2 . Review of Literature on Weak Form Market Efficiency
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MacKinlay (1988), Worthington et al. (2004). And the variance ratio test also used
by Dockery and Vergari (1997), Grieb and Reyes (1999); Alam et al. (1999); Chang
et al. (2000); Cheung et al. (2001); Abraham et al. (2002); Seddighi et al. (2004),
Loc (2006), Hafiz et al (2007). In this study we use all tests that mentioned above
(Run test, serial correlation, and variance ratio test, regression test, ARCH;
GARCH(1,1)) to enhance the findings of this study.
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1
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Evidence from developed markets
The empirical papers in developed markets generally have similar conclusions that
support the weak form efficiency. Groenewold (1997) conducts weak and semi
strong efficiency tests of Australian stock market by using aggregate share price
indexes and finds that the results are consistent with the weak form efficiency. In
addition, Hudson et al (1996) find that the technical trading rules have predictive
power but not sufficient to enable excess return in United Kingdom market.
Lee (1992) employs variance ratio test to examine whether weekly stock returns of
the United States and ten industrialized countries: Australia, Belgium, Canada,
France, Italy, Japan, Netherlands, Switzerland, United Kingdom, and Germany
follow random walk process for the period from 1967 to 1988. He finds that the
random walk model is still appropriate characterization of weekly return series for
majority of these countries.
Ayadi et al. (1994) apply variance ratio test to examine the efficiency hypothesis of
Korean Stock exchange for the period from 1984 to 1988. Under the assumption of
homoscedasticity, the authors reject the random walk hypothesis. However, under
the heteroscedasticity, they could not reject the random walk for daily data. In
addition, they also employ the weekly, monthly, 60 day and 90 day interval data.
The results also could not reject the random walk hypothesis.
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Chan et al (1997) examine the weak form and the cross country market efficiency
hypothesis of 18 international stock markets, including Australia, Belgium, Canada,
Denmark, Finland, France, Germany, India, Italy, Japan, Netherlands, Norway,
Pakistan, Spain, Sweden, Switzerland, the United Kingdom, and the United States
for the period from 1962 to 1992. They conclude that all stock markets in the
sample are individually weak form efficient and only a small number of stock
markets show evidence of co-integration with others by using Phillips-Peron (PP)
unit root and Johansen’s co-integration tests.
C.Cheung et al.(2001) employ variance ratio tests with both homoscedasticity and
heteroscedasticity to examine random walk hypothesis for Hang Seng Index on
Hong Kong Stock Exchange for period from 1985 to 1997. They conduct that Hang
Seng follows a random walk model and consequently that the index is weak form
efficient.
Worthington et al (2004) investigate random walk in 16 developed markets and four
emerging stock markets for the period from 1987 to 2003. By using various
methods including serial correlation, runs, three types of unit root test and multiple
variance ratio tests, the paper’s result indicates that the random walk hypothesis is
not rejected in major European developed markets. Particular, Germany and
Netherlands are weak form efficient under both serial correlation and runs tests,
while Ireland, Portugal and the United Kingdom are efficient under one test or the
other. Thus, rests of the markets do not follow a random walk. The ADF and
Phillips-Perron unit root tests reject the null hypothesis of random walk in the all 20
emerging and developed markets, while the KPSS unit root tests fail to reject the
null hypothesis excluding the Netherlands, Portugal and Poland. Under the variance
ratio test, the null hypothesis of homoscedasticity and heteroskedasticity are not
rejected in the United Kingdom, Germany, Ireland, Hungary, Portugal and Sweden.
The rejection of the null hypothesis of the homoscedasticity but not the
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heteroscedasticity is found for France, Finland, Netherlands, Norway and Spain.
Among the emerging markets, only Hungary satisfies the strictest requirements for
a random walk in daily returns.
In a more recent research, Kima et al (2008) examine efficiency of stock prices of
group Asian markets. The weekly, daily data from 1990 are considered in this
study. By using new multiple variance ratio tests, it is found that the Hong Kong,
Japanese, Korean and Taiwanese markets are efficient in the weak form. The other
markets of Indonesia, Malaysia and Philippines are shown no sign of market
efficiency. Singapore and Thai markets become efficient after the Asian crisis.
2.2.2. Evidence from developing markets
In contrast with the evidence from developed markets, the findings of weak form
efficiency on developing markets are mixed. Most of developing countries suffer
with the problem of thin trading. In addition, in smaller markets, it is easier for large
traders to manipulate the market. Though it is generally believe that the developing
countries are less efficient. However, the empirical evidence does not always
support this thought. Many papers report weak form efficiency in developing
countries. Lima et al. (2004) employ data of the daily stock price indexes of
Shanghai, Shenzhen (China), Hong Kong, and Singapore Stock exchange over the
period from 1992 to 2000. They find that the Hong Kong and A shares for both the
Shanghai, Shenzhen stocks exchanges are in weak form efficiency.
