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

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 US 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. In a continuous-time diffusion setting the instantaneous investment opportunity set is completely described by the real interest rate and the slope of the capital market line, or Sharpe ratio, as in the classic Sharpe-Lintner Capital Asset Pricing Model. The slope of the capital market line depends in turn on the risk premium and volatility of the market return, and there is now strong evidence of time variation both in the equity risk premium and in market volatility, implying variation in the market Sharpe ratio, as well as in the real interest rate. Kandel and Stambaugh (1990), Whitelaw (1997), and Perez-Quiros and Timmermann (2000) have all found significant cyclical variation in the market Sharpe ratio. Other studies that identify significant predictors of the equity risk premium include: Lintner (1975), the interest rate; Campbell and Shiller (1988) and Fama and French (1988), the market dividend yield; Fama and French (1989), the term spread and the junk bond yield spread; Kothari and Shanken (1999), the Book-to-Market ratio. The Intertemporal Capital Asset Pricing Model (ICAPM) of Merton (1973) suggests that when there is stochastic variation in investment opportunities, it is likely that there will be risk premia associated with innovations in the state variables that describe the investment opportunities. However, despite this evidence of time variation in investment opportunities, and despite the lack of empirical success of the classic single period CAPM and its consumption based variant, there has been relatively little effort to test models based on Merton’s classic framework, a significant exception being Campbell (1993). One reason for this lack of emphasis on the ICAPM may have been the tendency to lump the ICAPM and Ross’ (1976) Arbitrage Pricing Theory together as simply different examples of “Factor Pricing Models”. Yet this is to ignore the distinguishing characteristic of the ICAPM that the priced “factors” are not just any set of factors that are correlated with returns, but are the innovations in state variables that predict future returns. In this paper we estimate a simple “The multi-factor models of Merton (1973) and Ross (1976) . . . can involve multiple factors and the cross-section of expected returns is constrained by the cross-section of factor loadings . . .. The multi-factor models are an empiricist’s dream . . . can accommodate . . . any set of factors that are correlated with returns.” Fama (1991, p1594). It is surprising that papers testing conditional versions of the CAPM that allow for time variation in expected returns typically do not allow for the pricing of the state variables they use to describe the investment opportunity set. Jagannathan and Wang (1996) explicitly assume that “the hedging motives are not sufficiently important . . .. ”(to warrant consideration of the ICAPM).