Factor pricing in a finite economy

Abstract

Prior theoretical derivations of the Arbitrage Pricing Theory (APT) bound an aggregate measure of the deviation of mean asset returns from that predicted by a linear pricing equation. It is conceivable, given this bound, that some assets might be badly mispriced by the model. In this paper, a more intuitive derivation of the factor pricing equation is presented which describes the deviation on an asset by asset basis. The deviation is shown to be small for assets in a realistic finite economy and is arbitrarily close to zero for those assets with arbitrarily small size relative to aggregate wealth. It follows that the linear pricing equation provides a good approximation for the mean returns of all traded assets.