Cumulative Prospect Theory has been proposed as an alternative to expected utility theory to explain irregular behavior by economic agents. In particular in Finance it has used to clarify anomalies like the equity premium puzzle. There are certainly hopes and hints that CPT can explain the anomalies, but less attention has been paid to more basic questions. This paper answers some of those. A complete market is not sufficient to guarantee that the market portfolio is efficient so prices may not be determined at the margin by a representative investor. “Over-completion” of the market (the introduction of apparently extraneous derivative assets) can restore efficiency and result in a Pareto efficient allocation of risk. Mutual fund results also obtain only under very restrictive conditions for CPT investors. But mean variance analysis and the resulting CAPM does hold with only minor additional assumptions.