We build a model of the law of small numbers (LSN)—the incorrect belief that even small samples represent the characteristics of the underlying population—to study its implications for trading behavior and asset prices. In the model, LSN investors’ beliefs depend on past price trends: they expect short-term trends to revert and long-term trends to continue. In addition, asset prices exhibit excess volatility, short-term momentum, and long-term reversals. The model makes additional predictions about investor behavior, including the coexistence of return extrapolation and the disposition effect, a weakened disposition effect for long-term holdings, “doubling down” in buying, consistency between doubling down and the disposition effect, and heterogeneous trading propensities to past returns. By testing these predictions using account-level transaction data, we show that the LSN provides a parsimonious way for understanding a variety of puzzles about investor behavior.
