Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios

The arbitrage pricing theory (APT) attributes differences in expected returns to exposure systematic risk factors, which are typically assumed be strong. In this paper we consider two aspects of the APT. Firstly relate factors statistical factor model a theoretically consistent set defined by their conditional covariation with stochastic discount (mt) used price securities within inter-temporal asset models. We show that premia arise from non-zero correlation observed mt; and errors mt: Secondly compare estimates using portfolios ones obtained individual securities, identification conditions terms strength same that, general, no clear cut ranking small sample bias estimators is possible.