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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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  • 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

  • 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 60-day 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 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

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

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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

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

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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 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 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