In this paper we develop the complete analysis of the necessary and sufficient conditions for the full Pareto-efficiency of financial markets. We show that full-Pareto efficiency obtains in exchange markets if and only if a type of partition of events, called a market clearing sufficient partition, is available for contingent contracting. The minimal such partition is that generated by the market portfolio and certain densities of the beliefs, a property that makes it a sufficient statistic of the beliefs. All the known results of Hakansson, Ross, Arrow-Debreu, etc. are derived as special case corollaries.