Consumption-based asset pricing models with time-separable preferences can generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. We consider rational investors who entertain subjective prior beliefs about price behavior that are not equal but close to rational expectations. Optimal behavior then dictates that investors learn about price behavior from past price observations. We show that this imparts momentum and mean reversion into the equilibrium behavior of the price-dividend ratio, similar to what can be observed in the data. When estimating the model on U.S. stock price data using the method of simulated moments, we find that it can quantitatively account for the observed volatility of returns, the volatility and persistence of the price-dividend ratio, and the predictability of long-horizon returns. For reasonable degrees of risk aversion, the model generates up to one-half of the equity premium observed in the data. It also passes a formal statistical test for the overall goodness of fit, provided one excludes the equity premium from the set of moments to be matched.