Weak Form Efficiency of the Chittagong Stock Exchange: An Empirical Analysis (2006-2016)

We study the random walk behavior of Chittagong Stock Exchange (CSE) by using daily returns of three indices for the period of 2006 to 2016 employing both non-parametric test (run test) and parametric tests [autocorrelation coefficient test, Ljung– Box (LB) statistics]. The skewness and kurtosis properties of daily return series are non-normal, with a hint of positively skewed and leptokurtic distribution. The results of run test; autocorrelation and Ljung–Box (LB) statistics provide evidences against random walk behavior in the Chittagong Stock Exchange. Overall our result suggest that Chittagong Stock Exchange does not exhibit weak form of efficiency. Hence, there is opportunity of generating a superior return by the active investors.


INTRODUCTION
The growth of equity markets and the globalization of financial markets are often the subject of major research studies in developing countries. Additionally, testing different forms of the efficient market hypothesis seems to be the most popular theme of these empirical investigations. Market Efficiency is defined by Fama (1970 and1991) as a market in which prices always fully reflect all available information. He argues that the allocation of the ownership of the economy's capital stock, which represents the primary role of the capital market, is ideally fulfilled if the market is efficient, because prices from such a market provide accurate signals for resource allocation. Actually, the Efficient Market Hypothesis (EMH) says that the changes in price occur in an efficient market randomly and independently.
of listed securities, high liquidity, presence of large number of rational risk averse investors, low brokerage and commission cost etc. When all these factors meet, 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 (Ali, 2012). There are three different levels of efficiency which are defined based on the level of information reflected in the prices: weak-form, semi-strong and strong form. Weak form of efficiency indicates that price of financial assets reflects all information contained in the past prices. Semi strong form of efficiency asserts that prices reflect all the publicly available information where as strong form says that prices of financial assets reflect in addition to information on past prices and publicly as well as privately available information. The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the price changes in the stock market cannot be predicted. That is an investor can't make any superior return making any predictions using any co-relationship of future prices with past prices. The hypothesis states that stock price changes have the same distribution and are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. The EMH is also consistent with the random walk hypothesis.
In this paper, we have tried to analyze whether the Chittagong Stock Exchange is efficient in weak form or not. Here, the returns of CSE All Share Price Index, CSE Selective Index and CSE Selective Categories Index are tested using Autocorrelation, LB statistic and run test. In the first part of this article theoretical description has been given on these statistical tools. Then in the later part empirical analysis and results have been shown. In our findings, the descriptive statistic shows that none of the return series follow normal distribution. On the basis of the results of autocorrelation test, LB test and runs test carried out on the sample drawn from CSE, it can be concluded that the stock market returns do not follow random walk and they provide evidence against the weak form of efficiency of Chittagong Stock Exchange during our study period.

LITERATURE REVIEW
Pyemo Afego (2012) examined the weak-form efficient markets hypothesis for the Nigerian stock market by testing for random walks in the monthly index returns over the period 1984-2009. This paper showed the opportunity is existing to have superior earnings for market participants by using the nonparametric runs test. Finally, a range of policy strategies are suggested for improving the allocative capacity and quality of the information to ensure the environment of the NSE. Similar conclusion is drawn by Akram and Murad (2013) examining the weak-form efficiency of Palestine Exchange (PEX). They employ the serial correlation and the Augmented Dickey-Fuller test (ADF) as parametric tests and the runs test as a non-parametric test and concluded that results of both tests are consistent with the alternative hypothesis that the stock market is weak-form inefficient and the main index found to be moving non-randomly. Asma Mobarek and Keavin Keasey (2000)

DATA AND METHODOLOGY
To study whether random walk hypothesis is experimental in Chittagong Stock Exchange or not, we took three market indices of Chittagong Stock Exchange (CSE) into our analysis. All data was taken from the website of Chittagong Stock Exchange consisting of 2248 observations. The data was taken for the period of 1 st July, 2006 to 31 st October, 2016. The daily index data for different periods are converted into continuously compounded return because lognormal returns are more likely to be normally distributed (Strong, 1992). We calculate lognormal return by using following formula.
Where, Rt= logarithmic return in period t Pt= stock index price at time t Pt-1 = stock index price at time t-1 The analysis is done by using SPSS16 software package. Different techniques are used to find out the random walk hypothesis for stock market. Our study mainly focuses on parametric autocorrelation test and non-parametric run test to test the random walk hypothesis of Chittagong Stock Exchange (CSE).

