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 our model, a belief in the LSN induces investors to expect short-term price trends to revert and long-term price trends to persist. As a result, asset prices exhibit short-term momentum and long-term reversals. The model can reconcile the coexistence of the disposition effect and return extrapolation. In addition, it makes new predictions about investor behavior, including return patterns before purchases and sales, a weakened disposition effect for long-term holdings, doubling down in buying, a positive correlation between doubling down and the disposition effect, and heterogeneous selling propensities to past returns. By testing these predictions using account-level transaction data, we show that the LSN provides a parsimonious way of understanding a variety of puzzles about investor behavior.