This work presents the implications of the absence of arbitrage in a two period incomplete markets economy where default is allowed, but it is required that all the assets be backed by a collateral bundle. This collateral can be exogenously given or can be determined by the sellers of assets, as in the Collateralized Mortgage Obligation (CMO) markets. Also we show the existence of equilibrium, but without bounded short-sales assumption in the endogenous case. Finally we present some efficency results.