# Calculate excess returns for Sharpe Ratio with today's or past risk free rate of return?

I am struggling with the calculation of the Sharpe ratio. I am wondering whether to calculate the daily excess returns with today's risk free rate of return or the risk free rates corresponding to the date of the return observations?

E.g., I have the annualized fund returns r_fund and the risk free rate of return, which is the daily 3-months US treasury bill rates r_f. Today's risk free rate of return is 0.27% p.a.

date           r_fund      r_f      excess(r_fund-r_f)
2016-01-05     0.200       0.25     -0.050
2016-01-07     0.800       0.26      0.540
2016-01-08     0.900       0.24      0.660
...


Thus, should I calculate the excess return as shown in the table above or just subtract today's r_f (0.27%) from each r_fund?

• You should use the return on the risk-free rate and not just the rate itself. Then, use create the excess return by subtracting the risk-free return from the fund's return over the same period. (The rf return in the first period is thus (0.25-0.26)/0.25 or ln(0.26/0.25) – Tim Mar 14 '16 at 22:51