Measuring Dhaka stock exchange market efficiency : A stochastic frontier analysis

This study measures the status of technical efficiency of companies in Dhaka stock exchange (DSE) for panel data using the stochastic frontier production function, incorporating technical inefficiency effect model. For this study, we used the data collected from DSE market consisting 94 companies in Bangladesh for the period of 2000 to 2008. It was observed that the inefficiency increased over the reference period and translog production function was more preferable than Cobb-Douglas production function. This study showed that the estimated year-wise average efficiency of companies in DSE market was 0.8782 while group-wise average efficiency was 0.8571. At the company group level, GroupA companies was most efficient than the other two groups. The most efficient company was ICB and the most inefficient company was Bextex limited.


INTRODUCTION
Recently, Dhaka stock exchange has taken significant steps towards the development of its capital market.It is the main stock exchange of Bangladesh so we concentrated on the DSE, which is the country's oldest stock exchange, and according to Standard and Poor's Emerging Stock Markets Factbook (2000), the DSE is one of the frontier emerging markets of South Asia.By improving the technical efficiency of DSE market, it can play the desired role in the process of economic development of the country.In DSE, several studies have been conducted for market efficiency.Alam et al. (1999) studied the market efficiency of the DSE.Mobarek et al. (2000) sought evidence supporting existence of at least weak-form efficiency of DSE.Chowdhury et al. (2001) investigated the mean daily returns of DSE around the turn of the week, turn of the month, turn of the year, and around the holidays.A study by Ahmed (2002) revealed that the behavior of stock prices could not be described as obeying the random walk theory rather they follow some dependencies.*Corresponding author.E-mail: baten_math@yahoo.comHassan and Maroney (2004) examined the issue of nonlinearity and thin trading as a test for market efficiency in the context of Bangladesh.
Stock market economy is currently progressing rapidly due to the economical boost on South Asian region (Mursalin et al., 2006).Uddin and Alam (2007) examined the linear relationship between share price and interest rate, share price and growth of interest rate, growth of share price and interest rate, and growth of share price and growth of interest rate were determined through ordinary least square (OLS) regression.Uddin and Yasmin (2008) sought evidence supporting the existence of market efficiency in the DSE market.Researchers investigated technical efficiency of financial institutions used either methods, parametric Stochastic frontier approach (SFA) or non-parametric Data envelopment analysis (DEA) in abroad (Berger and Humphrey, 1997).
There have been a number of studies, which have compared parametric and non-parametric techniques to examine efficiency of financial institutions, for example, for banking industry (Ferrier and Lovell, 1990;Pastor et al., 1997;Resti, 1997;Bauer et al., 1998;Berger et al., 2000;Altunbas et al., 2001;Maudos et al., 2002;Weill, 2004); for the insurance industry (Fecher et al., 1993;Cummins and Zi, 1998).There seems to be no literature on the topics of measuring stock market efficiency of the companies listed in the DSE market in Bangladesh using DEA or SFA approach.It encouraged us to conduct the study to contribute to finance literature and motivates us to undertake this study to fill the gap.In this study we considered the Stochastic frontier approach to measure the technical efficiencies of selected companies in DSE market instead of DEA approach; because of the advantage of SFA which allows a firm to be off the frontier because of random noise and for the main disadvantage of DEA which does not impose any assumptions about production functional form and does not take into account random error, hence the efficiency estimates may be bias if the production process is largely characterized by stochastic elements (Kasman and Turgutlu, 2007).
The stochastic frontier production function was independently proposed in Aigner et al. (1977) and Meeusen and van den Broeck (1977), there has been considerable research to extend and apply the model.Reviews of much of this research are provided in Forsund et al. (1980), Schmidt (1986), Bauer (1990), Battese (1992), andKrikley et al. (1995).In this paper, we used the stochastic frontier production function model specified by Battese and Coelli (1995) for the panel data.The objective of this study is to apply the stochastic frontier production function to investigate the technical efficiencies of companies listed in the Dhaka stock exchange market of Bangladesh.The main focus of our study is to measure the company's technical efficiency in accordance with three groups: Groups A, B and Z and to identify the factors causing technical inefficiency of the stock market.

