The aim of the thesis is to emphasize the different dependence measures beyond the well known Pearson correlation. The study is developed in the setting of a fund that deals with multiple strategies hedge funds under risk constraints. The relevance of our analysis is made clears by noticing that the Pearson correlation is sensitive only to linear relationships and it does not capture tail co-movements. Specifically, the dependence measures we focus are Kendall's tau, Spearman's rho and tail dependence. This thesis attempts to suggest some other solutions to an effective optimization that combines various fund strategies by using the aforementioned dependence measures.