I evaluate the problems caused by the use of the mean-variance criterion, conceived by Markowitz, that addresses the allocation of financial portfolios. Many authors have suggested that the mean-variance criterion can not correctly proxy the expected utility with non-Normal returns. Thus, a strategy is needed that can enable us to understand whether the loss of optimality due to the mean-variance criterion is significant or negligible. I try to achieve this by developing an analysis on the composition of the optimal portfolio and on the cost of the Markowitz allocation compared to an allocation that uses models with copulas (Normal, Student-t, Clayton, Gumbel, Frank, mix copulas and Canonical Vine copulas) in portfolios composed by 2 or more assets, analyzing various combinations of indices to test whether the use of copulas improves the investor''s utility and revenue. Moreover I build models that considers return moments and co-moments till the fourth power in order to understand whether they can approximate the use of copulas to obtain optimal weights. The analysis should be interesting to Investment Fund Asset Managers, but also to academic researchers.