other information sets areproposed for whole market. First is the information from the other market except target market, called ‘theother’. Second is the information from all markets, called ‘both’. For example, we use two stock index data:
Shanghai Stock Exchange composite index and Shenzhen Stock Exchange composite index. When construct
strategies for Shanghai Stock Exchange composite index, ‘the other’ means the information from Shenzhen
Stock Exchange composite index while ‘both’ means the information from both markets. The second item of(4) is also substituted by mean return of one year’s interval but the mean return is mean value of all5

individual mean returns of one year’s interval, here, of cause, is mean value of mean returns of Shanghai and
Shenzhen Stock Exchange composite index. If results of hypothesis tests of most strategies are consistent
with H1 during some certain periods, in those periods strategy mean returns are higher than mean return of
one year’s interval and therefore profitable strategies exist and the market is inefficient under expected return
theory. Moreover, comparison among results of hypothesis tests calculated with three different information
sets will be drown to see whether the degree of market efficiency changes when market extends in size.
Fifth, find relationship between market efficiency and volatility. The final analysis will draw a comparison
between market efficiency and volatility. The former one uses the values of hypothesis test statistics
calculated above as the degree of marker efficiency and the latter, volatility, uses the standard deviation ofdaily return series in one year’s interval. We expect to see an efficient period with low volatility and an
inefficient period with higher volatility.
3. Summary statistics of the data
The data used in this paper are Shanghai Stock Exchange composite index (SSE composite index or SSEC)
collected from Shanghai Stock Exchange Statistics Annuals, monthly magazines and Shenzhen Stock
Exchange composite index (SZSE composite index or SZSEC) collected from Shenzhen Stock Exchange
Statistics Fact Book, monthly magazines from January 4th 2005 to June 28th 2019. We first examine market
efficiency in Shanghai Stock Exchange (SSE), Shenzhen Stock Exchange (SZSE) respectively and thenexamine it in an entire market containing SSE and SZSE. Before next step, review the evolution of two stock
exchanges in China.
Plot 1 shows the evolution of three indicators of two stock exchanges: the number of listed companies, thenumber of listed stocks, one year’s trading value from 2005 to 2018. In 2005, there were only 833 listedcompanies, 878 listed stocks in SSE, 544 and 586 in SZSE. The stock trading value were 1924021 millions
yuan in SSE and 1242457 millions yuan in SZSE. It seems SSE developed more quickly and better thanSZSE. While after 2009, the numbers of listed companies and stocks in SZSE were more than those in SSE
and after 2015, the yearly trading value of SZSE were also higher than that of SSE. It seems SZSE began tooutperform SSE. Despite that, both stock exchanges have been growing in high speed. Plot 2 shows theevolution of two composite indices. There are 3520 close prices for each index from January 4th 2005 toJune 28th 2019. Before the global financial crisis in 2008 there were a period of prosperity in stock markets.
After that markets tried to get back to high level. From 2014 two markets recovered gradually, welcomed asecond period of prosperity and then fluctuated. During whole period, the highest close price was 6092.06
points in October 16th 2007 and the lowest close price was 1011.5 points in July 11th 2005 for SSEC while
3140.66 points in June 12th 2015, 237.18 points in July 18th 2005 for SZSEC. The lowest stock return was-0.09256 in February 27th 2007 and the highest stock return was 0.09034 in September 19th 2008 for SSEC
while -0.08929 in February 27th 2007 and 0.08515 in September 19th 2008 for SZSEC. Both the highest
reruns and the lowest returns happening in the time around 2007, 2008 also indicates dramatical market
fluctuation during global financial crisis. Moreover, the lowest close price, the highest close price, the lowest
return and the highest return in a certain year, for example in 2010, are almost consistent in time for two
indices. In most cases these four indicators realize in the same day or realize in close days. Although there isno distribution for the lowest or highest stock return because of lack of data, it is true that the close price ofSSEC and SZSEC usually gets to the extreme values in quarter 1 and 4 of a year. The close price of SSEC
reached the highest value in quarter 1 and 4 expect 2009, 2011, 2015 and that of SZSEC reached the highest
value in quarter 1 and 4 expect 2015.

6

Plot 1 The overview of SSE and SZSE
Note: This plot shows three factors of SSE and SZSE: Listed companies, Listed stocks and Trading value
from 2005 to 2018.

Plot 2 The evolution of SSEC and SZSEC
Note: This plot shows daily close prices of SSEC and SZSEC from January 4th 2005 to June 28th 2019.
There are 3520 data for each index.

