Estimating The Anomaly Base Rate
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.
We would like to thank Justin Birru, Svetlana Bryzgalova, Zhi Da, Xavier Gabaix, Niels Gormsen, Sam Hartzmark, Christian Julliard, Ralph Koijen, Bob Korajczyk, Yan Liu, Stefan Nagel, Walt Pohl, Jeff Pontiff, Tarun Ramadorai, Alessio Saretto, Andrea Tamoni, Julian Thimme, Allan Timmermann, Rüdiger Weber, and Dacheng Xiu for extremely helpful comments and suggestions. This paper has also benefited greatly from presentations at the University of Chicago, the University of Illinois, the MFA meetings, AQR Asset-Management Institute’s Academic Symposium, the Future of Financial Information Conference, the 5th BI-SHoF Conference, the NBER Summer Institute, the SITE Asset-Pricing Theory and Computation Meetings, the EFA Meetings, the NFA Conference, and the SAFE Asset-Pricing Workshop. Bianca He provided excellent research assistance. Weber also gratefully acknowledges financial support from the University of Chicago, the Fama Research Fund, and the Fama-Miller Center. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.