I need to know what the annual risk-free rate of return has been. I know no such rate actually exists, so let's say I want to use the "overnight" rate as a proxy.
But the overnight rate is just an overnight rate. I need to know what my risk-free return rate would be over a whole year. How do I calculate this?
Assuming overnight percentage for each day is known, express that as an overnight multiplier (so .1% would be a multiplier of 1.001), then take the product of all those multipliers. To get it back from multiplier form to percent form, subtract 1 from the multiplier, then multiply by 100.
That will be close, though it ignores round-off.
As far as I know, when the rate varies every night, there is no alternative to multiplying it all out. A program, or spreadsheet, is recommended.
Or you could try websearching "effective APR history for overnight bank rate" and see if someone has already done the work for you.
Risk free rates are usually RFR OIS swaps. In the USD,that would be SOFR, in EUR ESTR and so forth. Risk free rates for the 1y term are directly market quoted (fixed float swaps where float leg is a overnight index like ESTR and the fixed leg is the quoted swap price).
If you need it retrospectively, what is the use case? That would be the compounded RFR rate as computed in the swap for actual payment.