Table 1 shows summary statistics of returns from 2005 to 2018. We can draw four main conclusions: First,
both indexes have small positive mean returns for whole period, 14 years, and have six years’ positive andfive years’ negative mean returns happening in the same year. However, in 2010, 2013, 2017, the sign ofmean returns were different but this did not result in a bigger margin between SSEC and SZSEC comparedwith the other years. The bigger margin appearing in 2007 and 2015 are caused by higher mean returns of
SZSEC. There was no strong evidence indicating that mean return of one index are higher than the other one
because the margin in fourteen years were with 8 times when the return of SSEC was higher and with 6 times
when the return of SZSEC was higher. Second, the highest standard deviation(SD) appeared in 2008 and the7

bigger margin between SSEC SD and SZSE SD was in 2012, 2016. Third, skewness values were negative
expect 2005 and 2012. The lowest absolute value was in 2014 for SSEC and in 2012 for SZSEC. In the
meanwhile, kurtosis values were very close to 3 in 2008 and 2011 but were always higher than 3 in the otheryears meaning a distribution with a sharp peak compared with normal distribution. Fourth, the values of
Jarque-Bera statistics confirm that null hypothesis of normal distributions are rejected in most years except
2011 for SSEC and except 2008, 2011, 2012 for SZSEC. Interestingly, the interval, when return distribution
is closest to normal distribution, is between 2008 and 2012 while these years was exactly suffering a global
crisis. We still consider the distribution of one year interval’s return series as normal distribution forsimpleness of calculation.
Table 1 Summary statistics of daily returns
Note: This table shows summary statistics of daily returns of SSEC and SZSEC from 2005 to 2018
including: mean, standard deviation, skewness, kurtosis and Jarque-Bera statistics.
Year

