We study return predictability using a model of speculative trading among competitive traders who agree to disagree about the precision of private information. Although traders apply Bayes' Law consistently, returns are predictable. In addition to trading on long‐term fundamental value, traders also trade on perceived short‐term opportunities arising from foreseen future disagreement, as in a Keynesian beauty contest. Contradicting conventional wisdom, this short‐term speculation dampens price fluctuations and generates time‐series momentum. Model calibration shows quantitatively realistic patterns of return dynamics. Consistent with empirical evidence, our model predicts more pronounced momentum for stocks with higher trading volume.