The purpose of this study is to test the impact of the sample size on the distributional characteristic of the stock returns of Nifty and Sensex. Many statistical tools are used by financial analysts and academicians for their analyses and researches under the assumption that stock returns are normally distributed for all kinds of sample size. Failure of the underlying assumption of normality can mislead the inferences. This study shows that sample size can distort the normality assumption of the stock returns. The study is based on statistical analysis and normality tests, such as Kolmogorov-Smirnov (K-S), Anderson-Darling (A-D), Jarque-Bera (J-B), the results of which indicate that large sample size daily stock returns do not follow the normal distribution, while small sample size monthly stock returns follow the normal distribution.

One of the widely used assumptions in financial market research is that stock returns are normally distributed, following a continuous probability density function. Many financial theories and models explain investors preference assuming mean variance behavior. Chamberlain (1983) shows that mean variance behaviors are usually justified through the assumption of normally distributed stock returns. This assumption of normal distribution is common and crucial for many statistical tools used by the stock market researchers and analysts. Normality is important in sampling theory based inference procedures because the properties of test statistics depend on normality. Failure of the normality assumption can lead to misleading inferences. This is because the calculation of standard error based on the normality assumption will be wrong if data is not normally distributed. Early studies basically concluded that there seemed to be no impact on inference. But the question is whether really the stock returns are normally distributed for different kinds of sample size.

The main objective of the study is to test the impact of the sample size on the distributional characteristic of the stock returns of Nifty and the Sensex. This study investigates the applicability of different statistical tools of the previous research work assuming normal distribution without considering the sample size. The findings clearly show that large size daily stock returns are not normally distributed, whereas small size monthly returns are distributed normally.

Applied Finance Journal, Distribution of Stock Returns, Normal Distribution, Financial Market, Probability Density Function, Normal Distribution, GARCH Model, Literature Review, National Stock Exchange, NSE, Stochastic Process Model, Stock Market Prices.