Indices

Mean

Sd

Skewness

Kurtosis

JB

200501~
201906SSEC

0.000248

0.016434-0.555815

7.389925

3006.862883

SZSEC

0.000459

0.018567-0.698657

5.848482

1475.977277

SSEC-0.000282

0.013655

1.047398

7.568059

253.605692

SZSEC-0.000449

0.014938

0.633275

5.468145

77.279539

SSEC

0.003407

0.013498-0.393371

5.537314

70.569228

SZSEC

0.002766

0.0141-0.85116

5.807838

107.818455

SSEC

0.002744

0.022377-1.032387

4.953596

81.134976

SZSEC

0.003986

0.023524-1.118219

4.824433

83.649192

SSEC-0.00434

0.028596

0.289299

3.890589

11.514218

SZSEC-0.003995

0.030336-0.09485

3.36327

1.714502

SSEC

0.002285

0.019014-0.639587

4.299188

33.657292

SZSEC

0.00306

0.021137-0.82613

4.359672

46.359075

SSEC-0.000598

0.014295-0.617571

4.561973

39.818585

SZSEC

0.000307

0.016919-0.683325

4.119841

31.347854

SSEC-0.00107

0.011561-0.271758

3.572117

6.305125

SZSEC-0.001704

0.014431-0.362393

3.1751525.62944SSEC

0.000186

0.01092

0.603574

4.64913842.1167

SZSEC

0.000179

0.014856

0.004887

3.708726

5.06575

SSEC-0.000309

0.011638-0.374843

5.326684

59.007946

SZSEC

0.000787

0.01428-0.674384

4.569848

42.300542

SSEC

0.001752

0.010868-0.208992

6.866447

153.761926

SZSEC

0.001153

0.012111-0.81555

4.30120444.261811

SSEC

0.000225

0.024675-0.936968

5.007839

76.373434

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

8

Year
2015

2016

2017

2018

Indices

Mean

Sd

Skewness

Kurtosis

JB

SZSEC

0.001952

0.02665-0.828936

3.823569

34.696389

SSEC-0.000248

0.014033-1.560887

10.119374

611.863453

SZSEC-0.000302

0.018329-1.317797

7.764225

300.147425

SSEC

0.000219

0.005447-0.31896

4.537579

28.057303

SZSEC-0.000184

0.009167-1.045148

5.850118

126.486701

SSEC-0.001217

0.012442-0.473597

4.972

48.258406

SZSEC-0.001713

0.015015-0.545365

5.276442

64.249788

4. Empirical results
In this part, we convert literal statements of empirical processes in part two to statistical forms and get someconclusions.
4.1 Tests of random walk hypothesis
First, calculate return autocorrelations and Ljung-Box statistics for whole periods and for each year from2005 to 2018 (data of 2019 is not complete) for both indexes. For saving space, only results of whole period
and rejected years are displayed in Table 2 and 3. In whole period, returns of SSEC are with noautocorrelation in lag1 and lag2 but from lag3 the null hypothesis considering zero autocorrelations fromlag1 to lagk is significantly rejected. There is even stronger evidence proving that returns of SZSEC areautocorrelated because all the null hypotheses from lag1 to lag15 are rejected in whole period. Although
hypothesis tests of Ljung-Box test are significantly rejected in whole periods for both indices, theautocorrelation values themselves, with biggest value 7.03%, are so small that they do not have enoughinformation for investors to make profits. On the other hand, conditions are quite different if data are divided
into small parts, year by year. There are four years, 2006, 2014, 2015, 2016, in which the no autocorrelation
hypotheses are rejected for SSEC and only two years, 2015, 2016 for SZSEC. Especially in 2015 and 2016,
null hypotheses of no autocorrelations are strongly rejected for both indices with high autocorrelations:
0.1489(lag1, 2015, SSEC), -0.145(lag2, 2015, SSEC), -0.1786(lag1, 2016, SSEC) and 0.2059(lag1, 2015,
SZSEC), -0.1813(lag5, 2016, SZSEC). The autocorrelation values during these years are about several times
compared with the other years. Although some studies think that significant autocorrelation is against
random walk model and therefore against weak-form market efficiency, some thinks that they are not highenough for investors to predict future or make profits. By the way, it is quite interesting that no evidence
indicating autocorrelation existing in return series during 2008 is found but clear evidence indicating theexistence of them during 2015 and 2016 is found, while close prices in both periods were volatile andchanged greatly although the former period rose and fell more dramatically. This phenomenon seems to be
the evidence that self-influence of stock market in China, such as policy and big events, is more important
than the influence from outside, for example influence from other markets, although outside influence may
be something throughout the world like global economic crisis.
Table 2 Autocorrelations and P values of Ljung-Box tests - SSEC
Note: This table shows autocorrelation values and P values of Ljung-Box tests of whole period and rejected
years for SSEC. ac means the autocorrelation value.
SSEC
Lag

200501~201906
ac

P value

2006
ac

P value

2014
ac

9

P value

2015
ac

P value

2016
ac

P value

SSEC

200501~201906

2006

2014

2015

2016

1

0.01950.2462

0.05340.40520.03180.61690.14890.0196-0.1786

0.0051

2-0.02470.1737-0.01650.68410.10490.2254-0.1450.00490.14830.001330.03520.04870.0481

0.723-0.0958

0.15340.00050.0138-0.09260.001540.06080.00030.05920.70130.16730.01550.13580.00420.09

0.0016

50.00270.00080.18570.0574-0.11220.00870.05550.0068-0.17520.0001

6-0.0627

0-0.13770.0172-0.00310.0172-0.11540.0036-0.0184

0.000370.03070-0.0626

0.02170.0571

0.02290.00380.0071-0.00460.000780.01670-0.04710.03060.09040.01890.14150.00190.01080.0014

9

0.007

0

0.06420.03520.00170.0315-0.01130.0036

0.11430.000810-0.004200.14160.01050.094

0.0241-0.15730.0006-0.01710.001411

0.023600.10490.00680.09070.0194-0.11310.00040.15150.0003120.020200.00190.0113-0.1470.005

0.06860.0004-0.11710.0002

13

0.057

0

0.00490.0178-0.0620.00590.09380.00030.18330

14-0.030300.05720.0211

0.06630.0066-0.08680.0003-0.2130150.050800.04990.02610.07360.0067-0.00470.00050.15970

Table 3 Autocorrelations and P values of Ljung-Box tests - SZSEC
Note: This table shows autocorrelation values and P values of Ljung-Box tests of whole period and rejected
years for SZSEC. ac means the autocorrelation value.
SZSEC

200501~201906

2015

2016

Lag

ac

P valueac

P valueac

P value

10.070300.20590.0012-0.1004

0.1152

2-0.02160.0001-0.04080.00440.11130.062730.045900.05780.0086-0.0846

0.0625

4

0.045

0

0.07150.0115

0.09680.046850.0003

00.09810.0089-0.18130.0031

6-0.0277

00.04540.0145-0.0086

0.00657

0.036900.06990.0167-0.05180.009780.014700.18180.00130.01820.01699-0.00090-0.06020.00180.08480.0152

10

0.003

0

-0.1858

0.0001-0.09960.010710SZSEC

200501~201906

2015

2016

11

0.038800.002

0.00020.13

0.0041120.017200.01320.0004-0.0352

0.006213

0.037400.10080.00030.07770.006114-0.01580-0.03710.0005-0.17380.0007150.04480-0.00120.00080.157

