# 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.

• Would I have to make sure the betas for the factors match the time period of the premiums (i.e. their regression period matches the length of the average)? Also, where would I find the betas for a specific stock. I have been looking at Portfolio Visualizer, but I am not sure if that is any good. Commented Aug 21, 2020 at 23:20
• Absolutely; those have to match. Betas tend to change over different pars of the business cycle, so that is one reason to make sure they match. You will need to do the regressions yourself. $R$ should make easy work of it if you write a loop. Not sure if you would find those betas pre-computed anywhere. Commented Aug 21, 2020 at 23:55