We model the law of small numbers (LSN)—the incorrect belief that even small samples represent the properties of the underlying population—to study its effects on trading behavior and asset prices. In our model, belief in LSN encourages investors to expect short-term price trends to reverse and long-term price trends to continue. As a result, asset prices show short-term momentum and long-term regression. The model can reconcile the coexistence of the disposition effect and return the extrapolation. In addition, it makes new predictions about investor behavior, including return patterns before buying and selling, the effect of a weak position on long-term holding, doubling in buying, positive correlation between doubling and the effect of the situation, and the tendency to sell various past returns. By testing these predictions using account-level transaction data, we show that LSN provides a low-level approach to understanding various mysteries about investor behavior.
That’s according to a new NBER working paper by Lawrence J. Jin and Cameron Peng. A good follow-up would be “what if non-investors overextrapolate from small samples?”
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