0.0001

Second, calculate the number of return sign (plus, minus, pplus, mminus, plusminus and minusplus) andruns test statistics. The null hypothesis of runs test is that the elements of the sequence are mutuallyindependent. For whole periods, runs test is not rejected for SSEC but rejected for SZSEC at alpha=0.01. The
conclusion of whole periods is similar with Ljung-Box test to some extent. For SSEC Plot 3 (A) shows thenumbers of positive and negative returns (or plus and minus) from January 2005 to June 2019. Every interval
is one quantitative year and the next interval after the former one steps two months. For example, the firstinterval is 200501~200512. The second interval is 200503~200602. It is obvious that there was a boom in
economic around 2005 with increasing numbers of positive returns and decreasing numbers of negative
returns. When the global crisis influence in 2008 reached Chinese stock markets, it struck the markets so
seriously that the numbers of positive returns declined dramatically during a short period and after
September 2007, it had already declined lower than the numbers of negative returns calculated in the sameintervals. The numbers of positive returns started going up and changing frequently after 2008 although they
have never gone back to the high level around 2006 up till now. Plot 3 (B) shows the numbers of positive
return following by positive return (pplus), negative return following by negative return (mminus) andpositive return following by negative return (minusplus), negative return following by positive return(plusminus). If the elements of return series are mutually independent, the four numbers should not have big
difference as well. Obviously the results did not stand up for this. pplus and mminus have the similar change
trend with plus and minus but clearly different from plusminus and minusplus. The results of runs tests for
SSEC are plotted in Plot 5. The solid line plots real runs of return series in each interval, with dotted line
meaning confidence interval at alpha=0.01. The solid line extends between two dotted lines, which means norejections of the null hypotheses around 2006 but stretched out of these lines, which means significantly
rejections around 2015 and 2016. This is consistent with the Ljung-Box test results. While SZSEC in Plot 4(A) and (B), the situations are similar to SSEC. As for runs test, except periods around July 2011 and January
2013, there is no sufficient evidence informing dependent relationship in return series. We indeed foundevidence against mutually independency or random walk.

11

Plot 3 The numbers of return signs - SSEC
(A)
Note: This plot shows the numbers of positive and negative returns (or plus and minus) from January 2005 toJune 2019 in every quantitative one-year-interval for SSEC.

(B)
Note: This plot shows the number of positive return following by positive return (pplus), negative returnfollowing by negative return (mminus) and positive return following by negative return (minusplus),
negative return following by positive return (plusminus) from January 2005 to June 2019 in every
quantitative one-year-interval for SSEC.

12

Plot 4 The numbers of return signs - SZSEC(A)
Note: This plot shows the numbers of positive and negative returns (or plus and minus) from January 2005 toJune 2019 in every quantitative one-year-interval for SZSEC.

(B)
Note: This plot shows the number of positive return following by positive return (pplus), negative returnfollowing by negative return (mminus) and positive return following by negative return (minusplus),
negative return following by positive return (plusminus) from January 2005 to June 2019 in every
quantitative one-year-interval for SZSEC.

13

Plot 5 Runs tests - SSEC
Note: This plot shows the results of runs tests in every quantitative one-year-interval for SSEC.

Plot 6 Runs tests - SZSEC
Note: This plot shows the results of runs tests in every quantitative one-year-interval for SZSEC.

