Semi-strong Factors in Asset Returns

This paper re nes the approximate factor model of asset returns by dividing sys- tematic factors into a) natural rate factors, whose sum of squared factor betas grow at the same rate as the number of assets, and b) semi-strong factors, whose sum of squared factor betas grow, but at a slower rate. We describe a methodology to estimate the cross-sectional mean and mean-square of semi-strong factor betas, and to di¤eren- tiate them from natural rate factors. We apply the methodology to US equity returns using daily changes in exchange rates and commodity prices as semi-strong factors. We nd that oil and gold price changes are signi cant factors while foreign exchange rate changes are only signi cant in more recent subperiods.