Empirical distributions of stock returns: Mixed normal or kernel density?

A preponderance of research evidence shows that normal distributions cannot capture the behaviour of stock returns. In some empirical experiments, alternatives to normal distributions have been applied to stock data on a case-by-case basis, but no simple and practical general solutions exist to capture stock behaviour. As a simple methodology, the normal mixture model is a linear combination of normal distributions that can be directly used to approximate the characteristics of stock returns. In this paper, we recommend usage of the normal mixture model as a general method to understand stock behaviour. We also compare the performance of different normal mixture models with kernel density estimations for ten major stock market indexes and two individual stocks from the years 2000 to 2016. Empirical results show that the normal mixture model with three components better represents the behaviour of stock returns, both statistically and economically, than models based on normal distributions and kernel density estimations.