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


  • Michael J. Brennan,

  • Ashley W. Wang,

  • Yihong Xia

    Search for more papers by this author
    • Michael Brennan is at the Anderson School, UCLA, and Ashley Wang is at the Graduate School of Management, University of California, Irvine, and Yihong Xia is at the Wharton School of University of Pennsylvania. The authors thank the referee for his comments, which have led to substantial improvements in the paper. We are also grateful to Andrew Ang, David Chapman, George Constantinides, John Cochrane, Eugene Fama, Rick Green (the editor), Ravi Jaganathan, Pascal Maenhout, Jay Shanken, Ken Singleton, Baskharan Swaminathan, Zhenyu Wang, and seminar participants at the Fifth Texas Finance Festival, Beijing University, Carnegie Mellon University, Concordia, European University of Saint Petersburg, Hong Kong University of Science and Technology, Indiana University, London Business School, NBER 2002 Asset Pricing Program, Notre Dame, National Taiwan University, NYU, Stanford, University of Hong Kong, University of Lausanne, University of North Carolina, University of Strathclyde, WFA 2002 Annual Conference, AFA 2003 Annual Conference, and Wharton Brown Bag Lunch Seminar for helpful comments. We acknowledge the use of data on the Fama–French portfolios from the Website of Ken French. Xia acknowledges financial support from the Rodney L. White Center for Financial Research. Earlier drafts of the paper were circulated under the title “A Simple Model of Intertemporal Capital Asset Pricing and Its Implications for the Fama–French Three-Factor Model.”


A simple valuation model with time-varying investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by 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 U.S. Treasury bond yields and expected inflation from January 1952 to December 2000, and as predicted, the estimated maximum Sharpe ratio is related to the equity premium. In cross-sectional asset-pricing tests, both state variables have significant risk premia, which is consistent with Merton's ICAPM.