International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6
ISSN: 22263624
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Comparative Efficiency in Emerging Stock Markets: The
Case of Dhaka Stock Exchange (DSE) and Chittagong
Stock Exchange (CSE)
Mohammad Bayezid Ali Assistant Professor, Department of Finance, Jagannath University,
Dhaka, Bangladesh. Email: [email protected]
Abstract
This paper examines the comparative efficiency to identify any discrepancy in stock prices
between Dhaka Stock Exchange (DSE) and Chittagong Stock Exchange (CSE) between February
2004 and August 2010. Daily, weekly as well as monthly stock price data from DSE and CSE have
been used to test whether they exhibit price behavior that resemble to random walk
hypothesis (RWH). Based on descriptive statistics, CSE stock prices are found to be more
volatile than DSE stock prices. Estimates of LjungBox Qstatistics provide that autocorrelation
exists in both DSE and CSE stock prices up to lag 10. Stationarity test provides that DSE and CSE
stock price are nonstationary time series at level but becomes stationary at their first
differenced form. Finally multiple variance ratio tests reveal that, with few exception, DSE and
CSE stock prices fails to exhibit random walk at daily and weekly data series. But for monthly
data, both stock prices follow random walk.
Key Words: Random Walk, Autocorrelation, Stock price, Variance Ratio Test.
JEL Classification: G11, G12, G14.
1.0 Introduction
The behavior of economic times series such as stock price has long been of interest to
researchers because of its implication on capital formation, wealth distribution and investors
rationality. The development of the stock market, along with many ways, can be measured in
terms of efficiency yardstick which argued that stock prices in the stock exchange is said to be
efficient if it can adjust very quickly and instantaneously with all relevant available information.
In such a situation, it is nearly impossible to gain above average return by applying strategic
trading rules. Efficiency in stock market requires to satisfy certain essential prerequisites like
availability of relevant information, frequent trading activity, sophisticated and developed
trading mechanism, large number of listed securities, high liquidity, presence of large number
of rational and risk averse investors, least brokerage and commission cost, relatively stable
International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6
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price level of stocks etc. when all these factors meet together, they can reasonably guarantee
that stock prices will react very quickly on the availability of any new information and the
behavior of stock prices can be explained by the arrival of any new information not by their
historical prices. When stock prices are information efficient, it also contributes to bring
operational efficiency and allocational efficiency in the stock market. This study is intended to
examine the comparative efficiency of two different stock exchanges in Bangladesh: Dhaka
Stock Exchange (DSE) and Chittagong Stock Exchange (CSE). The behaviors of two different
stock price indices (i.e. DSE Gen index and CSCX) have been examined to identify whether their
return distribution is independent or they exhibit some dependency on their past return.
1.1 Objectives
The main objective of this study is to examine the comparative pricing efficiency of stock prices
at Dhaka Stock Exchange (DSE) and Chittagong Exchange (CSE). The other objectives include:
i. Examine the development status of DSE and CSE. ii. Identify the comparative behavior of stock prices in DSE and CSE.
iii. Investigate whether the DSE and CSE stock prices follow random walk characteristics or not.
1.2 Review of Literature
Although the controversy relating to the random walk behavior of stock prices started after the
submission of Ph.D. thesis of Bachelier (1900) the issue is still vicinity of finance literature.
However, the classification of market efficiency did not emerge until 1959 (Robert, 1959).
Thereafter, we see a large volume of literature on the subject using different models. The most
general of these is the ‘fair game’ model. The ‘submartingale’ and ‘random walk’ models are
two special cases of the fair game model. The submartingale model shows that the expected
values of tomorrow’s share price in an efficient market should be equal to or greater than
today’s price. The random walk model, more familiar in the area of efficient market research
explains market efficiency in terms of lack of dependency between successive price movements
(Ahmed, 2002).
Ayadi and Pyun (1994) have applied Lo and Mackinlay (1988) variance ratio test methodology
to investigate the random walk characteristics in Korean Securities Market between 1984 and
1988. Daily, weekly and monthly data series have been used under homoskedastic and
heteroskedastic increments test assumptions to estimate variance ratio test statistics. They
have concluded that random walk hypothesis is rejected when daily data are used. But when
longer horizons such as weekly, monthly and 60day data are used, the random walk hypothesis
is not rejected.
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Chang and Ting (2000) have examined the VR test in Taiwan’s Stock Market from 1971 to 1996.
