Under the same assumptions that Ross used to assert the existence of an efficient fund (on which a spanning set of options can be written) we prove that almost any portfolio is an efficient fund. From a constructive point of view, a randomly chosen vector of portfolio weights yields an efficient fund. When the Ross assumptions are relaxed, a limited notion of efficiency‐maximal efficiency‐is the best attainable. The maximally efficient funds are also everywhere dense in the portfolio space. Some implications are discussed and illustrative examples given.