The Rodney L. White Center for Financial Research A Simple Model of Intertemporal Capital Asset Pricing and Its Implications for the Fama-French Three-Factor Model

Characterizing the instantaneous investment opportunity set by the real interest rate and the maximum Sharpe ratio, a simple model of time varying investment opportunities is posited in which these two variables follow correlated Ornstein-Uhlenbeck processes, and the implications for stock and bond valuation are developed. The model suggests that the prices of certain portfolios that are related to the FamaFrench HML and SMB hedge portfolios will carry information about investment opportunities, which provides a potential justification for the risk premia that have been found to be associated with these hedge portfolios. Evidence that the FF portfolios are in fact associated with variation in the investment opportunity set is found from an analysis of stock returns. Further evidence of time variation in the investment opportunity set is found by analyzing bond yields, and the time variation in investment opportunities that is identified from bond yields is shown to be associated both with the time-variation in investment opportunities that is identified from stock returns and with the returns on the Fama-French hedge portfolios. Finally, both pricing kernel and tracking portfolio approaches are used to provide estimates of the magnitude of the HML and SMB risk premia implied by our simple model.