Journal of Risk Model Validation

The daily returns of the Portuguese Stock Index: a distributional characterization

Sameer R. Rege, João C. A. Teixeira and António G. de Menezes


This paper compares the fitting of the normal, generalized hyperbolic, normal inverse Gaussian and Student t distributions with the daily returns of the Portuguese Stock Index PSI-20 over the period 1992-2013.We find that the distribution of the actual returns of the PSI-20 exhibits much higher kurtosis and extreme values than the normal distribution. Overall, the best fit is provided by the Student t and the generalized hyperbolic distributions. This pattern also applies to the tail behavior, as the density of the Student t distribution exhibits fatter tails than the density of the other distributions, followed by the density of the generalized hyperbolic distribution. Finally, we find that the normal inverse Gaussian and the normal distributions have the lowest fitting quality to the actual daily returns of the Portuguese Stock Index.