**4. Concluding Remarks**

Regulators for a number of national exchanges have banned the practice of short selling. This is often the case in emerging markets. Whether the reason is fear of market manipulation or simply the lack of an institutional framework to borrow shares, a short selling ban potentially impedes the impounding of information in market prices.

Previous studies typically consider the effect of a short selling ban on price discovery by examining price dynamics before and after changes in short selling regulations. However, for many exchanges in emerging economies, investors have never been able to short sell securities. Thus, testing for differences across regime shifts is not possible.

To address that problem, our analysis compares the return runs we observe to what we would expect if markets were otherwise efficient. We first construct a simple runs test for statistical independence of daily stock returns, a necessary condition for market efficiency. A run is a series of returns all of the same sign, and the test calls for comparing the total number of runs in a given time period to the expected number of runs. We use Monte Carlo simulation to determine the latter. We then extend the analysis by considering the number of days for each run and form a distribution of return clusters according to their duration. Again, we compare the distribution to expectations based on a Monte Carlo simulation. The extended analysis considers whether runs of longer duration appear more or less frequently than anticipated if markets are efficient.

Additionally, we examine the symmetry of the distribution to see whether any effects are obtained for both positive and negative return runs.

Using data from the Dhaka Stock Exchange, we examine whether a short selling ban affects market efficiency. The runs test provides strong evidence that returns are not independent. Moreover, a runs distribution reveals fat tails, implying that runs of longer duration appear more frequently in the DSE data than we would expect in efficient markets.<sup>4</sup> Thus, for both positive and negative return

<sup>4</sup> While a short selling ban appears to affect both tails of the runs distribution, the tests depend on the success rate, the percentage of positive returns observed. For all DSE stocks, the success rate is less than 50%, while for all Dow Jones stocks

runs, we observe a relatively large number of runs that are 5 days or longer. We next consider similar tests for the DJIA and stocks within the index. This list includes extremely liquid stocks that are easily shorted. In contrast to the DSE results, the runs tests generally accord with market efficiency. Finally, to further show causality, we examine Australian stock return runs before and after a ban on short selling. After the prohibition, the findings are similar to the DSE results and reproduce the longer time necessary for markets to reach a new equilibrium. The evidence taken as a whole suggests that a short selling ban delays the market's digestion of information. This is true for both positive and negative news. In light of these results, regulators may want to rethink the prohibition of short selling securities.

**Author Contributions:** The authors contributed equally to the research and writing of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We would like to thank our discussant at the 2017 Paris Financial Management Conference, Suk-Joong Kim, the University of Sydney, Australia and two anonymous reviewers. We also appreciate the help of Assistant Editor, Eliza Dou, and the encouragemen<sup>t</sup> and editorial guidance of Duc Khuong Nguyen.

**Conflicts of Interest:** The authors declare no conflict of interest.