Dickinson et al. (1994) also examine Nairobi Stock Exchange using the
autocorrelation and runs tests. Their data include weekly prices of the 30 most
actively traded stocks from 1979 to 1989. The results also support the weak form of
Efficient Market Hypothesis in Nairobi Stock Exchange.
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Mojustafa (2004) examines the behavior of stock prices in United Arab Emirate
market by using the nonparametric runs to test randomness. The data consists of
daily prices of 43 stocks for the period from 2001 to 2003. The results reveal that 40
stocks out of the 43 are random. Hence, this supports the weak form Efficiency
Market Hypothesis.
In more recent research, Oskooe et al.(2010) examine the random walk hypothesis
in Iran stock market. By applying Augmented Dickey Fuller, Philip-Perron,
Kwiatkowski, Phillips, Schmidt and Shin and one structural break perron unit root
tests for the period from 1999 to 2009. The results from the various unit root tests
imply that the Iran daily stock price index follow the random walks process.
Many authors, however, argue that markets of the developing countries are in the
weak form inefficiency. Mobarek et al. (2000) study the efficiency of the
Bangladesh Security on the Dhaka Stock Exchange by using the autocorrelation,
run test for the period of 1988 to 1997. Basing on the result of runs and the
autocorrelation tests, the authors argue that the returns of Dhaka stock market do
not follow random walks.
Abeysekera (2001) indicates that the Colombo Stock Exchange (CSE) in Sri Lanka
is weak form inefficient by using the serial correlation, runs and unit root tests for
the period from 1991 to 1996. The findings of three tests consistently reject the
random walk hypothesis. The author also examines a day of the week and month of
the year effect on the CSE, but neither effect found to be on the stock market in Sri
Lanka.
Smith et al.(2003) examine the random walk hypothesis for five medium size
European emerging stock markets by using the multiple variance ratio tests for the
period from 1991 to 1998. The findings of Greece, Hungary, Poland, Portugal
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markets are fail to support the hypothesis of random walk because the returns are
auto correlated. In Turkey, however, the Istanbul stock market follows a random
walk.
Abrosimova et al (2002) test weak form efficiency in Russian stock market ranging
from 1995 to 2001 by employing unit root, autocorrelation and variance ratio tests.
The results of both autocorrelation and variance ratio tests reject the hypothesis of
the random walk for daily and weekly, but not for monthly data. For monthly data,
the variance ratio under assumption of heteroscedasticity increments the hypothesis
of random walk can not be rejected.
Hoque et al. (2007) examine the random walk hypothesis for eight emerging equity
markets in Asia including Hong Kong, Indonesia, Korea, Malaysia, the Philippines,
Singapore, Taiwan and Thailand from 1990 to 2004. The result of variance ratio test
indicates that the stock prices of eight Asian countries do not follow the random
walk with the exceptions of Taiwan and Korea.
Abrim et al.(2009) employ the data of 35 stocks listed in the Palestine Security
stock exchange (hereinafter call PSE) to investigate whether the Palestine Security
stock exchange is of weak form efficiency by using autocorrelation test, unit root
test and run test. This paper’s result indicates that the PSE is inefficient at the weak
from all test results.
The findings from more recent research by Abdmoulah (2010) documents that the
stock market in Arab is not weak form efficiency by using the Garch M (1,1) model
implemented for 11 Arab stock markets including daily prices of the national
indexes of Saudi Arabia, Kuwait, Tunisia, Dubai, Egypt, Qatar, Jordan, AbuDhabi,
Bahrain, Morocco and Oman for periods ending in March 2009.
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Overall, the empirical results from both developed and developing markets show
contrasting evidence on weak form efficiency. Especially, results of whether or not
emerging markets follow a random walk are rather conflicting. Mixed results from
literature on emerging stock markets efficiency are not surprising since it is
observed that emerging stock markets are generally less efficient than developed
markets. In addition, with the characteristic as high level of liquidity and trading
activity, substantial market depth and low information asymmetry, developed
markets are seem to be in the weak form efficiency market while most of
developing markets are characterized as more information asymmetry, lower
volume and frequency of trading (thin trading) and weak institutional infrastructure,
settlement delays, weaker disclosure and accounting requirement, which all together
could cause market inefficiency (Islam et al., 2005). However, not all of developing
markets are necessarily entirely inefficient such as Hong Kong (Lima et al., 2004),
Nairobi Stock Exchange (Dickinson et al., 1994), United Arab Emirate (UAE)
(Moustafa, 2004), Iran stock market (Oskooe et al., 2010).
