Structural Breaks and the Normality of Stock Returns

This paper attempts to explain the distribution of actual stock index returns using a mixture of the normal distributions model. This paper first defines the concept of structural breaks and derives a special form of structural breaks under the normality framework. It then applies the derived methodology to the monthly returns of the Swiss stock index to confirm whether the observed non-normality of stock returns can be explained with the derived model. Empirical results provide evidence that the entire period consists of three or four sub-periods in which different normal distributions exist. To check the statistical power of the model, this study generates random data from the normal distributions. Simulation results support the statistical power of the new methodology, and indicate the possibility that, despite being a seemingly non-normal test statistic for the entire data set, the underlying distribution is made up of a mixture of normal distributions.