Making Equity Factor Models Meaningful?

Most researchers use classical statistical testing, with a t-statistic of 2.0 as the significance threshold for accepting an hypothesis. However, this threshold is valid only if the associated p-value derives from a single test. There are hundreds of published factor tests and an unknown number of unpublished tests. How far should researchers raise the significance threshold to account for multiple hypothesis testing? In their December 2025 paper entitled “What Threshold Should be Applied to Tests of Factor Models?”, Campbell Harvey, Alessio Sancetta and Yuqian Zhao address this issue by:

1. Clarifying applicable statistical methods, including how to measure the probability that the null hypothesis is true and insight on the False Discovery Rate (FDR), without knowing the number of tests.
2. Reconciling existing results in the literature.
3. Providing guidance on the threshold for deciding statistical significance.

They also discuss the plausibility of the assumptions embedded in their approach. Based on mathematical analysis in the context of financial research, they find that: (more…)