They have found that weekly valueweighted market index do not follow random walk
characteristics. They also found that RWH can not be rejected with monthly, quarterly and
yearly valueweighted market index.
Darrat and Zhong (2000) have tested RWH in stock indexes of two Chinese Stock Exchanges:
Shanghai and Shenzhen. They have used class ‘A’ share index from both stock exchanges and
collect daily data from Dec 20, 1990 to Oct 19, 1998 for Shanghai Exchange and April 4, 1991 to
Oct. 19, 1998 for Shenzhen Exchange. They have found that weekly VR test estimates are
statistically significant for lag 2, 4, 8 but not for lag 16 and 32 for Shanghai Stock Market. On the
other hand, for Shenzhen Stock Market weekly VR test estimates are statistically significant for
lag 2, 4, 8, 16 but not for lag 32.
Smith et al. (2002) have used ChowDenning multiple variance ratio test to examine the RWH
of 8 different African stock market index. They found that except South Africa, other countries
i.e. Egypt, Kenya, Morocco, Nigeria, Zimbabwe, Botswana and Mauritius stock market do not
follow random walk.
Ahmed (2002), have examined market efficiency of Dhaka Stock Exchange (DSE) by applying
LjungBox Qstatistics. Daily, weekly and month stock returns between January 1990 and April
2001 have been incorporated in that study and the test result reveals that positive
autocorrelations in the return series is dominant which actually result rejection of random walk
in the data series. He finally concluded that the behavior of DSE stock prices cannot be
described as obeying the random walk theory rather price behavior follows some dependencies
and from this point of view, DSE is said to be inefficient stock market.
Smith and Ryoo (2003) have tested the hypothesis of random walk in the stock market price
indices for five European Emerging Markets, using multiple variance ratio tests. Weekly data
has been employed from the 3rd week of April 1991 to the ending of the last week of August
1998 in four of the markets: Greece, Hungary, Poland, and Portugal, the null hypothesis of
random walk is rejected because returns have autocorrelated errors. In Turkey, however, the
Istanbul Stock Market follows random walk. They have explained that because of the largest
and the most liquid market, it provides an evidence of RWH.
Rahman, Uddin and Salat (2008), have examined the random walk hypothesis on Dhaka Stock
Exchange (DSE) general index (DSE Gen) for the period between January 1991 and December
2006. They have applied different econometric tools like autocorrelation test, JB normality
test, KS goodness of fit test and Stationary test. They concluded that return series deviates
from normal distribution and evidence of statistical dependence among the values. They also
found that data series is stationary and does not follow random walk.
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Hamid et al. (2010), have studied the weak form market efficiency of the stock market returns
of Pakistan, India, Sri Lanka, China, Korea, Hong Kong, Indonesia, Malaysia, Philippines,
Singapore, Thailand, Twaiwan, Japan and Australia. Monthly data have been used for the period
of January 2004 to December 2009. Autocorrelation, LB Q statistics, Run test, Unit Root test,
and Variance Ratio test have been employed to test the hypothesis that stock prices follow
random walk. They have concluded that monthly prices do not follow random walks in all the
countries of the Asia Pacific region.
Uddin et al. (2011) has examined the weak form efficiency of the Chittagong Stock Exchange
(CSE) in Bangladesh using daily data of two different indices for the period between January 01,
2001 and December 30, 2008. Unit root test and variance ratio test have been applied to
examine whether the indices follow a random walk and whether returns are predictable. The
test result reports that both the price series are nonstationary process, increments of the
associated return series are serially correlated. Finally, based on variance ratio test, they have
concluded that Chittagong Stock Exchange is not weak form efficient.
AlJafari and Kadim (2012) have applied variance ratio test to examine the RWH in Bahrain
Bourse. They have used daily data from February 2003 to November 2010 and under
homoskedastic and heteroskedastic test assumption for lag 2, 4, 8, 10, 16, and 32 they have
found that daily stock index does not conform to RWH.
AlAhmed (2012) examines the weak form efficiency of the Damascus Securities Exchange
(DSE). Daily returns of the DWX Index from 31st December 2009 to 30th November 2011 have
been used and unit root test and variance ratio test have been employed to test the hypothesis
that stock prices follow random walk. All the test estimates reveal that stock prices on DSE do
not follow random walk.
