*2.1. Data*

The analysis focuses on the 21 most liquid stocks on the Dhaka Stock Exchange (DSE). We use daily stock prices from January 1999 through December 2014. This yielded roughly 4000 stock prices for each of the 21 different stocks.

In addition to looking at individual stock price changes, we also consider stock indices representing the DSE market as a whole. As no single broad index exists for the entire sample period, we rely on two of the more popular indices. The DSE Broad Index, referred to as DSEX, represents 97% of market capitalization. This free-float broad index became effective in 2013. The previous broad index, the DSE General Index or DGEN, existed from December 2002 until July 2013. We thus use the DGEN index from December 2002 through July 2013, and continue with the DSEX index from August 2013 through the end of 2014. Hereafter, we will refer to the broad market index as the DSEX, recognizing that it represents both the DGEN and DSEX in their respective sample periods.

The Dhaka Stock Exchange library provided daily stock prices and data for the Dhaka Stock. We adjust all prices for cash and stock dividends, splits, bonus and right shares. It is important to remember that the 21 individual stocks chosen are the most liquid stocks, have trading on virtually every business day; therefore, they are likely among the most efficiently-priced stocks on the Dhaka Stock Exchange.

For matters of robustness, we compare the DSE results to similar tests using US data. Specifically, we consider the Dow Jones Industrial Average and the component stocks. The analysis covers the similar 1999–2014 period for individual stocks and 2002–2014 for the DJIA index. Because Visa was only a constituent stock of the index for part of the time, we exclude it from the analysis. Thus, we examine price dynamics for the DJIA index and the remaining 29 stocks.

### *2.2. Methodology—Calculating Runs and Testing for Statistical Independence*

The runs test is a non-parametric test that can be used to examine randomness in stock returns. Let returns be defined as (Pt+1 − Pt)/Pt, where Pt is the adjusted stock price on day t. We then define a run as a string of daily returns all of the same sign. If the data follows a binomial distribution, we assume that a 0 return continues the run. Thus, the end of a run and beginning of a new run is when the sign changes from either positive to negative, or vice versa. Put another way, the end of a run only occurs when there is a sign change.

To illustrate how runs are calculated, let P denote a positive return, N a negative return, and 0 denote no change in daily prices. Suppose that the price data yields the following string of returns:

### PPPP N0N PP N PPP0P NNNNN PPP NN

This string of 25 daily returns includes 8 separate runs, the shortest being a 1 day run with a negative return, and the longest a 5 day run for both positive and negative returns.

Suppose, for the moment, we believe that 50% of returns are positive and 50% are negative. Given this binomial distribution, we can calculate the number of runs and see if it is more or less than the number we expect. If the number of runs differs significantly from what we expect, we reject the null hypothesis that the data was randomly generated and accept the alternative that the sequence was not produced in a random manner.

Comparing the number of runs to the expected value is a test of statistical independence. If, for example, we find significantly fewer runs than expected, that would sugges<sup>t</sup> that the data is highly clustered. Thus, positive returns likely follow positive returns, and negative returns likely follow negative returns, a result that implies a positive serial correlation of returns. On the other hand, if there is little clustering and signs change frequently, such a pattern would indicate negative autocorrelation.

From the above discussion, we compare observed runs patterns to what we expect. In turn, expectations depend upon the true probability of success, for example, the probability of observing a positive return and the number of trials or observations in the sample. In our samples, the number of observations is approximately 4000 for stocks and 3200 returns for each index. With large samples, it is reasonable to assume as a first approximation that the observed frequency of positive outcomes is equal to the true probability of "success." Mollik and Bepari (2009) implicitly follow this line of reasoning and make this assumption in their runs tests.

Table 1 presents the percentage of positive returns and negative returns for each asset class. For both the DSEX and Dow Jones indexes, the observed frequency of positive returns is close to 53%. For stocks, however, the Dhaka and U.S. stocks diverge in the proportion of positive returns. For DSE stocks, the average frequency of positive returns is 46.33%, whereas for stocks in the Dow, the average percentage of positive returns is 51.13%.


**Table 1.** Proportion of Positive and Negative Returns (DSE vs. DJIA).
