Cumulative Prospect Theory (CPT) has been used as a possible explanation of aggregate pricing anomalies like the equity premium puzzle. This paper shows that, unlike in expected utility models, a complete market is not sufficient to guarantee that the market portfolio is efficient and that the standard representative-agent analysis is valid. The separation or mutual fund theorems hold only under very restrictive conditions for CPT investors. Without them, aggregation breaks down, and assets are not necessarily priced as if there were one investor who behaved according to CPT. Under more limited conditions, the market portfolio can be efficient in a complete market with equally probable states. But in this case, individual CPT investors behave in the aggregate like a standard expected utility investor. Similarly, when faced with elliptically distributed assets, the capital asset pricing model (CAPM) holds for any combination of CPT investors and expected utility maximizers.