The Law of Small Numbers in Financial Markets: Theory and Evidence

We build a model of the law of small numbers (LSN)—the incorrect belief that even small samples represent the properties of the underlying population—to study its implications for trading behavior and asset prices. In the model, a belief in the LSN induces investors to expect short-term price trends to revert and long-term price trends to continue. As a result, asset prices exhibit excess volatility, short-term momentum, and long-term reversals. The model makes additional predictions about investor behavior, including the coexistence of the disposition effect and return extrapolation, 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.

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