An Investigation into non-normality of stock returns

This paper proposes a new methodology to investigate the non-normality of stock returns, such as to do with what insights emerge from making use of the Mixture of Distribution Hypothesis. Typically, researchers check for non-normality using standardized residuals of GARCH, Jarque-Bera test or by making use of the built-in functions for descriptive statistics offered by various software. The major limitation of the above-mentioned methods is that those methods work under the assumption of parameters being constant over the time period under study. We propose a new method, called the K-month analysis to overcome the limitation due to this unrealistic assumption. This method is tested using data from five different stock indices. What we find is that in general, when parameters are held constant over a longer period, the kurtosis becomes increasingly significant indicating that the long term stock returns are not normally distributed but remain a mixture of normal.