2.0 Microstructure of Stock Exchanges in Bangladesh
Bangladesh stock markets are represented by two stock exchanges viz. Dhaka Stock Exchange
(DSE) and Chittagong Stock Exchange (CSE). Both DSE and CSE are corporate bodies under
Companies Act 1994. Although DSE was first established in 1954, its activities were suspended
for a brief period of from 1971 to 1976. DSE resumed its activities in the middle of 1976 with
the change of government policy. DSE started functioning with 9 listed companies in 1976,
however the number has reached to 224 on June 30, 2001 and 513 on July 30, 2012. CSE
started its activities in 1995. On the other hand CSE started its journey with 61 listed securities
in 1995 which reached to 212 in 2006 and 251 in June, 2012.
The activities of DSE can be visualized from Table: 1. The data on annual growth of trading
volume, growth of trading value and growth of market capitalization from 198687 to 201011
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has been presented. It appears that annual growth in trading volume is significantly positive in
19 years out of 25 sample years and the average growth is found to be 104.76 percent between
1986 and 2011. In the same way, annual growth in trading value corresponds with the annual
growth in trading volume in terms of their nature of growth. It is found that the average annual
growth in trading value is 105.61 percent between 1986 and 2011. Annual growth in market
capitalization also found to be significantly increasing in 20 different years out of 25 sample
years and the average growth is found to be 39.51 percent. A satisfactory number of IPOs is
also found from 199394 50 201011 except in the year 199899 and 200405.
Table 1: Development of Dhaka Stock Exchange (DSE)
Year Growth in
Trading Volume (%)
Growth in
Trading Value (%)
Growth in Market
Capitalization (%) No. of IPO
198687 187.91 343.48 64.07
198788 44.17 20.71 121.1
198889 54.69 27.71 6.99
198990 61.64 21.65 11.35
198991 16.41 24.76 10.34
199192 69.88 84.78 19.53
199293 12.94 54.59 19.5
199394 167.65 505.26 107.86 4
199495 124.46 8.92 49.69 24
199596 72.66 208.14 35.78 22
199697 166.33 331.92 61.5 23
199798 17.62 64.37 42.37 12
199899 1,254.38 311.3 18.94 5
199900 50.57 46.63 10.07 10
200001 65.28 76.93 33.63 7
200102 14.59 29.07 12.52 11
200203 12.83 12.77 9.61 9
200304 51.13 19.61 97.46 13
200405 78.54 208.94 62.5 2
200506 37.69 39.19 2.98 15
200607 232.76 256.7 120.89 11
200708 90.28 230.61 95.65 14
200809 52.81 63.78 33.33 12
200910 76.13 187.93 117.57 16
201011 95.04 27.72 4.3 14
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Table: 2 present the activities of CSE from 2005 to 2011. Annual growth in total trade is found
to be positive in every year except 2011 and their average growth is 49.70 percent during the
period. Significant growth in annual trading volume and trading value data is also found and
their average growth is 121.58 and 59.61 respectively. Annual growth in market capitalization is
found to be positive in different years except 2011 and their average growth is 48.24 percent.
From this analysis, it is revealed that trading volume growth significantly higher than trading
value and market capitalization which indirectly represent the liquidity of the stock market.
Table 2: Development of Chittagong Stock Exchange (CSE)
Year Growth in
Total Trade (%)
Growth in
Total Volume (%)
Growth in
Total Value (%)
Growth in Market
Capitalization (%)
2005 26.05863 34.2497 0.725951 3.304627167
2006 25.323 257.8037 113.0622 21.39656926
2007 47.17068 71.9552 29.60647 127.9048444
2008 141.4072 356.4046 173.7692 30.03477948
2009 11.25871 1.12717 61.67877 87.85781663
2010 156.2768 401.9184 113.7999 100.3650364
2011 59.5617 57.7166 75.4038 33.18110081 Note: Authors own calculation based on data compiled from various CSE publications.
Figure: 1 shows the comparative monthly trend of DSE Gen index and CSCX index from February
2004 to August 2010. It is important to mention than although base index for CSCX index (i.e.
1000 as on April 15, 2001) is higher than DSE Gen index (i.e. 817.63704 as on November 24,
2001), CSCX index seems to be more volatile than DSE Gen index throughout the period under
study.
