# Are the explanatory factors for a firm's expected returns and its expected earnings/valuation multiples the same?

For example, the 3 factor Fama French model explains much of the cross-sectional variation in equity returns. Would these same 3 factors also explain the cross sectional variation in earnings/EV to EBITDA across equities? If not, why would the determinants of future earnings be different from future returns?

• I would say, the Fama-French 3 factor model explains cross-sectional variation in expected returns using cross-sectional variation in regression betas on the three factors. – Matthew Gunn Sep 11 '18 at 16:42
• I'm not quite sure what you're precisely asking? Could you be more clear in distinguishing cross-sectional variation in $X_{it}$ versus cross-sectional variation in the expectation $\operatorname{E}[X_{it}]$? Factors $F_j$ themselves versus regression betas $\beta_{ij}$ from a time-series regression on the factors? – Matthew Gunn Sep 11 '18 at 16:44
• Thanks. Apologies, I was unclear. The Fama-French 3 factor model is capable of capturing much of the cross-section of average equity returns. They show that these factors are useful in explaining a significant fraction of the time series variation in equity portfolio returns. What I am asking is whether these same FF factors could also be applied to earnings by extension. Would market, value and size factors in returns be useful in explaining time series variation in earnings? Or is there a different model that would be better for this purpose? – beeba Sep 11 '18 at 17:18
• Is the question, what fraction of a firm's time-series variation in earnings can be explained by time-series variation in the Fama French factors? What fraction of the time-series variation in earnings for the S&P500 can be explained by time-series variation in the Fama French factors? – Matthew Gunn Sep 11 '18 at 17:40
• The latter - what fraction of the time-series variation in earnings for the S&P500 can be explained by time-series variation in the Fama French return factors – beeba Sep 11 '18 at 19:48