DHAKA STOCK EXCHANGE (DSE): A BRIEF DESCRIPTION
The Dhaka stock exchange (DSE) was first incorporated as the East Pakistan stock exchange association limited on April 28, 1954.It was renamed as Dhaka stock exchange limited on June 23, 1962.
After the liberation of the country, until 1976, the trading activities of the stock exchange remained closed due to the liberation war and the economic policy pursued by the government.The Securities and Exchange Commission (SEC) which is the regulator of the capital market of Bangladesh was established on 8 June, 1993 under the Securities and Exchange Commission Act, 1993.On August 10, 1998, DSE introduced screen-based state-ofthe-art automated online real-time trading through Local area network (LAN) and Wide area network (WAN) on January 24, 2004.Later, the DSE upgraded its automated trading system on August 21, 2005 (Report on Dhaka Stock Exchange" School of Business, University of Information Technology and Sciences, Dhaka, Bangladesh).
There are four markets in the system: (1) public market: Only for market lot share; (2) spot market: Only for spot transactions which must be settled within 24 h; (3) block market: Only for bulk quantities of shares; (4) odd lot market: Only for odd lot scripts.In the public and spot market, securities are traded through automatic matching and block market and odd lot market is traded through pick and fill basis.All transactions are done by the software called TESA.There are three indices in the DSE as follows: (1) DSI index (comprises all listed securities of the exchange), (2) DSE general index (comprises all companies excluding the Z-category companies) and (3) DSE20 index (comprises leading 20 shares with a base index of 1000).
DSE classified the shares in four groups, such as A, B, Z, and N. Group A companies do regular annual general meeting (AGM) and provide dividend minimum which is 10% of EPS.On the other hand, group B companies do regular AGM but provide dividend less than 10% of EPS.Z group companies are irregular in terms of dividend paying and AGM and N (new) groups companies are newly listed companies placed in this category and their settlement system is like B-category companies.The number of listed securities including debentures and bonds in the DSE market is 444 as of 10 December, 2010.In 444 listed securities, there are 217-A category, 11-B category, 7-N category, 15-Z category companies and 8-Debentures, 186-Bonds in the stock exchange market (DSE website: www.dsebd.org;and SEC website: www.secbd.org).

Stochastic frontier model
Technical efficiency measurement by frontier method is based on the assumption that a gap normally exists between a firm's actual and potential levels of technical performance.Thus, the technical efficiency is measured as the ratio between actual output and the potential output.In stochastic frontier analysis, the assumption is that the production function of the fully efficient firm is known.Lovell et al. (1993) have shown that econometric approaches like the stochastic frontier analysis can distinguish the effects of noise from the effects of inefficiency.
Since one of the objectives of this research is to examine the production efficiency (scores) of listed companies in DSE market, the stochastic frontier analysis was selected as the tool to measure efficiency in this study.So, we considered the stochastic frontier model introduced by Battese and Coelli (1995)  Where, Yit denotes the logarithm of output for the i-th company in the t-th time period; it X denotes the vector of input quantities; is a vector of unknown parameters to be estimated; Vit's are the error components of random disturbances, distributed i.i.d.N (0, 2 v ) and independent from Uit; .Uit' s are non-negative random variables associated with the technical inefficiency of production and to be independently distributed as truncations at zero of the N (µ, where Zit is a (1×p) vector of variables which may influence the inefficiency of companies and is a (p×1) vector of parameters to be estimated.
The parameterization from Battese and Corra (1977)  .it Z Parameters of the stochastic frontier, given by equation ( 1) and inefficiency model given by equation ( 2) are simultaneously estimated using maximum likelihood estimation.
After obtaining the estimates of it U the efficiency of i-th company at t-th time period is given by:

Data set
The data collected from Dhaka stock exchange (DSE) market consists of 94 companies in Bangladesh for the period of 2000 to 2008.In DSE market, 22 types of category of company exist and this study covered 14 types of category of company as: Banks, Financial Institutions, Mutual Funds, Engineering, Food and Allied Products, Fuel and Power, Textile, Pharmaceuticals and Chemicals, Service and Real Estate, Cement, Tannery Industries, Ceramic Industry, Insurance and Miscellaneous.Out of 94 companies, the data represents both financial and non financial company.In this study, 58 companies are from non financial sector and 36 companies are from financial sector.The data also covered 3 out of 4 groups in DSE market.There are 76 companies belonging to Group-A, 15 companies to Group-B and 3 companies to Group-Z.In short, we can say that, the data represents the overall market.

