The effects of common risk factors on stock returns: A detrended cross-correlation analysis

In this paper, we investigate the cross-correlations between Fama and French three factors and the return of American industries on the basis of cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). Qualitatively, we find that the return series of Fama and French three factors and American industries were overall significantly cross-correlated based on the analysis of a statistic. Quantitatively, we find that the cross-correlations between three factors and the return of American industries were strongly multifractal, and applying MF-DCCA we also investigate the cross-correlation of industry returns and residuals. We find that there exists multifractality of industry returns and residuals. The result of correlation coefficients we can verify that there exist other factors which influence the industry returns except Fama three factors.