We show that consumption-based asset pricing models with time-separable preferences generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. Rational investors with subjective beliefs about price behavior optimally learn from past price observations. This imparts momentum and mean reversion into stock prices. The model quantitatively accounts for the volatility of returns, the volatility and persistence of the price-dividend ratio, and the predictability of long-horizon returns. It passes a formal statistical test for the overall fit of a set of moments provided one excludes the equity premium.