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.