In a single‐period model with options on the market portfolio, linear factor pricing holds if and only if the variance of the market conditional on the factors is zero. There is no need for factors other than nonlinear functions of the market. For accurate linear pricing of all payoff patterns the factors must be rotationally equivalent to Hakansson's “supershares.” In a multiperiod model, a similar set of results holds, but with consumption replacing the market payoff. The methodology of the empirical Arbitrage Pricing Theory literature is not consistent with either the single‐period model or the multiperiod model.

In a single-period model with options on the market portfolio, linear factor pricing holds if and only if the variance of the market conditional on the factors is zero. There is no need for factors other than nonlinear functions of the market. For accurate linear pricing of all payoff patterns the factors must be rotationally equivalent to Hakansson's “supershares.” In a multiperiod model, a similar set of results holds, but with consumption replacing the market payoff. The methodology of the empirical Arbitrage Pricing Theory literature is not consistent with either the single-period model or the multiperiod model.

This paper proposes a new definition of the Efficient Markets Hypothesis with respect to information, which is more formal and precise than those of Rubinstein [13] , Fama [4] , Jensen [6] , and Beaver [1] , and which fits well as a framework for interpreting the many tests of the Efficient Markets Hypothesis in the literature. Security markets are here considered “efficient with respect to information set ϕ ” if and only if revealing ϕ to all agents would change neither equilibrium prices nor portfolios. In addition to other desirable features, this definition has the “subset property”: efficiency with respect to ϕ implies efficiency with respect to any subset of ϕ .