Monthly DSEGEN
Monthly CSCX

5,000.00
10,000.00
15,000.00
20,000.00
25,000.00
Feb
04
Jun
04
Oct
04
Feb
05
Jun
05
Oct
05
Feb
06
Jun
06
Oct
06
Feb
07
Jun
07
Oct
07
Feb
08
Jun
08
Oct
08
Feb
09
Jun
09
Oct
09
Feb
10
Jun
10
Ind
ex v
alu
e
Figure 1: Trend of DSE Gen and CSCX Indices
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3.0 Research Methods
This study is intended to identify the comparative pricing efficiency of stock prices held in
Dhaka Stock Exchange (DSE) and Chittagong Stock Exchange (CSE). In this case DSE general
index from DSE and CSCX index from CSE has been chosen to examine their comparative pricing
efficiency. Here pricing efficiency implies informational efficiency which denotes that stock
prices quickly and instantaneously reflects all relevant information that is available about the
intrinsic value of that asset. And it is commonly believed that in an efficient market, stock prices
tends to follow random walk which means price movements are independent and past stock
prices cannot be used to predict stock prices in the future. Therefore different statistical and
econometric tools like descriptive statistics, autocorrelation test, LjungBox Qstatistics and Lo
Mackinlay (1988) and ChowDenning (1993) variance ratio test have been employed to examine
and compare the relative stock price behavior at DSE and CSE.
3.1 Descriptive Statistic
Descriptive Statistics for the stock returns includes the arithmetic mean, median, maximum
value, minimum value, standard deviation, skewness, and kurtosis. In this estimates the value
of mean explain the simple average of all the data in time series, median implies the middle
value, maximum and minimum value implies the largest and smallest value respectively in the
data series; standard deviation represent the average spread of all the data from its mean
value. The skewness measures whether the distribution of the data is symmetrical or
asymmetrical. Positive skewness value of the all variables indicates that distribution of all the
data series has a long right tail. On the other hand kurtosis measures the peakedness and
flatness of the distribution of the series.
3.2 Autocorrelation Test
Autocorrelation is used to test the relationship between the time series of its own values at
different lags. In this paper we have used Ljung Box (LB) Qstatistics (1978) which is widely
used to test autocorrelation in different time series. This test is an improvement of BoxPierce
Qstatistic of 1970. The LB Qstatistic sets out to investigate whether a set of correlation
coefficients calculated at various lags for returns of time series may be deemed to be
simultaneously equal to zero (Gujarati, 1995). LjungBox test also provides a superior fit to the
chisquare distribution for little samples. The LB Qstatistic at lag k is a test statistic for the null
hypothesis that there is not autocorrelation up to order k and is computed as
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k
j
j
LBjT
TTQ1
2
)2(
Where the jth autocorrelation and T is is the number of observations. If the series is not
based upon the results of ARIMA estimation, then under the null hypothesis, Q is asymptotically
distributed with degrees of freedom equal to the number of autocorrelations.
3.3 Unit Root Test
Phillips and Perron (1988) propose an alternative nonparametric method of controlling for
serial correlation in the error terms without adding lagged difference terms. The PP method
estimates the nonaugmented DF test equation and modifies the tratio of the α coefficient so
that the serial correlation does not affect the asymptotic distribution of the test statistics. The
PP test is based on the following statistics:
Where is the estimate, and t is the tratio of the )( se is the coefficient standard error,
and s is the standard error of the test regression. In addition, 0 is a consistent estimate of
the error variance in the following ADF test equation:
The remaining term, 0f is an estimator of the residual spectrum at frequency zero. Under the
null hypothesis that 0 , the PP test statistics have the same asymptotic distribution as the
ADF tstatistics.
3.4 Variance Ratio Test
Variance ratio tests have been widely used and are particularly useful for examining the
behavior of stock price indices in which returns are frequently not normally distributed. These
tests are based on the variance of returns and have good size and power properties against
interesting alternative hypotheses and in these respects are superior to many other tests
(Campbell et al. 1997) Consider the following random walk with drift process:
ttt pp 1 ………..….(1)
sf
sefT
ftt
21
0
00
21
0
0
2
))()((
tttt xYy 1
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Or
ttp …………………(2)
In which tp is the stock price index, is an arbitrary drift parameter and t is a random
disturbance term. The t satisfy 0tE , and 0,0, gE gtt , for all t. the random walk hypothesis has two implications: uncorrelated residuals and a unit root. Variance ratio test
focus on uncorrelated residuals and are preferable to unit root tests for two reasons: the latter
focus on establishing whether a series is difference stationary or trend stationary (Campbell et
al. 1997) and are known to have very low power and can not detect the departures from the
random walk, Shiller and Perron (1985), Hakkio (1986) and Gonzalo and Lee (1996). This
contrasts with the multiple variance ratio tests which has good size and power properties,
Chow and Denning (1993).
