Estimation and Test of a Simple Model of Intertemporal Capital Asset Pricing

Abstract

A simple valuation model that allows for time variation in investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by two state variables, the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein-Uhlenbeck processes. The model parameters and time series of the state variables are estimated using data on US Treasury bond yields and inflation for the period January 1952 to December 2000. The estimated state variables are shown to be related to the equity premium and to the level of stock prices as measured by the dividend yield. Innovations in the estimated state variables are shown to be related to the returns on the Fama-French arbitrage portfolios, HML and SMB, providing a possible explanation for the risk premia on these portfolios. When tracking portfolios for the state variable innovations are constructed using returns on 6 size and book-to market equity sorted portfolios, the tracking portfolios explain the risk premia on HML and SMB, and these state variable tracking portfolios perform about as well as HML and SMB in explaining the cross-section of returns on the 25 size and book-to market equity sorted value weighted portfolios. An additional test of the ICAPM using returns on 30 industrial portfolios does not reject the model while the CAPM and the Fama-French 3 factor model are rejected using the same data.

Note: Previously titled "A Simple Model of Intertemporal Capital Asset Pricing and Its Implications for the Fama-French Three-Factor Model"