How is the cost of equity for a specific stock calculated using the Fama-French 5 factor model? The Fama-French 5 factor model is as follows:
$$R_a = R_f + \beta_m \left( R_m - R_f\right) + \beta_s\text{SMB} + \beta_v\text{HML} + \beta_p\text{RMW} + + \beta_i\text{CMA}$$
It is quite easy to find $\beta_m$ for a specific stock (most stock websites have it listed), and the market premium is also quite easy to determine since $R_f$ the US Treasury 1-month bond and the annual return of the market in the long term (at least in the U.S.) hovers around 8-10%.
However, I am not able to find a resource to find out the size, value, profitability, and investing premiums nor can I find the specific betas for each risk factor for a specific stock.
My question is if I want to calculate the cost of equity for a specific stock, using the CAPM model is quite easy as most of the numbers are readily available, but how could I go about finding the relevant figures for the rest of the risk factors?
If you visit Ken French's website (specifically, his data library), you can download monthly and daily returns for the 5-factor model (as well as similar returns for the Carhart momentum factor).
You can then find annual averages for those and compute the cost of equity in a similar way as for the CAPM.