Multiple Hypothesis Testing, Empirical Asset Pricing, and Factor Investing

Abstract

This paper explores the critical issue of multiple hypothesis testing in empirical asset pricing, where the simultaneous testing of numerous factors from the same dataset increases the likelihood of false discoveries due to noise. Traditional hypothesis testing approaches, such as using a t-statistic cutoff of 2.0, often lead to a high rate of Type I errors, misidentifying factors as significant purely by chance. To address this, both frequentist and Bayesian methodologies have been developed. Frequentist methods, such as the Bonferroni and Holm corrections, aim to control error rates like the family-wise error rate (FWER) and false discovery rate (FDR), often leading to more stringent thresholds for significance. Bayesian approaches, on the other hand, incorporate prior knowledge and probabilistic frameworks to assess the validity of factors, offering greater flexibility but requiring complex computations. Recent advancements, such as the use of bi-modal mean distributions and double-bootstrap methods, have further refined these techniques, balancing Type I and Type II errors more effectively. This paper reviews the evolution of these methodologies, highlights their applications in financial research, and discusses their implications for factor investing.

Keywords: multiple hypothesis testing, empirical asset pricing, factor investing

JEL Classification: G12