The Factor Space in Financial Markets

We show assets can be classified into diversifiable risks and non-diversifiable risks based on aggregate endowment and spanning so that in equilibrium agents eliminate diversifiable risks which must have zero values. Consequently, the benchmark portfolio that represents a pricing operator should have only a non-diversifiable risk, aggregate endowment should earn a positive risk premium over a riskless asset, and, even in incomplete markets, there should be a pricing operator represented by a function of aggregate endowment if any asset mean-independent of aggregate endowment is diversifiable. These results apply to both the CAPM and a representative agent model.