Anomalies and False Rejections

We use information from over 2 million trading strategies randomly generated using real data and from strategies that survive the publication process to infer the statistical properties of the set of strategies that could have been studied by researchers. Using this set, we compute t-statistic thresholds that control for multiple hypothesis testing, when searching for anomalies, at 3.8 and 3.4 for time-series and cross-sectional regressions, respectively. We estimate the expected proportion of false rejections that researchers would produce if they failed to account for multiple hypothesis testing to be about 45%.