Models of Stock Returns—A Comparison

In this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis (fat tails) and significant positive skewness in the distribution of daily rates of returns for a sample of common stocks and indexes. Stationarity tests on the parameter estimates of this discrete mixture of normal distributions model revealed significant differences in the mean estimates that can explain the observed skewness and significant differences in the variance estimates that can explain the observed kurtosis. An alternative explanation for the observed fat tails is the symmetric student model. The result of a comparison between the models is that the discrete mixture of normal distributions model has substantially more descriptive validity than the student model.