Factor to explain factor

The new fama-french model replaces the existing five-factor model.  The new five-factor fama-french model includes  profitability and investment factors.

Profitability factor: Robust minus weak operating profit (RWA )= (SR + BR) / 2 – (SW + BW) / 2 = [(SR – SW) + ( BR - BW)] / 2 

Investment factor:  Conservative minus aggressive Investment (CMA)  = (SC + BC) / 2 – (SA + BA) / 2 = [(SC – SA) + ( BC -BA)] / 2

S = small ; B = big; R = Robust; W= Weak; C= Conservative; A = Aggressive 

The new model is:

$R_{t}-RF_{t} = \alpha + \beta_{1}[RM_{t}-RF_{t}] + \beta_{2}SMB_{t}  + \beta_{3}HML_{t}  + \beta_{4}RMW_{t}  + \beta_{5}CMA_{t}  + \epsilon_{t}$

$RM_{t}-RF_{t}$ = excess market return
$SMB_{t}$ = the Size factor
$HML_{t}$ = the value factor
$RMW_{t}$ = the profitability factor
$CMA_{t}$ = the investment factor
$RF_{t}$ = risk free rate