We build a model of the law of small numbers (LSN) – the erroneous belief that even small samples represent properties of the underlying population – to study its implications for trading behavior and asset prices. In our model, belief in the LSN induces investors to expect short-term price trends to reverse 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 the extrapolation of the return. Additionally, it makes new predictions about investor behavior, including return patterns before purchases and sales, a weakened disposition effect for long-term holdings, doubling of purchases, a positive correlation between doubling and the disposition effect, and heterogeneous sales propensities with past returns. By testing these predictions using account-level transaction data, we show that LSN provides a parsimonious way to understand various puzzles regarding investor behavior.
It’s from a new NBER working paper by Lawrence J. Jin and Cameron Peng. A nice follow-up would be “what if non-investors overextrapolate from small samples?” »
