Incidentally, the Federal Reserve has extensive time series of interest rates. Almost any short term rate on the list would be appropriate and would not change the analysis.
You might just take the 4-week Treasuries and consider the stated is the yield for that day. You may need to convert this to a one day returns to get a "risk free rate" for your CAPM type calculations.
Do not worry about the change in the prices of the T-bills --- just take the returns like they were the returns from a pass book account and do the logical arithmetic.
For longer-term bonds this would b a big mistake, but it is close enough for 30 day T-bills.
In T-bill world, the year has 360 days, so you may want to compute the daily return on that basis. Alternatively, you could allocate the T-bill return to 250 (or so) trading days. There is good sense to either of these.
What would be silly would be to just plug in the T-bill rate into the CAPM model. This would mean a daily benchmark of more than 4%, which simply doesn't happen in a relatively stable currency.
The Suggestion from the WRDS Help Desk --- It Helps Too!
"Hi, The easiest way to get the daily 'risk free rate' is in our Fama-French Factors located in our web site
The 'Risk Free Rate' is the one month treasury bill rate."
NOTE: The URL is not hot-linked. You'll need to use your password access to get to the file.
This is a good suggestion and it may be easier than working with the Fed data linked above. Some people have gone this way and it worked fine for them.
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