In this paper we compare several well-known probabilistic models for returns on key glo­bal stock market indices along with a new probabilistic model based on t-distribution with vector of degrees of freedom. The models are compared in terms of in-sample fit and out-of-sample predictive ability for the whole conditional density function. The focus is on the effects produced by the shape of density function, especially multivariate heavy tails. We consider t-distribution with scalar and vector of degrees of freedom as well as modifications of multivariate normal distribution, which allow heavy tails: generalized error distribution and Gram – Charlier distribution. We conduct pairwise comparisons of estimated models using a test based on Kullback – Leibler information criterion. We then rank the models according to their quality of fit and predictive ability and discuss the possible reasons of superiority of this or that density specification over others.