Although there are many authors study about the market efficiency for both
developed and developing markets. However, there are not many researches
empirically investigating the market efficiency in Vietnam. In lieu of the current
literature, Loc et al. (2010) employ the weekly price of the market index and the
five oldest stocks listed at Ho Chi Minh stock exchange for the period from 2000 to
2004. The result from autocorrelation test, run and variance ratio tests indicate that
the Vietnam stock market is inefficiency in the weak form.
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3. DATA AND METHODOLOGY
3.1. Data Description
The employed data in this study consists of time series (daily and weekly
frequency) of Vietnam stock market index and stock price in real estate and seafood
processing companies for the period from 2007 to 2010. All data is obtained from
electronic database from the website cophieu68.com. A total of 996 daily and 202
weekly observations for market index and individual stock are obtained. Vnindex is
selected as a representative for Vietnam stock market index to be studied in this
research. The stocks in real estate and seafood processing companies are chosen
because stocks in real estate sector are highly sensitive to any change in the
economy while the stocks in seafood processing industry are stable and less
changeable. Hence, some real estate stocks including CII, ITA, SJS, TDH which
listed before 2007 to be selected for studying in this literature. The oldest seafood
processing stocks including ABT, AGF, TS4, FMC also employed in the study as
those stocks listed before 2007 at Hose.
Returns are calculated as Rt = ln( Pt / Pt −1 )
(3.1)
Where Rt is return at time t, Pt and Pt-1 are price at time t and t-1 respectively.
In this study, we follow previous empirical works and employ the most familiar
econometrics methods that used in the literature to test the independence of prices
data. The study applies parametric and non-parametric methods to test the random
walk hypothesis. In particular, we use the parametric serial correlation test which
measures the relationship of the current stock return and its value in the previous
period. We will then use the run test, a nonparametric test, which is computed to
test the randomness of stock return. Furthermore, variance ratio test which is
proposed by Lo and Mackinlay (1988) will be carried out to check whether
uncorrelated increments exist in the series, under the assumption of homoscedastic
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and heteroscedastic random walks. Finally, the OSL, ARCH, GARCH(1,1) models
have been employed in the literature to explore the calendar anomalies existing in
Ho Chi Minh Stock exchange.
Table 3. 1 Descriptive statistics of daily returns
Share
ABT
TS4
FMC
AGF
TDH
SJS
ITA
CII
VNINDEX
Observations 992
990
991
992
992
993
993
993
996
Mean
-0.0001
0.0005
-0.0014
-0.0013
-0.0009
0.0006
-0.0002
0.0003
-0.0004
Median
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
Maximum
0.0489
0.0491
0.0489
0.0488
0.0488
0.0488
0.0488
0.0488
0.0465
Minimum
-0.0513
-0.05156
-0.05856
-0.0513
-0.05133
-0.0513
-0.05132
-0.05129
-0.04802
Std. Dev.
0.0255
0.03434
0.02893
0.02745
0.02866
0.03098
0.02994
0.02764
0.01939
Skewness
0.0018
-0.0113
0.0285
0.0906
0.0801
0.0022
0.0230
0.0192
-0.03244
Kurtosis
2.5786
1.67762
2.08469
2.30382
2.23305
1.90021
2.11803
2.28742
2.92193
Jarque-Bera 7.34030** 72.15447*** 34.72820*** 21.39102*** 25.37381*** 50.04514*** 32.27168*** 21.06988*** 0.42763
Note: ***, ** and * denote a significance level of 1%, 5% and 10% respectively
Table 3. 2 Descriptive statistics of weekly returns
Share
Observations
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
ABT
TS4
201
200
-0.0009
0.0017
0.0000
-0.0087
0.1455
0.2424
-0.2459
-0.2459
0.0640
0.1058
-0.5419
0.1692
4.0181
2.6302
18.5197*** 2.0939
FMC
201
-0.0078
-0.0073
0.2343
-0.2089
0.0715
0.0904
3.8685
6.5908**
AGF
201
-0.0067
-0.0091
0.2113
-0.1671
0.0715
0.3352
3.6033
6.8138**
TDH
201
-0.0042
-0.0095
0.2339
-0.2433
0.0765
0.1837
3.8466
7.1340**
SJS
201
0.0030
-0.0063
0.2276
-0.2427
0.0943
0.1547
2.9262
0.8474
ITA
201
-0.0010
-0.0016
0.2372
-0.1973
0.0844
0.2754
3.4604
4.3161
CII
201
0.0008
0.0000
0.2373
-0.1906
0.0742
0.3171
3.6433
6.8338**
VNINDEX
202
-0.0023
-0.0037
0.1332
-0.1626
0.0538
-0.1065
3.2305
0.8291
Note: ***, ** and * denote a significance level of 1%, 5% and 10% respectively
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Table 3.1 presents a summary of descriptive statistics of the daily returns for
Vnindex and eight individual stocks returns. Sample means, maximums, minimums,
standard deviations, skewness, kurtosis and Jacque-Bera statistics and p-values are
reported. It can be seen that except TS4 (0.0005), SJS (0.0006), CII (0.0003), all
indexes have the negative mean of return. The lowest minimum return is in FMC
(-0.05856) while the highest maximum return is TS4 (0.04905). The standard
deviations of returns range from 0.01939 (Vnindex) to 0.03434 (TS4).