Dependent variable
i. Individual return (Y): In this study, we took individual company's return as a dependent variable.DSE prepares individual company's daily closing price.Using the closing price of individual company, we calculate the return of individual company as follows: Individual company's return = In (Pt) -In (Pt-1) Hasan et al. 8893 where Pt = closing price at period t; P t-1= closing price at period t-1 and ln = natural log.
In order to obtain the individual company's return, we do not adjust company's dividend, bonus and right issues since many researchers confirmed that their conclusions remained unchanged whether they adjusted their data for dividend, bonus and right issues or not (Lakonishok and Smidt, 1988;Fishe et al., 1993).The reasons to take logarithm returns are justified theoretically and empirically.Theoretically, logarithmic returns are analytically more tractable when linking returns over longer intervals.Empirically, logarithmic returns are more likely to be normally distributed which is a prior condition of standard statistical techniques (Strong, 1992).

Independent variables
i. Market return (X1): DSE prepares daily price index from daily weighted-average price of daily transaction of each stock.The name of the index is "All share price index".Market return is calculated as follows: where Pt = price index at period t; P t-1= price index at period t-1 and ln = natural log.
ii.Market capitalization(X2): Market capitalization is the total value of a company's issued share capital as determined by its share price in the stock market.It is calculated as the number of ordinary shares in issue multiplied by the previous day's closing share price and is expressed in millions.The formula is given thus: Market capitalization = (Previous day's closing share price * Shares in issue).
iii.Book to market ratio (X3): The book value of a company is total assets minus intangible assets and liabilities.Here we took the company's net asset value per share as a book value of that company.The market value is the share value in the current market price.After establishing the book value and the market value of a company, simply dividing the book value by the market value, we got the book to market ratio as: Book to market ratio = (Book value/Market value).iv.Market value (X4): The total money value of securities traded in a specific period is called the market value of that period.We calculated the market value by multiplying share price by the number of securities traded as: Market value = (Share price * number of securities traded).

Explanatory variables
i. Time (Z1): Time is used in this study as influencing variable.A, B and Z are company group specific dummies for Group-A, Group-B and Group-Z respectively.The dummy variables can take either 1 or 0, depending on data availability or not respectively.

Specification of the stochastic frontier translog model and technical inefficiency effects model
In order to select the best specification for the production function (Cobb-Douglas or Translog) for the given data set, we conducted hypothesis tests for the parameters of the stochastic frontier production model using the generalized likelihood -Ratio (LR) statistic defined by: Table .This value was compared with the critical value of Kodde and Palm (1986)  where, the subscripts i and t represent the i-th company and the t-th year of observation, respectively; i=1,2,…,94; t=1,2,….,9;Yitrepresents the individual return of the i-th company in the t-th period; MRit represents the market return of the i-th company in the t-th period; MCit represents market capitalization of the i-th company in the t-th period; BMit represents book to market ratio of the i-th company in the t-th period; MVit represents market value of the i-th company in the t-th period."ln" refers to the natural logarithm; the βi's are unknown parameters to be estimated; Vit follows N (0, 2 v ) and Uit follows a truncations at zero of the N (µ, 2 u ) distribution.
Further, the company specific inefficiency is considered as a function of some explanatory variables and the inefficiency effects model is defined as: where 0 is the intercept term and is the parameter for the j-th explanatory variable, T =Year of observation, A is the dummy variable for Group-A companies; A=1 if an observation involves the Group-A, zero otherwise; B is the dummy variable for Group-B companies: B =1 if an observation involves the Group-B, zero otherwise; Z is the dummy variable for Group-Z companies: Z =1 if an observation involves the Group-Z, zero otherwise.

