Risk Free Rate and Fama French factors

Throughout 2012 Risk Free Rate for US and US has consistently been one of our top posts.

For a US risk free rate, Ken French’s site provides downloadable files of Fama/French factors that include this.

Fama French factors from Kenneth R. French Data Library (click to expand)

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]

Key Tip

There are two important steps to finding a good proxy for the risk free rate:

1. 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.
2. 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.

For further tips on potential sources, see earlier posts Risk Free Rate for US and US and Risk Free Interest Rate.