Summary: In a portfolio problem with given asset returns, the portfolio efficient set is the set of portfolios chosen by any risk averse agent. Using an approach of \textit{B. Peleg} and \textit{M. E. Yaari} [Econometrica 43, 283--292 (1975; Zbl 0314.90025)], we characterize the portfolio efficient set and derive some of its properties. In particular, we show that it may not be convex, proving that a central result of mean variance theory, the efficiency of the market portfolio, does not generalize. Finally, a characterization of the efficiency of several observations gives a version of revealed preference theory for incomplete markets.