Market anomaly

A market anomaly in a financial market is predictability that seems to be inconsistent with (typically risk-based) theories of asset prices.^[1] Standard theories include the capital asset pricing model and the Fama-French Three Factor Model, but a lack of agreement among academics about the proper theory leads many to refer to anomalies without a reference to a benchmark theory (Daniel and Hirschleifer 2015^[2] and Barberis 2018,^[3] for example). Indeed, many academics simply refer to anomalies as "return predictors", avoiding the problem of defining a benchmark theory.^[4]

Academics have documented more than 150 return predictors (see List of Anomalies Documented in Academic Journals). These "anomalies", however, come with many caveats. Almost all documented anomalies focus on illiquid, small stocks.^[4] Moreover, the studies do not account for trading costs. As a result, many anomalies do not offer profits, despite the presence of predictability.^[5] Additionally, return predictability declines substantially after the publication of a predictor, and thus may not offer profits in the future.^[4] Finally, return predictability may be due to cross-sectional or time-variation in risk, and thus does not necessarily provide a good investment opportunity. Relatedly, return predictability by itself does not disprove the efficient market hypothesis, as one needs to show predictability over and above that implied by a particular model of risk.^[6]

The four primary explanations for market anomalies are (1) mispricing, (2) unmeasured risk, (3) limits to arbitrage, and (4) selection bias.^[4] Academics have not reached a consensus on the underlying cause, with prominent academics continuing to advocate for selection bias,^[7] mispricing,^[3] and risk-based theories.^[8]

Anomalies can be broadly categorized into time-series and cross-sectional anomalies. Time-series anomalies refer to predictability in the aggregate stock market, such as the often-discussed Cyclically Adjusted Price-Earnings (CAPE) predictor.^[9] These time-series predictors indicate times in which it is better to be invested in stocks vs a safe asset (such as Treasury bills). Cross-sectional anomalies refer to the predictable out-performance of particular stocks relative to others. For example, the well-known size anomaly^[10] refers to the fact that stocks with lower market capitalization tend to out-perform stocks with higher market capitalization in the future.