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This paper discusses and examines the performance of Gaussian and non-Gaussian portfolio selection models. We analyze some allocation problems considering different distributional portfolio models. In particular, for each allocation problem, we compare the maximum expected utility obtained when the portfolios of the returns are either heavy tailed distributed or uniquely determined by the mean and the variance.

In this paper we compare different approaches to computing VaR (Value-at-Risk) for heavy tailed return series. Using data from the Italian market, we show that almost all the return series present statistically significant skewness and kurtosis. We implement (i) the stable models proposed by Rachev et al. (2000), (ii) an alternative to the Gaussian distributions based on a Generalized Error Distribution and (iii) a non-parametric model proposed by Li (1999). All the models are then submitted to backtest on out-of-sample data in order to assess their forecasting power. We observe that when the percentiles are low, all the models tested produce results that are dominant compared to the standard RiskMetrics model.