Tests of hypothesis
The hypothesis tests are obtained using the generalized likelihoodratio test statistic (4).This test statistic is assumed to be asymptotically distributed as mixture of chi-square distribution with degree of freedom equal to the number of restrictions involved.The restrictions imposed by the null hypothesis are rejected when exceeds the critical value (Taymaz and Saatci, 1997).These are obtained by using the values of the log-likelihood functions for the companies and the stochastic frontier production function. .This is done with the calculation of the maximum likelihood estimates for the parameters of the stochastic frontier models by using the computer program frontier version 4.1 developed by Coelli (1996).If the null hypothesis is accepted, this would indicate that 2 u is zero and hence that the it U term should be removed from the model, leaving a specification with parameters that can be consistently estimated using ordinary least square (OLS).Further, , 0 : 0 H the null hypothesis that the technical inefficiency effects are time invariant, that is, there is no change in the technical inefficiency effects over time.If the null hypothesis is true, the generalized likelihood ratio statistic is asymptotically distributed as a chi-square (or mixed chi-square) random variable.

RESULTS AND DISCUSSION
Here, maximum likelihood estimates (MLE) of the parameters were reported in the context of company specific efficiency of Dhaka stock exchange followed by translog stochastic frontier model.The MLE of parameters in the model are shown in Table 1.The results showed that the maximum-likelihood estimates of the coefficients of market return, market capitalization, book to market ratio and market value were found significant at 1% level of significance.The square effects and interaction effects of the input variables-market return, market capitalization, book to market ratio and market value were also statistically significant at different level of significance.The estimates of the parameters of the inefficiency effects model were reported in the Table 2.In the inefficiency effects model, a positive coefficient value increased the level of inefficiency and vice-versa.Hence from the result, it was reported that Groups -A and -B companies were found decreasing the level of inefficiency.These indicated that the Groups -A and -B companies were inversely related with inefficiency.There  was no significant effect of Group-Z companies though it was negative.Other explanatory variable in the inefficiency model was "Time".The positive coefficient of time indicated that the technical efficiency level tended to decrease by 50.58% per year over the time period 2000 to 2008.The value of γ was estimated at 0.8643 which was positive and significant at 1% level of significance.It could be interpreted as follows: 86% of random variation around in stock market returns due to inefficiency and 14% due to stochastic random error.This could be interpreted that 86% variations in output among the companies were due to the differences in technical efficiency.It is evident from Table 2 that, the estimate of σ was 0.3784 which was significantly different from zero, indicated a good fit.The year wise mean efficiency of 94 companies in DSE market is displayed in Table 3. From this investigation, we observed that the highest mean efficiency was in 2000 and the score was 93.60% and the lowest mean efficiency was in 2008 and the score was 75.68%.In 2008, the mean efficiency decreased by 19.15 from 2000.Time was observed as an important affect in increasing inefficiency.It was also revealed from Table 3 that the mean technical efficiency of the companies of DSE market during the period 2000 to 2008 was found to be 0.8782.This implied that 87% of potential output was being realized by the companies of DSE market.The group wise mean efficiency of 94 companies in DSE market is displayed in Table 4.It was observed that in case of higher efficiency, the Group-A companies were most efficient (88.29%).These findings are in line with the argument that the companies included in Group-A were found to be superior as they were regular in holding the annual general meetings and declared dividend at the rate of 10% or more in a calendar year.The Group-B (86.51%) and the Group-Z (82.32%) companies were relatively less efficient than Group-A companies because the companies included in Group-B were regular in holding the annual general meetings (AGM) but failed to declare dividend at least at the rate of 10% in a calendar year and the companies included in Group-Z were also failed to hold the annual general meetings or failed to declare any dividend.But during the period 2000 to 2008, the efficiency of Group-A companies (91.63%) was lower than Group-B companies (92.39%) in the year 2002 and also the efficiency of Group-A companies (85.37%) was lower than Group-B (88.08%) and Group-Z (87.71%) companies in the year 2006.The rest of the years in the study period the companies included in Group-A showed higher efficiency than the other two groups.Company's year-wise technical efficiency in DSE market showed a more clear perception about the performance of an individual company was displayed in Table 5.There was a variation in the technical efficiencies among the different companies in DSE market: it ranged from a low of 0.7650 for company Bextex Limited, to a high of 0.9219 for company ICB.
The actual range in this case was found to be 0.1569.The most efficient companies during the study period were found to be ICB (with 92.19%), Apex Adelchy Footwear (92.01%),ACI Limited (91.67 %), 7th ICB M.F.(91.28 %), and 1st BSRS (91.14%).On the contrary, the most inefficient companies during the data period were Bextex Limited (76.05%),Al-Arafah Islami Bank (78.90%),Aramit Cement (81.39%),Anwar Galvanizing (82.70%) and BD.Autocars (with 82.87%).From the investigation, it was observed that the top five companies are Group-A companies and among the bottom five companies there were three Group-Z companies.

