Abstract
The multiple testing problem plagues many important issues in finance such as fund and factor selection. Many look good purely by luck. There are a number of statistical techniques to control for multiplicity that reduce Type I errors - but it is unknown by how much. We propose a new way to calibrate both Type I and Type II errors. We start with the researcher's prior belief on the proportion of managers that are skilled. Using a double bootstrap method, we then establish a t-statistic hurdle that is associated with a specific false discovery rate (e.g., 5%). We also establish a t-statistic hurdle that is associated with a certain acceptable ratio of misses to false discoveries (Type II error scaled by Type I error) | effectively allowing for differential costs of the two types of mistakes. Evaluating current methods within our framework, we find that they lack the power to detect outperforming managers.
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