The selection of portfolios of oil projects is an important concern for managers of large oil companies because of the huge amount of investment, requirements of production of oil and gas, limitation of money, staff, rigs, etc. The traditional analytical tool for selection of portfolios is the Markowitz’s Mean-Variance model where the focus is purely on financial return. The final product of the Markowitz’s model is the efficient frontier, which is a geometric curve composed by infinite number of viable portfolios. The choice of the optimal portfolio among infinite possibilities is the final problem, but the Mean-Variance model does not recommend which one is the best portfolio. We extend the Mean-Variance model in order to consider some goals of the corporation such as yearly production, constraint on investment, etc. Similarly, we find the efficient frontier of portfolios of projects. Again, we have the problem of which portfolio to select, that is, the one with high return and risk or the other with lower return and risk? In this paper we argue that if investors are diversified, managers should select projects with highest return, regardless of risk. However, in practice, if bonuses of managers are tied to their performance, the choice for portfolio with lower return and risk is possible, what is a classic agency problem.