Investors' subjective capital gains expectations are a key element explaining stock price fluctuations. Survey measures of these expectations display excessive optimism (pessimism) at market peaks (troughs). We formally reject the hypothesis that this is compatible with rational expectations. We then incorporate subjective price beliefs with such properties into a standard asset-pricing model with rational agents (internal rationality). The model gives rise to boom-bust cycles that temporarily delink stock prices from fundamentals and quantitatively replicates many asset-pricing moments. In particular, it matches the observed strong positive correlation between the price dividend ratio and survey return expectations, which cannot be matched by rational expectations.