A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. An improved method (in terms of speed and accuracy) is developed for the computation of the stable Paretian density. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. Because of the tractability of the stable Paretian characteristic function, the model is straight forwardly extended to support portfolio selection using expected shortfall as the downside risk measure by using an independent component analysis framework.