14

4.2 Tests of sub-martingale hypothesis
Under sub-martingale hypothesis, returns produced by strategies are always lower than returns produced byholding stocks during the same interval because stock price is rising all the time. However, from Plot 2, it isclear that the stock prices are not rising all the time. Although sub-martingale hypothesis of stock price is notrational, here, not only this phenomenon can be analyzed but also some other useful conclusions can be
drawn: what time should investors construct own strategy rather than holding portfolio all the time. The
construction process of strategies is: during one certain interval, such as interval from January 2005 to
December 2005, check the return value from the start date. Find the first day of strategy when the return ishigher (lower) than a (b). If no days satisfy this condition before day Z and day Z satisfies this condition, day
Z is the first day for this strategy. Start one strategy through buying (selling) one share in day Z. Then findthe next transaction day Y when the return is lower (higher) than b (a) and sell (buy) two shares, one forcovering the former transaction and the other for starting a new investment action. Find the third transaction
day X when the return is higher (lower) than a (b) and buy (sell) two shares. If the return is higher than b but
lower than a, do nothing but wait. Repeat the processes above until the end of the interval. While in the last
day of strategy, just buy or sell one share to end the strategy. In the end, calculate the total return of thisstrategy. This type of strategy is named s(a,b) in this paper. In the meanwhile, calculate total return ofholding the portfolio from the first day of the strategy to the last day of the strategy. Here, let a in the rangeof (0.002,0.02) stepped by 0.002 and b in the range of (-0.002,-0.02) stepped by 0.002. Therefore, one
hundred strategies are constructed, returns of all strategies and of all holdings are plotted respectively in Plot
7 and Plot 8. The lines of strategy returns fluctuate and intertwine so tightly that it is difficult to capture
specific characteristics but we also can see that during periods around 2008 and 2015 there are strategies
performing better than holding portfolio all the time. While in the same interval, different strategies havedifferent path, some similar but some far more different. For example, in interval of 200811~200910, thehighest strategy return of SSEC is about 0.75 while the lowest strategy return is about -0.5 but both with alittle positive holding return around 0.5. How to make a wise strategy is a big challenge for investors. In
order to have a deep look, calculate ratios for 100 strategies respectively, which indicate the proportion ofstrategy returns when strategy returns are higher than holding returns in a certain interval. Plot 9 pictures theratio lines of SSEC and SZSEC. Now it is clear to declare that all 100 strategies have the time during which
they performed better. For SSEC, the highest ratio is 0.61 from s(0.02,-0.02) and for SZSEC is 0.707 froms(0.002,-0.002). Apparently, the sub-martingale hypothesis is false. Plot 10 are two exact examples ofstrategies. However, few strategies failed to be constructed because of lack of suitable returns: interval
201609-201708, s(0.02,b) (b is from -0.002 to 0.002) do not exist because of no enough positive returns.
Under this circumstance, the return of strategy is actually equal to zero. There are always strategies existingalthough some failed to be constructed in the same period. It is easy to find that the line of strategies are little
fluctuant and more smoother compared with the line of holdings. Moreover, around 2008 and 2015, whenholding returns were in valley, the strategy returns were much higher so that using strategies is a smarterchoice for these time. While around 2006 and 2014, when stock prices were rising constantly, strategies
preformed worse. These results are consistent with the change trend of stock prices of two indexes. In award, sub-martingale hypothesis implying nonexistence of strategy returns higher than holding returns does
not hold for both indexes.

15

Plot 7 Strategies and holdings - SSEC
(A)Itself
Note: This plot shows returns of one hundred strategies in every quantitative one-year-interval for SSEC
using information of SSEC itself.

(B)Itself
Note: This plot shows returns of holdings which is consistent with periods of corresponding strategies inevery quantitative one-year-interval for SSEC using information of SSEC itself.

16

Plot 8 Strategies and holding - SZSEC(A)Itself
Note: This plot shows returns of one hundred strategies in every quantitative one-year-interval for SZSEC
using information of SZSEC itself.

(B)Itself
Note: This plot shows returns of holdings which is consistent with periods of corresponding strategies inevery quantitative one-year-interval for SZSEC using information of SZSEC itself.

17

Plot 9 Strategies vs holdings - Itself
Note: This plot shows ratios of 100 strategies indicating the proportion of strategy returns when strategy
returns are higher than holding returns in 82 quantitative one-year-interval.

Plot 10 Examples of strategies(A) s(0.02,-0.02) for SSEC
Note: This plot shows a concrete example of strategies, s(0,02,-0.02), for SSEC.

18

(B) s(0.002,-0.002) for SZSEC
Note: This plot shows a concrete example of strategies, s(0,002,-0.002), for SZSEC.

