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International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6 ISSN: 2226-3624 237 www.hrmars.com 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 Ljung-Box Q-statistics 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 non-stationary 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 pre-requisites 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

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Page 1: Comparative Efficiency in Emerging Stock Markets: The … · stock price indices (i.e. DSE Gen index and CSCX) have been examined to identify whether their

International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6

ISSN: 2226-3624

237 www.hrmars.com

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 Ljung-Box Q-statistics 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 non-stationary 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 pre-requisites 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

Page 2: Comparative Efficiency in Emerging Stock Markets: The … · stock price indices (i.e. DSE Gen index and CSCX) have been examined to identify whether their

International Journal of Academic Research in Economics and Management Sciences November 2012, Vol. 1, No. 6

ISSN: 2226-3624

238 www.hrmars.com

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 60-day data are used, the random walk hypothesis

is not rejected.

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ISSN: 2226-3624

239 www.hrmars.com

Chang and Ting (2000) have examined the VR test in Taiwan’s Stock Market from 1971 to 1996.

They have found that weekly value-weighted market index do not follow random walk

characteristics. They also found that RWH can not be rejected with monthly, quarterly and

yearly value-weighted 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 Chow-Denning 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

Ljung-Box Q-statistics. 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, J-B normality

test, K-S 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, L-B 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 non-stationary 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.

Al-Jafari 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.

Al-Ahmed (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 1986-87 to 2010-11

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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 1993-94 50 2010-11 except in the year 1998-99 and 2004-05.

Table 1: Development of Dhaka Stock Exchange (DSE)

Year Growth in

Trading Volume (%)

Growth in

Trading Value (%)

Growth in Market

Capitalization (%) No. of IPO

1986-87 187.91 343.48 64.07

1987-88 -44.17 -20.71 121.1

1988-89 54.69 27.71 6.99

1989-90 61.64 21.65 -11.35

1989-91 -16.41 -24.76 -10.34

1991-92 69.88 84.78 19.53

1992-93 12.94 54.59 19.5

1993-94 167.65 505.26 107.86 4

1994-95 124.46 8.92 49.69 24

1995-96 72.66 208.14 35.78 22

1996-97 166.33 331.92 61.5 23

1997-98 -17.62 -64.37 -42.37 12

1998-99 1,254.38 311.3 -18.94 5

1999-00 -50.57 -46.63 10.07 10

2000-01 65.28 76.93 33.63 7

2001-02 14.59 -29.07 -12.52 11

2002-03 -12.83 -12.77 9.61 9

2003-04 -51.13 -19.61 97.46 13

2004-05 78.54 208.94 62.5 2

2005-06 -37.69 -39.19 -2.98 15

2006-07 232.76 256.7 120.89 11

2007-08 90.28 230.61 95.65 14

2008-09 52.81 63.78 33.33 12

2009-10 76.13 187.93 117.57 16

2010-11 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, Ljung-Box Q-statistics and Lo-

Mackinlay (1988) and Chow-Denning (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 (L-B) Q-statistics (1978) which is widely

used to test autocorrelation in different time series. This test is an improvement of Box-Pierce

Q-statistic of 1970. The L-B Q-statistic 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). Ljung-Box test also provides a superior fit to the

chi-square distribution for little samples. The L-B Q-statistic 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 j-th 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 non-parametric method of controlling for

serial correlation in the error terms without adding lagged difference terms. The PP method

estimates the non-augmented DF test equation and modifies the t-ratio 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 t-ratio 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 t-statistics.

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 sub-hypotheses.

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 m

1

* )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 Ljung-Box (L-B) Q-statistics are presented in Table: 4. The

p-values of autocorrelation and L-B Q-statistics 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 non-stationary 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 Phillips-Perron (P-P) 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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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

Q-Stat

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)

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both of this two Indexes i.e. daily, weekly and monthly data for both of these two indices are

found to be non-stationary 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 P-P Test between DSE Gen and CSCX Indexes

Stock Indexes Data Types P-P Test

at Level Data

P-P 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.t-statistics.

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 appendix-1. Chow-Denning multiple variance ratio test and

Lo-Mackinlay 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 non-random in both

homoskedastic and heteroskedastic increments test assumption. Under homoskedastic

increments test assumption, CSCX weekly index is found to be non-random at 5 percent

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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 non-synchronous 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 non-random 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 L-B Q-statistics 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

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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 chow-Denning (1993) multiple variance ratio test and

Lo-Maclinlay (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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Appendix-1

Chow-Denning 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

Chow-Denning 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

Chow-Denning 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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Lo-MacKinlay 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

Z-Statistic 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

Z-Statistic -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

Lo-MacKinlay 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

Z-Statistic 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

Z-Statistic -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

Lo-MacKinlay 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

Z-Statistic 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

Z-Statistic 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