With uncorrelated residuals and hence uncorrelated increments in tp , the variance of these
increments increases linearly in the observation interval,
)()( 1 ttqtt ppqVarppVar ……………(3)
in which q is any positive integer. The variance ratio is given by
)1(
)(
)(
)(1
)(2
2
1
q
ppVar
ppVarq
qVRtt
qtt
………….….(4)
And under the null hypothesis VR(q) =1.
Lo and Mackinlay (1988) generates the asymptotic distribution of the estimated variance ratios
and derive two test statistics Z(q) and Z*(q), under the null hypothesis of homoskedastic
increments random walk and heteroskedastic increments random walk respectively. If the null
is true then the associated test statistic has an asymptotic standard normal distribution. Their
test statistics are both flexible and simple to compute. However, Lo and Mackinlay approach
focuses on testing individual variance ratios for a specific aggregation interval, q, but the
random walk hypothesis requires that VR(q)= 1 for all q. The multiple variance ratio (MVR) tests
provide a joint test through controlling the size of the test.
Chow and Denning (1993) provide a procedure for the multiple comparison of the set of
variance ratio estimates with unity. For a single variance ratio test, under the null hypothesis,
VR(q)= 1 and hence .01)()( qVRqMr Now consider a set of m variance ratio tests
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},......2,1)({ miqM r associated with the set of aggregation intervals },......2,1{ miq . Under
the random walk null hypothesis there are multiple subhypotheses.
0)(: qiMH roi for all i =1,2,…….m
0)(: qiMH rli for any i =1,2,…….m ………(5)
Rejection of any one or more oiH rejects the random walk null hypothesis. Consider a set of Lo
and Mackinlay test statistics, say Z(q), },......2,1)({ miqZ i . Since the random walk null
hypothesis is rejected if any of the estimated variance ratios is significantly different from one,
it is only necessary to focus on the maximum absolute value in the set of test statistics. The
core of Chow and Denning’s MVR test is based on the result
1)];;())(,........)([max( TmSMMqZqZPR mi ……..(6)
In which );;( TmSMM is the upper point of the Studentized Maximum Modulus (SSM)
distribution with parameter m and T (sample size) degrees of freedom. Asymptotically, when T
is indefinite,
2/*);;( ZTmSMM ……………..(7)
in which m1
* )1(1 . Chow and Denning control the size of a MVR test by comparing the
calculated values of the standardized test statistics, either )(qiZ or Z*(qi), with the SSM critical
values. If the maximum absolute value of, say, Z(qi), is greater than SSM critical value at a
predetermined significance level then the random walk hypothesis is rejected.
3.5 Sample Size and Data Sources
This study incorporates DSE Gen Index from Dhaka Stock Exchange (DSE) and CSCX Index from
Chittagong Stock Exchange (CSE) to examine their relative pricing efficiency. For both stock
prices, daily, weekly and monthly stock price data have been collected from February 2004 to
December 2011. After then the period of 16 months (i.e. from September 2010 to December
2011) data have been trimmed because of abnormal stock price behavior during that period. In
this case DSE Gen Index data have been collected from Research and Publication Division of
Dhaka Stock Exchange (DSE). On the other hand, CSCX index data have been collected from the
official web sites of Chittagong Stock Exchange (CSE).
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4.0 Empirical Result
4.1Summary of Descriptive Statistics
The descriptive statistics for CSE and CSE stock price have been presented in Table: 3. It is found
that the mean and median value for DSE stock prices is smaller than CSE stock prices. Maximum
and minimum value also shows the same tendency. The estimates of standard deviation reveal
that CSE stock prices are distributed far away from its mean value than DSE stock prices. This
result indirectly explains that CSE stock prices are more volatile than DSE stock prices. Positive
skewness value for DSE as well as CSE stock prices indicates that they all have a long right tail.
Finally, daily, weekly and monthly data for DSE and CSE stock prices are found to be more
peaked than normal curve i.e. leptokurtic.
Table 3: Descriptive Statistics
Note: Author’s Own Estimation
4.2. Estimates of Autocorrelation Test
The estimates of autocorrelation and LjungBox (LB) Qstatistics are presented in Table: 4. The
pvalues of autocorrelation and LB Qstatistics at the level data indicate we cannot accept null
hypothesis from lag 1 to 10 at 5 percent significance level. Therefore it is inferred that the
historical returns can be used to predict future returns. Basically the null hypothesis for random
walk is rejected if the autocorrelation contains the positive coefficients over different lags. The
further analysis requires that whether the time series is nonstationary or stationary.
