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

71 Pages Posted: 8 Nov 2017 Last revised: 18 Oct 2023

See all articles by Lawrence J. Jin

Lawrence J. Jin

SC Johnson College of Business, Cornell University; National Bureau of Economic Research (NBER)

Cameron Peng

London School of Economics & Political Science (LSE) - Department of Finance

Date Written: November 6, 2017

Abstract

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.

Keywords: The Law of Small Numbers, Trading Behavior, Disposition Effect, Return Extrapolation

JEL Classification: G02, G11, G12

Suggested Citation

Jin, Lawrence J. and Peng, Cameron, The Law of Small Numbers in Financial Markets: Theory and Evidence (November 6, 2017). Available at SSRN: https://ssrn.com/abstract=3066369 or http://dx.doi.org/10.2139/ssrn.3066369

Lawrence J. Jin

SC Johnson College of Business, Cornell University ( email )

310E Warren Hall
Ithaca, NY 14850
United States
607-255-0581 (Phone)

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Cameron Peng (Contact Author)

London School of Economics & Political Science (LSE) - Department of Finance ( email )

United Kingdom

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