# How to calculate daily risk free interest rates

I'm working on an assignment in which I need to calculate excess return for six stocks plus the S&P 500. I have computed daily logarithmic returns for every stock and for the market, I now need to calculate the risk free interest rate in order to be able to compute the excess return for every stock and the market.

Interest rates on three months T-Bills are a good proxy for the risk-free rate of return, but I have a lot of doubts on how to use data provided by Yahoo! Finance in order to compute the daily risk-free. Here are my assumptions and procedures:

• I use the 13 week treasury bill (ticker: ^IRX) historical quotes provided by Yahoo! Finance;
• Under the assumption that on Yahoo! Finance bonds yields are quoted as Effective Annual Rate (EAR), daily risk-free interest rate at time $t$ ($r_{f,t}^{daily}$) is computed as:

$$r_{f,t}^{daily}=(1+r_t)^{1/365}-1$$

where $r_t$ is the EAR rate at time $t$ provided by Yahoo.

Once computations are done, excess return for stock $i$ at time $t$ is defined as:

$$\text{Excess Return}=r_{i,t}-r_{f,t}^{daily}$$

Questions:

• Is this procedure correct? Note that I do not need it to be exceptionally precise, it is just a basic exercise, but I would like it to be at least conceptually correct.
• The Federal Reserve also provide data for three months T-Bills. Are this rates also provided as EAR?
• I have the same question. Have you found out the question? Could you share? Thanks. – user233051 Mar 17 '17 at 7:54
• @user233051 : I have answered your question and his. See your posed question here. – Mike O'Connor Aug 12 '18 at 8:33

The rates are annual. So if you want log returns just take the log of $1+r^f_t$ and divide by 365.
I think we can find daily risk free using following equation $$1 + r_{90} = (1 + r_1)^{90}$$ This follows from the fact there are no arbitrage opportunity. Here we assume that $$r_1$$ in the following periods will stay the same, that is non random. Thus, doing simple algebra we get $$r_1 = (1+r_{90})^{\frac{1}{90}} - 1$$