Statistical
Estimates
DSE Gen Index CSCX Index
Daily Weekly Monthly Daily Weekly Monthly
Mean 2499.299 2532.993 2538.726 4349.270 4453.674 5909.790
Median 1950.556 2005.000 2003.580 2753.500 3250.040 5059.730
Maximum 6777.957 6743.207 6657.975 12967.94 12937.77 15664.37
Minimum 934.9537 946.3594 953.8100 6.940000 1146.290 1155.700
Std.
Deviation 1334.896 1347.457 1359.613 2863.895 2890.414 3854.724
Skewness 1.575316 1.539827 1.537427 1.281709 1.227221 0.666663
Kurtosis 4.894161 4.757835 4.697706 3.919718 3.761829 2.319044
Observations 1612 300 79 1619 301 103
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Table 4: Estimates of Autocorrelations between DSE Gen and CSCX Indices
Note: Author’s own estimation
4.3. Estimates of Stationary Test
The estimates of stationary test based on PhillipsPerron (PP) methodology has been
presented in Table: 5. Different time horizon data like, daily, weekly and monthly data for DSE
Gen index and CSCX index has been used in this test. The estimated result is very similar for
Lag Order of
Estimates
DSE Gen Index CSCX Index
Daily Weekly Monthly Daily Weekly Monthly
1
AC
QStat
Prob.
0.996
1602.7*
(0.000)
0.980
290.96*
(0.000)
0.920
69.380*
(0.000)
0.997
1610.8*
(0.000)
0.983
293.65*
(0.000)
0.970
100.61*
(0.000)
2
AC
QStat
Prob.
0.992
3194.1*
(0.000)
0.958
570.07*
(0.000)
0.842
128.32*
(0.000)
0.993
3212.1*
(0.000)
0.964
577.31*
(0.000)
0.948
196.91*
(0.000)
3
AC
QStat
Prob.
0.989
4774.3*
(0.000)
0.936
837.46*
(0.000)
0.763
177.36*
(0.000)
0.990
4803.9*
(0.000)
0.946
851.18*
(0.000)
0.921
288.73*
(0.000)
4
AC
QStat
Prob.
0.985
6343.2*
(0.000)
0.915
1093.7*
(0.000)
0.679
216.67*
(0.000)
0.987
6385.9*
(0.000)
0.928
1115.6*
(0.000)
0.894
376.12*
(0.000)
5
AC
QStat
Prob.
0.981
7900.7*
(0.000)
0.895
1339.5*
(0.000)
0.603
248.10*
(0.000)
0.983
7958.3*
(0.000)
0.911
1371.3*
(0.000)
0.866
458.93*
(0.000)
6
AC
QStat
Prob.
0.977
9446.2*
(0.000)
0.873
1574.4*
(0.000)
0.523
272.08*
(0.000)
0.980
9520.4*
(0.000)
0.893
1618.0*
(0.000)
0.840
537.58*
(0.000)
7
AC
QStat
Prob.
0.973
10980*
(0.000)
0.852
1798.7*
(0.000)
0.439
289.24*
(0.000)
0.976
11072*
(0.000)
0.876
1856.3*
(0.000)
0.816
612.59*
(0.000)
8
AC
QStat
Prob.
0.968
12501*
(0.000)
0.829
2012.0*
(0.000)
0.357
300.75*
(0.000)
0.973
12614*
(0.000)
0.859
2085.8*
(0.000)
0.794
684.34*
(0.000)
9
AC
QStat
Prob.
0.964
14011*
(0.000)
0.808
2215.0*
(0.000)
0.300
308.97*
(0.000)
0.969
14145*
(0.000)
0.842
2307.3*
(0.000)
0.760
750.76*
(0.000)
10
AC
QStat
Prob.
0.960
15508*
(0.000)
0.785
2407.5*
(0.000)
0.244
314.49*
(0.000)
0.960
15667*
(0.000)
0.824
2520.2*
(0.000)
0.723
811.50*
(0.000)
International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6
ISSN: 22263624
249 www.hrmars.com
both of this two Indexes i.e. daily, weekly and monthly data for both of these two indices are
found to be nonstationary at I(0) that means unit root exist in level data. But the presence of
unit root is eliminated in I(1) process. It implies that all the data in different time horizon
becomes stationary at the first differenced form.