Hypothesis testing
The results of various hypothesis tests for the model are presented in Table 6.The all hypothesis tests were obtained using the generalized likelihood-ratio statistic (4).The second null hypothesis is 0 : 0 H , which Spe- cified that there was no technical inefficiency effect in in the model.The hypothesis was rejected, so we concluded that there was a technical inefficiency effect in the model.The third null hypothesis is H 0 : η = 0, which specified that the technical inefficiency effect did not vary significantly over time.The null hypothesis was rejected indicating that the technical inefficiency effect varied significantly.

Conclusion
This study focused on the estimation of the technical efficiency of the companies listed in the DSE market applying the stochastic frontier approach.We observed that the variables market return, market capitalization, book to market ratio and market value show significant  Kodde and Palm (1986).The null hypothesis which includes the restriction that is zero does not have a chi-square distribution , because the restriction defines a point on the boundary of parameter space.
affects for MLE estimation of the translog production function.These results indicated that these input variables significantly affect the return of individual company of the share market in Bangladesh.From the inefficiency effects model, we found that the variable Groups -A and -B significantly contributed to improve technical efficiency of return in DSE market.The result showed that the explanatory variable "time" has significant impact.It indicated that technical inefficiency increased over the reference period.This means that, the technical efficiency rate was found gradually decreasing over time in the stock market in Bangladesh.According to the results obtained from the stochastic frontier estimation, the mean technical efficiency of DSE market during the period 2000 to 2008 given by the translog model was 0.8782.This implies that 87% of potential yield was being realized by the companies in the market and also indicated that there was a scope to further increase the output by 13 % without increasing the levels of inputs.In this study we also found that the companies which are listed in Group-A were the most efficient companies among the three groups.As a result, this study examined the efficiency and other characteristics of DSE markets which would be of great benefit to investors at home and abroad, policy makers and local and foreign listed and unlisted companies and has important practical implications to different capital market participants.Finally, it may also be useful for international organizations and governments of development partners who are interested in the development of capital markets in the emerging countries.
function for the frontier model under the null and alternative hypotheses.The values of the log likelihood for the Cobb-Douglas and Translog production frontiers are -132.9089and -74.7714, respectively.By employing Equation (4 specifies that the technical inefficiency effects in companies are zero.This is rejected in favor of the presence of inefficiency effects.Here is the variance ratio, explaining the total variation in output from the frontier level

Table 1 .
Maximum-likelihood estimates of translog stochastic frontier production model.

Table 2 .
Maximum likelihood estimates of the parameters of inefficiency effects model.

Table 3 .
Year wise mean efficiency of companies in Dhaka stock exchange.

Table 4 .
Group wise mean efficiency of companies in Dhaka stock exchange.

Table 5 .
Company's year-wise efficiency in Dhaka stock exchange market.

Table 6 .
Likelihood-ratio test of hypothesis of the stochastic frontier translog model.critical values are at 5% level of significance.*The critical values are obtained from table of All