In this paper we discuss the existence of an optimal portfolio for every investor in a two-period Arrow -Debreu economy in which risky assets are contingent claims on aggregate consumption. Since we derive an optimal portfolio for every investor, the pricing kernel is endogenously determined. Hence the sufficient conditions for the existence of optimal portfolios given in this paper do not involve the pricing kernel; instead they are directly on investors preferences and beliefs. We also present a new approach to the equilibrium, which works with the space of investors first-period consumption. The case where investors have background risk is also discussed.