Table 5: Estimates of PP Test between DSE Gen and CSCX Indexes
Stock Indexes Data Types PP Test
at Level Data
PP Test at
1st Differenced Data
DSE Gen
Index
Daily 0.974342
(0.9999)
39.16381
(0.0000)
Weekly 0.468913
(0.9992)
15.07102
(0.0000)
Monthly 0.211142
(0.9978)
8.033308
(0.0000)
CSCX
Index
Daily 1.050464
(0.9999)
49.44785
(0.0000)
Weekly 0.849102
(0.9998)
14.21916
(0.0000)
Monthly 1.635583
(0.7720)
9.770144
(0.0000) Note: The value within parentheses presents p value for adj.tstatistics.
4.4. Estimates of Variance Ratio test
The randomness of daily, weekly as well as monthly data for DSE Gen index and CSCX index has
been estimated and presented in appendix1. ChowDenning multiple variance ratio test and
LoMackinlay variance ratio test for lag 2, 4, 8, and 16 have been estimated where data series
are assumed to follow random walk under null hypothesis. When we consider DSE Gen daily
index, null hypothesis cannot be accepted at 5 percent level of significance under
homoskedastic error terms but for heteroskedastic increments error terms we cannot reject
null hypothesis at 5 percent level. For CSCX daily index, when we assume homoskedastic error
terms, null hypothesis cannot be accepted at 5 percent significant level. But for heteroskedastic
error terms, we cannot reject null at 5 percent level. This result is also supported by Lo
Mackinlay individual lag variance ratio test for lag 2, 4, 8, and 16.
When we consider weekly data, DSE Gen index are found to be nonrandom in both
homoskedastic and heteroskedastic increments test assumption. Under homoskedastic
increments test assumption, CSCX weekly index is found to be nonrandom at 5 percent
International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6
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significant level, but we cannot reject null hypothesis of random walk under heteroskedastic
increments test assumption.
In the case monthly data, both DSE Gen index and CSCX index are found to follow random walk
at 5 percent level of significance in both homoskedastic and heteroskedastic increments test
assumption. So it can be concluded that DSE Gen index does not follow random walk at 10
percent level in short horizon data (i.e. daily and weekly index) but for longer time horizon like
monthly data, the same index is found to follow random walk. The presence of autocorrelation
that is induced by to over shooting and under shooting of prices and nonsynchronous or
infrequent trading is very obvious in case of emerging stock market like DSE. According to Lo
and Mackinlay (1988), small capitalization stocks trade less frequently than larger stocks. As a
result, new information is impounded first into large capitalization stock prices and then into
smaller capitalization stock prices with lag. This lag subsequently, induces a positive
autocorrelation in short horizon stock price data. But the impact of new information gradually
eliminates when the time horizon increases.
However, CSCX daily and weekly index under homoskedasticity error terms is nonrandom but
for monthly data it follows random walk. On the other hand, under heteroskedasticity error
terms, CSCX index have been appeared to follow random walk in daily, weekly and monthly
data. This result can be explained as availability of information may be more symmetrical in CSE
rather than DSE. This may be due to the fact that CSE is considered to be sophisticated stock
exchange than DSE and advanced trading environment can also be found over there. According
to the findings of of Shleifer (2000), we can conclude that the variance ratio test result for CSCX
could be attributed by any one of the following three reasons:
i. Investors are rational and hence value securities rationally. ii. Some investors are irrational but their trades are random and cancel each other out.
iii. Some investors are irrational but rational arbitrageurs eliminate their influence on price.
5.0. Findings and Conclusion
This study investigates the comparative market efficiency in Dhaka Stock Exchange (DSE) and
Chittagong Stock Exchange (CSE) through examining pricing behavior of DSE Gen index and
CSCX index. Different econometric tools have been employed to test whether these two
indexes exhibit the same pricing behavior or not. In analyzing descriptive statistics, DSE stock
prices are found to be less volatile than CSE stock prices. Both of these stock prices are
influenced by their past prices and therefore null hypothesis of LB Qstatistics cannot be
accepted at 5 percent significance level. Stationary test provides that unit root existed in level
data for both of these two indices but the data set becomes stationary at its first differenced
International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6
ISSN: 22263624
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form. Multiple variance ratio tests reveals that under homoskedastic error terms daily and
weekly DSE Gen and CSCX do not follow random walk but for monthly data they do follow
random walk. Under heteroskedastic error terms, CSCX index is found to be more random than
DSE Gen Index for daily data set. For weekly data DSE Gen index is not following random walk
where CSCX does. For monthly data set both indexes are found to be random at 5 percent
significance level. Therefore in the case of chowDenning (1993) multiple variance ratio test and
LoMaclinlay (1988) individual lag variance ratio test gives us slightly different result between
two indexes and based on that result we can say that CSCX seems to be more random than DSE
Gen index for daily, weekly and monthly data set.