4.3 Expected return theory of efficient market model - one market
Under expected return theories, profitable strategies can not exist. Here, we make the following hypothesis:
H0: mean return_year = strategy mean returnH1: mean return_year < strategy mean return.
If strategy mean return is high enough to reject H0, profitable strategy exists, meaning an inefficient market
under expected return theory. Because it may be improper to use daily mean return of one year’ interval as a
substitute for expected strategy return, another rational explanation is that whether daily strategy mean returnis statistically higher than daily mean return of one year’ interval. If the answer is yes, we can also say thatusing one certain specific strategy is a better choice for a certain interval. Here, because the distribution of
one year interval’s return series is considered as normal distribution, the distribution of daily mean return of
one year interval’s is also normal distribution. Now we can calculate statistical values of hypothesis tests:(daily mean return of one year interval’s - daily strategy mean return)/(standard deviation of daily mean
return of one year interval’s). Again, daily strategy mean return are calculated from strategy constructedabove. That means in this part, ‘itself’ is considered as information set.
Plot 11 shows the movement trends of statistics of hypothesis tests for one hundred strategies. The straight
red lines are critical lines for H1. Both indices indicate inefficient markets around 2008, 2011 and 2018
under expected return theory. SSEC also indicates market inefficiency around 2013 and 2015. Almost all
strategies performed better around 2008 indicating solid evidence of market inefficiency. Correspondingly, it
is clear that holding market portfolio is a better choice around 2006, 2014 and 2016 while making own
strategies is a better choice around 2008, 2011 and 2018. Here, the rejection ratio, conditional on strategiess(a,b) (a and b have the same values as defined above), of 100 hypothesis tests during one certain interval isused as a substitute for the level of market inefficiency. There are calculated by the number of rejections
divided by the total number of strategies, 100. Rejection ratios only higher than 0.1 for either index aresummarized in Table 4 (B). Obviously, the most inefficient time under expected return theory with theconsiderably high conditional rejection ratios very close to 1 was around 2008. As for each strategy, rejection
ratios of strategies are calculated by the number of rejections in 82 intervals divided by the total number ofintervals, 82. Among 82 intervals s(0.02,-0.002) has the highest rejection ratio 0.207 for SSEC and 0.22 for

19

SZSEC. Another interesting finding is that except little intervals all the other ratios of SZSEC are higher than
the ratios of SSEC. If the same external environment and conditions are assumed, we can find that SZSEC ismore sensitive to all these things because the ratios of SZSEC higher than 0 happened early and ended latethan the ratios of SSEC did. The affected scope of time is always longer for SZSEC. It may be the evidence
that SZSEC is more appealing to investors than SSEC is.
Plot 11 The results of hypothesis tests(A)SSEC-itself
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SSEC using information of SSEC itself.

(B)SZSEC-itself
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SZSEC using information of SZSEC itself.

20

Table 4 Rejection ratios - itself(A)Different strategies
Note: The rejection ratio, conditional on strategies s(a,b), of one certain strategy, is calculated by the numberof rejections during all intervals divided by the total number of intervals, 82.
Strategies

SSEC

SZSEC

s(0.02,-0.002)

0.207

0.22

(B)Different intervals
Note: The rejection ratio, conditional on strategies s(a,b), of 100 hypothesis tests during one quantitative oneyear-interval, is calculated by the number of rejections in one certain one-year-interval divided by the total
number of strategies, 100.
Intervals

SSEC

SZSEC

200705-200804

0

0.38

200707-200806

0

0.37

200709-200808

0.51

1

200711-200810

0.99

1

200801-200812

0.71

0.97

200803-200902

0.5

0.99

200805-200904

0.01

0.53

201011-201110

0.07

0.21

201101-201112

0.13

0.78

201103-201202

0.04

0.46

201105-201204

0.05

0.24

201107-201206

0.05

0.11

201109-201208

0.06

0.13

201505-201604

0.23

0

201707-201806

0.06

0.22

201709-201808

0.17

0.23

201711-201810

0.22

0.58

201801-201812

0.19

0.51

4.4 Expected return theory of efficient market model - whole market
Part 4.3 analyzed market efficiency level of one market only using information from targeted market itself.
In this part, other information sets, ‘the other’ and ‘both’, are used to construct new strategies. Again, whenmake strategies of SSEC, use return change of SZSEC as benchmark or use return changes of both indexes
as benchmark. Not only do information sets change, actually the contents of hypothesis test, or substitutes ofmean return_year and strategy mean return in H0 and H1, have a litter change. When ‘itself’ is used, the21hypothesis test concentrates on testing the efficiency of the market itself, or efficiency of one market. When‘the other’ and ‘both’ are used, hypothesis test concentrates on analyzing the efficiency of the markets
producing information. That is analyzing the efficiency of whole market. Two groups of strategies based on‘the other’ and ‘both’ are newly constructed. In the meanwhile, mean value of two mean returns of two
indexes is used as the mean return of one year’s interval in hypothesis.
The same phenomenon as Plot 11 can also be observed from Plot 12 and 13: In the whole market consisting
SSE with SZSE, inefficient markets exited around 2008, 2011 and 2018. SSEC also indicates inefficiency ofmarket around 2013 and 2015. Similarly, it is a better choice for investors to hold market portfolio around2006 and 2014 but make own strategies around 2008, 2011 and 2018 whatever information set is used.

Plot 12 The results of hypothesis tests - SSEC(A)The other
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SSEC using information of SEZEC (‘the other’).

