It is shown that the arbitrage pricing theory holds in each infinitesimal period of a continuous trading model under the assumption that dividend payoffs are functionals of factor and idiosyncratic uncertainty. This generalizes the one-period model's result that the arbitrage pricing theory holds under the assumption that price changes in a given period satisfy a factor structure. Since instantaneous returns in a multiperiod model are endogenously determined, the theory is derived under assumptions that may be viewed as restricting more primitive characteristics of the economy than the assumptions made for the one-period model. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

[It is shown that the arbitrage pricing theory holds in each infinitesimal period of a continuous trading model under the assumption that dividend payoffs are functionals of factor and idiosyncratic uncertainty. This generalizes the one-period model's result that the arbitrage pricing theory holds under the assumption that price changes in a given period satisfy a factor structure. Since instantaneous returns in a multiperiod model are endogenously determined, the theory is derived under assumptions that may be viewed as restricting more primitive characteristics of the economy than the assumptions made for the one-period model.]

The Arbitrage Pricing Theory (APT) implies that if asset returns have a factor structure, then an approximate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables which may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the APT are also discussed.

The arbitrage pricing theory implies that if asset returns have a factor structure, then an approximate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables that may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the arbitrage pricing theory are also discussed.

The paper provides sufficient conditions under which a nonrandom economic variable specific to some asset (the dependent variable) can be represented as a linear combination of the betas of some random characteristics of the asset (the independent variables) with some economy-wide factors. This generalizes Ross' APT that proves the above in the case where the dependent variables are expected returns and the independent variables are returns. This generalization will provide a theoretical basis for many existing multibeta relationships beyond the setting of asset pricing models and, thus, motivate their wider use in empirical and theoretical research.