A Re-Interpretation of 'Significant' Empirical Financial Research

Abstract

Currently, the use and interpretation of t statistics and p-values is under scrutiny in various scientific fields for several reasons: p-hacking, data dredging, misinterpretation, multiple testing, or selective reporting, among others. To the best of our knowledge, this discussion has hardly reached the empirical finance community. Thus, the aim of this paper is to show how the typical p-value based analysis of empirical findings in finance can be fruitfully enriched by the supplemental use of further statistical tools. We revisit popular studies regarding the validity of the CAPM and determine Bayesian measures for hypothesis testing. In comparison to the typical yes and no decisions made under frequentist approaches, these measures allow a direct interpretation regarding the strength of the empirical finding. For instance, while Fama and MacBeth (1973) find an expected risk premium that is significantly different from zero for systematic risk, we observe that the likelihood for an expected risk premium to be zero is approximately 43% at the same time.

Keywords: p-value; t statistic; empirical finance; CAPM; Bayesian statistics

JEL Classification: F30; G00; G11; G15