22

(B)Both
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SSEC using information of SSEC and SEZEC (‘both').

Plot 13 The results of hypothesis tests - SZSEC(A)The other
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SZSEC using information of SSEC (‘the other’).

23

(B)Both
Note: This plot shows the movement trends of statistics of hypothesis tests for one hundred strategies inevery quantitative one-year-interval for SZSEC using information of SSEC and SZSEC (‘both’).

Plot 14, 15 and 16, show something interesting and important. Plot 14 draws ratios of ‘itself’, ‘the other’and ‘both’ per strategy, which are calculated by the number, when they are the highest return respectively in acertain interval, divided by 82. For example, the solid black line in Plot 14 plots ratios, or proportion of
returns of strategy based on ‘itself’, when they are the highest returns among three returns in a certain
interval. There is no strong evidence indicating that strategies with higher return exiting when information
set changes because no matter which information set three lines fluctuate from strategy s(0.002,-0.002) tos(0.02,-0.02) and there is even a little evidence supporting ‘itself’ to be more important. In some strategies,
such as s(0.012,-0.01) of SSEC, ‘itself’ are higher than ‘the other’ and ‘both’ in 82 intervals with probability
over 0.5. It seems that the information contained in one certain market plays a comparatively more importantrole for investors when they make their own strategies. On the other hand, strategies like s(0.008,-0.016)
supported the ‘both’ for SSEC. Apparently, the value of filter ratios are somewhat relevant to what strategy isunder consideration. Anyway, during half of intervals solid black line is above the other two lines for both
SSEC and SZSEC.
One more interesting thing is that in Plot14 (A) and (B) the returns of ‘itself’ are higher when roughly (notexactly) a>0.01 for SSEC and when a<0.014 for SZSEC. That is to say: what kind of information we haveleads to different strategy construction, referring to the setting of a and b. Although conclusions fromdifferent information sets about the level of market efficiency and investment timing are the same andinformation sets except ‘itself’ did not play an important part in making strategies of higher returns, however,
the rejection ratios become higher when information sets change, which indicates a more inefficient market.
(A) of Plot 15 and Plot 16 show rejection ratios among 82 intervals per strategy based on three different
information sets. The dotted lines indicating ‘both’ and the solid-dotted lines indicating ‘the other’ are always
above the solid lines expect few intervals. This means a rise in probability of rejection of hypothesis tests
when information set changes. (B) of Plot 15 and Plot 16 show rejection ratios of hypothesis tests among 100
strategies per interval. Similarly, the dotted lines and solid-dotted lines are always above the solid lines inalmost all intervals, indicating a rise in probability of rejection of hypothesis tests that the market is efficient.
In a ward, when market extends in size, here meaning that SSE or SZSE individually extends to the union of
SSE and SZSE, the level of whole market efficiency declines.

24Plot 14 Filters ratios- different information sets
(A)SSEC
Note: This plot shows ratios of itself’, ‘the other’ and ‘both’ per strategy for SSEC, which are calculated by
the number, when they are the highest return respectively in a certain interval, divided by 82.

(B)SZSEC
Note: This plot shows ratios of itself’, ‘the other’ and ‘both’ per strategy for SZSEC, which are calculated by
the number, when they are the highest return respectively in a certain interval, divided by 82.

25

Plot 15 Rejection ratios - SSEC
(A)Different strategies
Note: This plot shows rejection ratios among 82 intervals per strategy based on three different information
sets, ‘itself’, ‘the other’ and ‘both’, for SSEC.

(B)Different intervals
Note: This plot shows rejection ratios of hypothesis tests among 100 strategies per quantitative one-yearinterval based on three different information sets, ‘itself’, ‘the other’ and ‘both’, for SSEC.

26

Plot 16 Rejection ratios - SZSEC(A)Different strategies
Note: This plot shows rejection ratios among 82 intervals per strategy based on three different information
sets, ‘itself’, ‘the other’ and ‘both’, for SZSEC.

(B)Different intervals
Note: This plot shows rejection ratios of hypothesis tests among 100 strategies per quantitative one-yearinterval based on three different information sets, ‘itself’, ‘the other’ and ‘both’, for SZSEC.

