Risk Free Rate and Fama French factors
For a US risk free rate, Ken French’s site provides downloadable files of Fama/French factors that include this.
On the data library page:
Scroll down to U.S. Research Returns Data (Downloadable Files)
The Fama/French Factor downloadable files are available in default/monthly, weekly or daily format.
The risk free rate in these files is based on the returns for a 1 month (4 week) Treasury Bill, and these are expressed in terms of monthly, weekly or daily returns.
For example, the monthly risk free return values include:
- 200701 - 0.44
- 200801 - 0.21
For January 2007 the risk free monthly return is 0.44%, and for January 2008 0.21%
If rather than Ken French’s site you go to the FRED Economic Data (Federal Reserve Bank of St. Louis Economic Data) and download the 4-Week Treasury Bill: Secondary Market Rate (Series id TB4WK) from Board of Governors of the Federal Reserve System H15 Selected Interest Rates, they you will get a file expressing the annualised yield on a T-Bill.
For example, the monthly yield figures for TB4WK include:
- 2007-01-01 – 4.84
- 2008-01-01 – 2.68
For January 2007 the annual yield on a 4-week T-Bill was 4.84% and for January 2008 2.68%
Converting annual yield to monthly return
To make an annual yield, downloaded from FRED Economic Data or Datastream or Bloomberg etc., comparable with the monthly return from the downloadable Fama/French factors we need to convert. We could use an Excel formula
4.84% annually – POWER( (1 + 4.84/100), 1/12 ) = 1.003947 – monthly return 0.39%
2.68% annually – POWER((1 + 2.68/100), 1/12 ) = 1.002206 – monthly return 0.22%
[Converting to weekly would be POWER( (1+r/100), 1/52 ) where r is the annual yield
- converting to daily POWER( (1+r/100)/1/250 ) assuming 250 trading days per year]
There are two important steps to finding a good proxy for the risk free rate:
- Finding a series that is as close to risk free as possible for the analysis you are doing, and where you have data available for the relevant dates.
- Comparing the data you retrieve with the data format you want and converting between an annual yield and monthly/weekly/daily return as appropriate
In academic work, we recomend that you what you have chosen for your risk free rate and any data conversion that you have applied.