By and large, the statistics shows that the returns of Vnindex and all stocks are not
normal distributed. Given that the parameters skewness and kurtosis represent the
standardised fourth and third moments of a distribution. These parameters are used
with Jarque-Bera statistics to indicate whether a data set is normally distributed or
not. Skewness measures the extent to which a distribution is not symmetric about its
mean value. The skewness of the normal distribution is zero. Positive skewness
means that the distribution has a long right tail and negative skewness implies that
the distribution has a long left tail (Oskooe et al., 2010). Table 3.1 shows that the
returns of all stocks except Vnindex, TS4 are positive skewed although the
skewness statistics are not large. The positive skewness implies that the return of
distributions of the shares traded on the exchanges have a long right tail of large
values and hence a higher probability of earning positive returns.
Moreover, Kurtosis measures the peakness or flatness of the distribution of the
series. The kurtosis of the normal distribution is three. If the kurtosis exceeds three,
the distribution is peaked which is indicating as leptokurtic; if the kurtosis is less
than three, the distribution is flat, this is indicating as platykurtic. The kurtosis value
of all stocks and Vnindex are smaller than three, different from that of a normal
distribution, there by indicating the platykurtic frequency distribution of all stocks
return series.
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Finally, the calculated Jarque-Bera statistics and corresponding p-values in table 3.1
are used to test the null hypothesis that the daily distribution of all stock market
returns is normally distributed. All p-values are smaller than the 0.01 level of
significance suggesting the null hypothesis can be rejected. Therefore, none of these
return series is then well approximated by normal distribution (Chen et al., 2001).
The weekly returns are calculated from the stock prices from Wednesday’s closing
price. If the following Wednesday price is not available, then the Thursday price (or
Tuesday if Thursday is not available) is used. If both Tuesday and Thursday prices
are not available, the return for that week is reported as missing. The choice of
Wednesday price aims to avoid the effects of weekend trading and to minimize the
number of holidays. Table 3.2 presents a summary of descriptive statistics of the
weekly returns for Vnindex and eight individual stocks returns. By the same
analysis with daily return, the weekly returns do not normally distributed.
3.2. Methodology
3.2.1. Auto Correlation Test
Autocorrelation test is the most common test which has been used as the first tool
for testing of either dependence or independence of random variables. The
Autocorrelation measures the correlation coefficient between the values of a
random variable at time t and its value in the previous period. In particular the
autocorrelation measures the relationship between the current stock return and its
value in the previous period. Hence, this test is employed in many empirical studies
(Mobarek et al., 2000, Abraham, 2002, Dickinson et al., 1994, Groenewold, 1997,
Lima et al., 2004, Islam et al., 2005, Loc et al., 2010). It is calculated as:
N −k
ρk =
∑ (r − r )(r
t +k
t
− r)
t =1
(3.2)
N
∑ (r − r )
2
t
t =1
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Where ρk is the serial correlation coefficient of stock returns of lag k; N is the
number of observations; rt is the stock return over period t; rt+k is the stock return
over period t+k; r is the sample mean of stock returns; and k is the lag of the
period.
The test aims to examine whether the autocorrelation coefficients are significantly
different from zero. If the autocorrelation is zero, then the sample of
autocorrelations are approximately normally distributed with mean 0 and variance
1/T. Then this sample autocorrelation can be used to conduct significance tests for
the autocorrelation coefficients in a given confidence interval for an estimated
autocorrelation coefficient to determine whether it is significantly different from
zero. Statistically, the hypothesis of weak form efficiency should be rejected if
stock returns (price changes) are successively correlated (ρk is significantly
different from zero).
To carry out the examination, this study used the Ljung–Box portmanteau statistic
(Q) to test the joint hypothesis that all autocorrelations are simultaneously equal to
zero, has been computed as follow:
k
QLB = N ( N + 2)∑
j =1
Where
ρj
ρ 2j
N−j
(3.3)
th
is the j autocorrelation and N is the number of observations. Under the
null hypothesis of zero autocorrelation at the first k autocorrelations (ρ1 =ρ2 = ρ3 =
. . . = ρk = 0), the Q-statistic is distributed as chi-squared with degrees of freedom
equal to the number of autocorrelations (k).
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