*3.2. Run Results for Individual Stock Returns*

In order to examine runs for individual stocks, we must first investigate the success rate of a positive return occurring for each firm in our sample. Figure 3A,B graph the percentage of positive and negative returns for the 21 DSE and 29 DJ stocks in our sample. As reported earlier, the average success rate for DSE stocks is 46.33% and equals 51.13% for DJ stocks. The figures reveal that the success rate for each individual stock is near the relevant average; therefore, we base our confidence intervals for DSE and DJ stocks on the 46.33% and 51.13% success rates, respectively.

Table 4A displays the number of runs in the middle of the distribution for each of the 21 DSE stocks. From before, that includes runs that are between 1 and 4 days, and represents almost 90% of the distribution. Table 4B exhibits the number of runs for the same 21 firms, except in this panel, |n| is equal to or greater than 5. This region represents the tails of the distribution, and covers approximately 10% of all runs.


**Table 4.** (**A**) Number of Runs in the Middle of the Distribution (n between −4 and +4) for DSE Stocks. (**B**) Number of Runs in the Tails of the Distribution (|n| equal to or greater than 5) for DSE Stocks.


At the top of Table 4A,B are 95% confidence intervals for each n day run. For example, the number of expected 2-day, negative return runs (n = −2) is between 221 and 278. This assumes nearly 4000 stock returns and a success rate equal to 46.33%. Any violation below the lower bound of the confidence interval is shaded a dark gray, while a light gray cell denotes an upper bound violation.

From Table 4A, we observe a number of confidence interval violations. All but one breach the lower bound of the relevant 95% band. In contrast, Table 4B reveals several violations of the confidence interval's upper bound. Taken together, these results sugges<sup>t</sup> that the n day run distributions have a skinnier than expected middle, and have fat tails. This evidence implies that the short sale ban on the Dhaka Stock Exchange contributes to market lags in fully digesting information. Long runs for both positive and negative returns occur more frequently than you would expect if returns were independent.

As a matter of robustness, we compare these findings to the run distributions of U.S. stocks and see if similar results are obtained. Table 5A,B replicate the analysis for 29 of the 30 stocks in the DJIA. The Dow Jones results are in stark contrast to those of the stocks in the DSE. Specifically, we note relatively few violations for the U.S. stocks. Roughly 5% of the entire sample breach the confidence intervals, as we would expect. Moreover, the violations are not all in one direction for the middle of the distribution and the other direction for the tails. Breaches of the upper and lower bound violations appear randomly sprinkled throughout Table 5A,B. Thus, the Dow Jones stocks, unlike those in the DSE, have n day return distributions which are consistent with return independence. Thus, the results sugges<sup>t</sup> that U.S. markets incorporate information readily, and that returns follow some type of Markov process.


**Table 5.** (**A**) Number of Runs in the Middle of the Distribution (n between −4 and +4) for Dow Jones Stocks. (**B**) Number of Runs in the Tails of the Distribution (|n| equal to or greater than 5) for Dow Jones Stocks.


**Table 5.** *Cont.*