AUTOCORRELATION
Autocorrelation measures the similarity of changes in returns between two successive time intervals. It calculates the correlation between return in the current period and those in the previous period. A Weak form efficiency of the Chittagong stock exchange ...
International Journal of Business and Social Research (IJBSR) 61 significant positive autocorrelation means the series do not follow random walk. The serial correlation coefficient at lag k, denoted by pk, is defined as Where, Rt and Rt-1 represent return in period t and t-1 respectively.
According to Bartlett (1946), the standard error of the autocorrelation coefficient, Pk, is equal to:  (pk) = n / 1 Test statistics (Z) for the autocorrelation can be written as The following hypothesis is to be tested: Ho: There is no autocorrelation between the returns of CSE. H1: There is autocorrelation between the returns of CSE. The null hypothesis of the autocorrelation coefficient is equal to zero and rejected when calculated Z value of autocorrelation exceeds the critical Z value from normal distribution at chosen level of significance.
In addition, the null hypothesis that all coefficients are simultaneously equal to zero up to lag k tested by applying the Ljung-Box (LB) statistics. This statistic is defined as: The hypothesis for LB statistic can be written as follows: Ho: All the autocorrelation coefficients of Returns of CSE up to a certain lag are simultaneously equal to zero. H1: Stock returns do not follow random walk. The null hypothesis is rejected if the calculated LB value exceeds critical LB value from chi-square distribution at the chosen level of significance.

RUN TEST
Run test is a non-parametric test for testing the randomness of a financial time series. A nonparametric test does not require returns to be normally distributed. A run can be defined as an uninterrupted sequence of one symbol or attribute such as + or -and length of run is the number of elements in it. Under the assumption of random walk, actual number of runs (U) and expected number of runs are same. If there are too many runs, it indicates negative serial correlation. If there are too few runs, they may suggest positive serial correlation. Run test converts total number of run into z statistic.
To perform this test on stock return of CSE, X is assigned to each return that equals or exceeds the median value and Y for the items that are below the median. Let nX and nY be the sample sizes of items X and Y respectively and U is the observed number of runs. For large sample size, where, nX > 10 and nY > 10, the following test statistic is used. Null hypothesis of independence is rejected, if computed Z value exceeds the critical Z value at chosen level of significance.

EMPIRICAL ANALYSIS AND RESULT
4.1 DESCRIPTIVE STATISTICS Table 1 presents a summary of descriptive statistics of the returns for three indices of CSE. Sample means, maximums, minimums, skewness, kurtosis and Jarque-Bera statistics are reported to analyze the normality of the returns. The summary statistics show positive mean daily return for all indices in the sample. The lowest returns (-8.65) and the highest returns (14.33) are in CSE30 index. The standard deviations of returns range from 1.4474 (CASPI Index) to 1.5513 (CSE 30 Index). The coefficients of skewness and kurtosis are asymptotically distributed as N (0, 6/n) and N (0, 24/n). The following ratios could be compared with the critical values from a standard normal distribution in order to test the hypothesis of normality. The ratios are:  The value of skewness and kurtosis indicate that the distribution is not normal. The coefficients of skewness are significantly positive and kurtosis represent a leptokurtic distribution. They provide evidence against the null hypothesis of normality of returns. Again, we used Jarque Bera test to find out the normality of returns. The following hypothesis is to be tested. Ho: There is normal distribution of stock returns of CSE. H1: There is non-normal distribution of stock returns of CSE.
The normal distribution of stock return is found if the calculated results of JB statistics don't exceed the critical value at chosen level of significance Here, we see that the calculated results of JB statistics reject the null hypothesis at 1% level of significance. This conclude that non-normal frequency distribution of stock returns is in Chittagong Stock Exchange. Table 2 presents the results of run test. The calculated z statistics of daily market return for every index is significantly negative. Thus, the negative z-values is a dictation that the actual number of runs is less than the expected number of runs under the null hypothesis of return independence at the 0.01 level or lower for all indices. Our results reject the null hypothesis showing that CSE doesn't follow the random walk and therefore, the market is not efficient in weak form.  . Descriptive statistics reveals that the series of return is not normally distributed. There is existing a large spread between the minimum and maximum values. The coefficients of skewness are significantly positive and kurtosis represent a leptokurtic distribution Again the calculated results of JB statistics reject the null hypothesis at 1% level of significance and put argument in favor of non-normal frequency distribution of stock returns. Similarly autocorrelation test, LB test and runs test have rejected the null hypothesis and the independent movement of stock returns. Therefore, CSE do not follow random walk hypothesis and inefficient in weak form in our study period. Our findings have similarity with the study of Hasan (2015), Mudassar, Arshad, Maryam and Amir (2013), Chaity and Sharmin (2012), Khandoker, Siddik, and Azam (2011), Gupta andBasu (2007), Maghyereh (2003), Hassan, Islam, and Basher (2002). The trend of daily returns of CSE shows the opportunity of superior returns for market players. So there is a chance of predicting the future price movement by analyzing the past which could be contradicts with the goal of maximizing of shareholders wealth. This situation informs the authority of Bangladesh Securities and Exchange Commission (BSEC) to take immediate steps to safe the general investors in the stock market. However, our study is based on market index rather than individual securities. Above all this study undoubtedly requires further research based on individual securities listed in Chittagong Stock Exchange.