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Estimating The Anomaly Base Rate -- by Alexander M. Chinco, Andreas Neuhierl, Michael Weber

The academic literature literally contains hundreds of variables that seem to predict the cross-section of expected returns. This so-called "anomaly zoo" has caused many to question whether researchers are using the right tests of statistical significance. But, here's the thing: even if researchers use the right tests, they will still draw the wrong conclusions from their econometric analyses if they start out with the wrong priors---i.e., if they start out with incorrect beliefs about the ex ante probability of encountering a tradable anomaly.
So, what are the right priors? What is the correct anomaly base rate?
We develop a first way to estimate the anomaly base rate by combining two key insights: 1) Empirical-Bayes methods capture the implicit process by which researchers form priors based on their past experience with other variables in the anomaly zoo. 2) Under certain conditions, there is a one-to-one mapping between these prior beliefs and the best-fit tuning parameter in a penalized regression. We study trading-strategy performance to verify our estimation results. If you trade on two variables with similar one-month-ahead return forecasts in different anomaly-base-rate regimes (low vs. high), the variable in the low base-rate regime consistently underperforms the otherwise identical variable in the high base-rate regime.