Indeed, many academics simply refer to anomalies as "return predictors", avoiding the problem of defining a benchmark theory.
[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.
[6] The four primary explanations for market anomalies are (1) mispricing, (2) unmeasured risk, (3) limits to arbitrage, and (4) selection bias.
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).
The mispricing explanation is natural, as anomalies are by definition deviations from a benchmark theory of asset prices.
The deviation from this theory is measured by a non-zero intercept in an estimated security market line.
Among academics, a common response to claims of mispricing was the idea that the anomaly captures a dimension of risk that is missing from the benchmark theory.
[12] Perhaps the most well-known example of this unmeasured risk explanation is found in Fama and French's seminar paper on their 3-factor model: "if assets are priced rationally, variables that are related to average returns ... ..., must proxy for sensitivity to common (shared and thus undiversifiable) risk factors in returns.
Moreover, the ICAPM generally implies the expected returns vary over time, and thus time-series predictability is not clear evidence of mispricing.
Empirical shortcomings primarily regard the difficulty in measuring wealth or marginal utility.
A large literature documents that trading costs greatly reduce anomaly returns.
For example, Sullivan, Timmermann, and White (2001) show that calendar-based anomalies are no longer significant after adjusting for selection bias.
McLean and Pontiff (2016) use an out-of-sample test to show that selection bias accounts for at most 26% of the typical anomaly's mean return during the sample period of the original publication.
[4] In contrast, Harvey, Liu, and Zhu (2016) adapt multiple testing adjustments from statistics such as the False Discovery Rate to asset pricing "factors".
They refer to a factor as any variable that helps explain the cross-section of expected returns, and thus include many anomalies in their study.
It has been debated in academic journals as to whether the effect is real or arises due to certain systemic errors.