Many of the works in finance, as the ones that involves financial models, are concentrated in fetching the forms to reject the assumptions on which these are based.However, an important question is to verify if one specific model surpasses or is surpassed by the other alternatives. Thus, it was made in this work, which main objective is showing that the active pension funds portfolio management, with all those legislation restrictions, creates value when it was compared to the passive management. In other words, the active portfolio management surpasses the passive management. Basically, in this work, we present the restrictions of the pension funds legislation and the methodology of the portfolio construction.The passive portfolio was built according to the concepts presented in the Elton, Gruber and Padberg algorithm. The active portfolio was built according to the process considered by Grinold and Kahn to transform signs / information into alphas / forecasts. For the second step of the process of the portfolio construction, there are three generic classes of procedures that cover the vast majority of institutional portfolio management, that are used: Screens; Stratification; and Quadratic Programming, in which we used AEGIS 3.0 of BARRA consult. After the portfolio construction we match the results to validate the main objective.