Semi-strong factors in asset returns

This paper refines the approximate factor model of asset returns by dividing factors into pervasive factors, whose associated eigenvalues grow at the same rate as the number of assets, and second-order factors, whose associated eigenvalues grow but at a lower rate. We show that in a many-asset economy, second-order factor exposures are not individually identified, but it is possible to measure aggregate features of the cross-section of second-order factor exposures if the time-series sample size is also large. We apply the methodology to US equity returns using changes in exchange rates as second-order factors.