Dynamic Present Values and the Intertemporal CAPM

Abstract

Merton’s (1973) intertemporal Capital Asset Pricing Model is dicult to reconcile with present value computation when investment opportunities are random and time-varying. Merton assumes a geometric price process, and his equilibrium is constructed by solving for the instantaneous expected rate of return. We argue that this method is generally inconsistent with present value computations. We derive an alternative version of the Intertemporal CAPM based explicitly on present value computation with a strictly exogenous cash ow. Our model is derived without restrictive assumptions about the structure of the equilibrium price process. An essential feature of our model is that prices respond endogenously to shocks in expected return. In an example model, we show that shocks to stochastic volatility is negatively correlated with stock returns in equilibrium. The correlation increases in absolute magnitude with risk aversion.