# How to calculate daily risk free interest rates

I'm working on an assignment in which I need to calculate excess returns 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.

The interest rate on three months T-Bills is 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 weeks treasury bill (ticker: ^IRX) historical quotes provided by Yahoo! Finance;
• Under the assumption that on Yahoo! Finance bond yields are quoted as Effective Annual Rate (EAR), the 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, the excess return of 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 provides data for three months T-Bills. Are these 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 $$r_1 = (1+r_{90})^{\frac{1}{90}} - 1$$