Equilibrium asset pricing and the cross section of expected returns

In a mean-variance framework with a representative agent, any linear model for the cross section of expected returns can be supported as an equilibrium as long as the market portfolio is spanned by the factor mimicking portfolios. Any set of factors is admissible as long as the spanning condition is satisfied. Factors based on size, book-to-market, momentum, investment, profitability, behavioral biases, principal components, or any combination of these can be used as equilibrium factors. An equilibrium model with M risk factors can be reduced to a collection of M models where each model has a single risk factor, which is covariance with the market portfolio.