Test of Data Normality, Return Similarity and Variance Analysis in South Asian Stock Markets

Abstract

This paper analyzes the data distribution on stock market returns in SAARC nations (Bhutan, India, Bangladesh, Nepal, Sri Lanka and Pakistan) for weekly data from January 2006 to December 2011 to see if market returns are normally distributed. Secondly we have also tested if returns are similar across different markets using pair sample t-tests. While comparing differences or similarities in returns we compare associated risks for each pair to see if there exist opportunity for similar returns at lower risk or higher returns at a given risk. Finally we analyzed variance analysis using one-way ANNOVA with multiple comparisons to find out if time varying effect is present in any of the stock market return. Our finding suggests that the data distributions on stock returns of all the markets in the region are not normal. We observe high skewness, kurtosis and further the hypothesis of normal distribution have been rejected based on Jarque-Bera test for full sample data of 2006 to 2011 for all countries although, the data of Bangladesh and India seems to possess lower levels of skewness and Jarque-Bera statistics indicating lesser degree of non-normality. When data was run after splitting the sample annually, we found that the distribution was normal for most years for majority of markets. This suggested impacts of sample size on data distribution. We crosschecked the results with non-parametric test using Kolmogorov-Smirnov (K-S) since it is one of the very popular tests statisticians would use. We found that the data distributions of Indian and Bangladeshi stock returns are normal and the rest are non-normal. While analyzing the return similarities/difference using paired sample t-tests, we found that there exits no statistical differences in the average returns between different pairs of stock returns except some difference with few pairs of returns when sample was split annually. We have observed difference in the levels of risks (standard deviation). This indicates opportunity for investors to earn similar returns at lower risks by changing their investment destinations. We conducted multiple comparisons of variances using annual, weekly and seasonal codes and found that some annual time effect with some stock returns. However, we found no week of the month effect and season of the year effect. Difference in time per se for entry into the stock market and exit from it does not provide extra benefits.