Reassessing the evidence on factor and portfolio premia

Using the modelling and estimation framework of W. Cao, C. Hurvich and P. Soulier (2017), we perform a test of the mean ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>T</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> {T₂} statistic) for a large collection of daily Fama–French factors and portfolio returns, and compare the results with those based on the standard t test. The <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>T</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> {T₂} -based results provide clearly weaker evidence in favor of various premia and in some cases suggest their absence. On the US market, the discrepancy between the tests is particularly large for the momentum factor. Caution should be exercised when assessing the presence of a given premium with the t test.