Semi-Strong Factors in Asset Returns

Abstract

We refine the approximate factor model of asset returns by distinguishing between strong factors, whose sum of squared factor betas grow at the same rate as the number of assets, and semi-strong factors, whose sum of squared factor betas grow to infinity, but at a slower rate. We develop a test statistic for strength of factors based on the cross-sectional mean-square of regression-estimated betas. We also describe an adjusted version of the test statistic to differentiate semi-strong factors from strong factors. We apply the methodology to daily equity returns to characterize some pre-specified factors as strong or semi-strong.