Applications of E-values to asset pricing

This dissertation examines the application of a new class of hypothesis tests, E-value tests, to empirical asset pricing. This class of hypothesis tests offer greater flexibility than classical hypothesis tests such as the ability to average test statistics across multiple analysis. When certain conditions are satisfied, it is even possible combine test statistics to come up with a measure of total significance across multiple analyses, each of which may not be significant on its own but when combined are significant. Furthermore, the specific E-value hypothesis test I chose to use, the Split Likelihood Ratio Test (SLRT), has the property of being free of regularity conditions while still maintaining a bounded Type I error. In my first essay I take advantage of the flexibility of E-values to re-analyze several classic asset pricing anomalies on individual stock characteristics by individual monthly cross sections and using a measure of cumulative significance over the entire period to show that several classic asset pricing anomalies are not significant. I also use the flexibility of the E-value based approach to show that the January Effect is real for certain stock characteristics. My choice of the SLRT as the specific test I use allows me to avoid several issues that have previously been discussed in the finance literature regarding the proper estimation of standard errors in empirical asset pricing. As far as I know, this is the first application of E-values (in general) and the SLRT to multiple regression, panel data and finance. In my second essay I replicate the key analyses from the classic Fama and French 3-Factor (1993) and 5-Factor (2015) papers using the original data and extended data through June 2024 and compare the results from a traditional regression t-test to the regression SLRT. I find that the regression intercept term is frequently no longer significant when the SLRT is used. Furthermore, the frequency at which this occurs, and the very small values of the SLRT statistics make it extremely unlikely that this is simply due to the SLRT having lower statistical power. I also use an SLRT based test that tests the joint significance of intercepts like the GRS test Fama and French (2015) used and find that all the 5-factor model intercepts are jointly non-significant, though the 3-factor intercept is significant. The implication is that while Fama and French and other researchers who use their research as a starting point take the existence of significant intercepts when using classical t-tests as a sign that the models do not fully explain the cross section of stock returns, in fact, the intercepts may not actually be significant when alternative hypothesis tests that rely on fewer assumptions, such as the SLRT, are used. If so, the Fama-French models may perform better than previously thought in explaining the cross section of stock returns.