27

In the end of this part, selection rules of strategies are summarized in Table 5 based on historical SSEC andSZSEC data.
Table 5 Selection rules of strategies
SSEC
itselfa>=0.01b>=-0.01

the othera<=0.08b>=-0.14

both

Not recommend

SZSEC
a<=0.012b>=-0.014

Not recommend
Not recommend

4.5 Efficiency and volatility
Finally, investigate the relationship between values of hypothesis tests and market volatilities for finding
some linkage between market efficiency and market volatility. Calculate volatility of one year’s interval for
82 intervals and draw Plot 17. Use standard deviation of one year’s daily return series as volatility. Because
relationship of these two variables shows similar change trend whatever information set is considered, here
just use SSEC on ‘itself’ as an analytical object.
Plot 17 Efficiency vs Volatility - SSEC(itself)
Note: This plot shows the movement trends of hypothesis tests results of SSEC using information ‘itself’ andquantitative one-year-interval’s standard deviations.

Generally speaking, the change trend of volatility is consistent with the results of hypothesis tests. Around2008 and 2015, the volatilities were much higher than normal level and the level of market efficiency
declined in these periods. When volatility rises, the value of hypothesis test tends to drop. However, there isanother interesting phenomenon that can not be explained rationally. Around 2011 and 2013, volatilities weremuch lower compared with the other time but there were profitable strategies indicating inefficient market.
Therefore, although market volatilities are at low level, we can not conclude the market is efficient. From
this point volatility observing in this way is not a very good criterion for market efficiency under expected
return theory.
There is a useful finding which can help investor to judge if it is the time to make strategies. From Plot 17,
the rise of standard deviation always happens early than the fall of hypothesis test value. Therefore, the riseof standard deviation can be seen as a signal for strategies. Roughly when standard deviation of one year’s

28interval is gradually rising and when it is high than 0.3, it is the time to construct strategies. The value of 0.3
can be seen as a critical values.
All critical values of SSEC and SZSEC in different information set are summarized in the Table 6. There
are two conditions for strategy construction: constant rise of standard deviation and critical values.
Table 6 Judgement of strategy construction
SSEC

SZSEC

itself0.3

0.3

the other

0.2

0.25

both

0.25

0.25

There is also another situation for strategy construction. That is when the standard deviation is pretty low
and in the following step strategies should be considered. 2016~2017 is exactly this type of time. Obviously,
now it is the time to think about some strategies.
5.Conclusions and problems
This paper studied market efficiency under expected return theory from weak form aspect using data of
Shanghai Stock Exchange composite index and Shenzhen Stock Exchange composite index from January 4th
2005 to June 28th 2019.
The concrete contents are tests of random walk hypothesis, tests of sub-martingale hypothesis, tests of
expected return theory in three different information sets and comparison between market efficiency andvolatility. Conclusions of these empirical results are summarized as follow.
First, zero autocorrelations of return series hypotheses are significantly rejected for whole periods for bothindices, but the autocorrelation values themselves are so small that they do not have enough information forinvestors to make profits. Especially in 2015 and 2016, null hypotheses are strongly rejected for both indiceswith high autocorrelations. As for runs test, it is not rejected for SSEC but rejected for SZSEC at alpha=0.01
in whole periods. We found evidence against random walk model.
Second, sub-martingale hypothesis implying nonexistence of strategy returns higher than holding returns
does not hold for either index. All 100 strategies have the time during which they performed better thanholding stock all the time.
Third, under information ‘itself’, both indices indicate inefficient markets around 2008, 2011 and 2018
under expected return theory. Holding market portfolio is a better choice around 2006, 2014 and 2016 while
making own strategies is a better choice around 2008, 2011 and 2018. It is known from rejection ratios thatthe most inefficient time with the considerably high conditional rejection ratios very close to 1 was around2008. Moreover, SZSEC is more sensitive to information and therefore may be more appealing to investors.
Fourth, there is no strong evidence indicating that strategies of higher return exiting when information setchanges. Conclusions from different information sets about inefficient markets and investment timing are thesame and the information contained in one certain market seems more important. Moreover, when market
extends in size the level of market efficiency declines.
Fifth, the change trend of volatility is consistent with the results of hypothesis tests to some extent. Around2008 and 2015, the volatilities were much higher and the level of market efficiency declined. Around 2011
and 2013, volatilities were much lower but there were strategies indicating inefficient market, which meansthat volatility is not a good criterion for market efficiency. From volatility value it is the time to think about
doing some strategies.
Two problems are proposed for future study. First, as we said above the substitutes of elements in (4) may
not be proper. We expect to find other proper substitutes. Second, yearly volatility is not a good criterion for29

market efficiency. We want to find if there are some other criteria which have closer relationship with market
efficiency and are easier for investors to make judgement.
In the end, it is an interesting topic that 2008 is a mysterious year containing a lot of phenomena andproblems. We hope to find more interesting things and if possible reasonable answers to these phenomena
and problems.

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