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Appendix1
ChowDenning Multiple Variance Ratio Test Estimates (Daily Data between February 2004 and August 2010)
Stock Indexes
Test Estimates Homoskedastic Assumption
Heteroskedastic Assumption
DSE GEN
Studentized Max z Statistic @ 5 percent level 3.113713 2.306427
Probability 0.0074 0.0817
CSCX Studentized Max z Statistic @ 5 percent level 20.02391 0.999300
Probability 0.0000 0.7832
ChowDenning Multiple Variance Ratio Test Estimates
(Weekly Data between February 2004 and August 2010)
Stock Indexes
Test Estimates Homoskedastic Assumption
Heteroskedastic Assumption
DSE GEN
Studentized Max z Statistic @ 5 percent level 3.789194 3.756717
Probability 0.0006 0.0007
CSCX Studentized Max z Statistic @ 5 percent level 2002391 0.999300
Probability 0.0000 0.7832
ChowDenning Multiple Variance Ratio Test Estimates (Monthly Data between February 2004 and August 2010)
Stock Indexes
Test Estimates Homoskedastic Assumption
Heteroskedastic Assumption
DSE GEN
Studentized Max z Statistic @ 5 percent level 1.838711 1.821142
Probability 0.2389 0.2474
CSCX Studentized Max z Statistic @ 5 percent level 0.687514 0.651919
Probability 0.9333 0.9444
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LoMacKinlay Individual Lag Variance Ratio Estimates (Daily Data between February 2004 and August 2010)
Stock Indexes
Test Estimates
Homoskedastic Test Assumption
Heteroskedastic Test Assumption
2 4 8 16 2 4 8 16
DSE GEN
Var. Ratio 1.077 1.063 1.151 1.295 1.077 1.063 1.151 1.295
ZStatistic 3.113 1.354 2.054 2.693 2.257 0.997 1.607 2.364
Prob. 0.001 0.175 0.039 0.007 0.024 0.318 0.107 0.021
CSCX
Var. Ratio 0.502 0253 0.130 0.069 0.502 0.253 0.130 0.069
ZStatistic 20.0 16.0 11.8 8.50 0.99 0.99 0.99 0.49
Prob. 0.000 0.000 0.000 0.000 0.317 0.318 0.318 0.319
LoMacKinlay Individual Lag Variance Ratio Estimates (Weekly Data between February 2004 and August 2010)
Stock Indexes Test Estimates
Homoskedastic Test Assumption
Heteroskedastic Test Assumption
2 4 8 16 2 4 8 16
DSE GEN
Var. Ratio 1.149 1.310 1.558 1.964 1.149 1.310 1.558 1.964
ZStatistic 2.585 2.873 2.266 3.789 2.194 2.623 3.187 3.756
Prob. 0.009 0.004 0.001 0.000 0.028 0.008 0.001 0.000
CSCX
Var. Ratio 0.502 0.238 0.130 0.069 0.502 0.253 0.130 0.069
ZStatistic 20.0 16.0 11.8 8.50 0.99 0.99 0.99 0.99
Prob. 0.000 0.000 0.000 0.000 0.317 0.318 0.318 0.319
LoMacKinlay Individual Lag Variance Ratio Estimates (Monthly Data between February 2004 and August 2010)
Stock Indexes Test Estimates
Homoskedastic Test Assumption
Heteroskedastic Test Assumption
2 4 8 16 2 4 8 16
DSE GEN
Var. Ratio 1.03 1.25 1.61 1.29 1.03 1.25 1.61 1.29
ZStatistic 0.318 1.22 1.83 0.59 0.32 1.19 1.82 0.61
Prob. 0.750 0.22 0.06 0.54 0.74 0.23 0.06 0.53
CSCX
Var. Ratio 1.005 1.08 1.20 1.18 1.00 1.08 1.20 1.18
ZStatistic 0.058 0.45 0.68 0.43 0.04 0.39 0.65 0.43
Prob. 0.953 0.64 0.49 0.6 0.96 0.69 0.51 0.66
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