Which Risk Free rate you should use to calculate performance ratios?

Hello,

Im wondering “what” risk free rate you should use in performance ratios, for example sharpe or traynor.

Lets say using excel and simple equations I calculate the expected return of Markte (Mean SP500) expected return of a porfolio of mine (mean of historical returns) and I calculate the sample standard deviation.

If I want to know the Sharpe ratio and having a excel sheet with monthly data, which risk free rate should I use and should a use a Mean of the series of risk free?

For example: tnx (10 year us) is at 2.16%. should i use this last rate and convert it to months 2.16^(1/12)? Should a use a mean/median of the TNX rates and then convert it to months? Or should I use a 1 month treasury and also convert the rate to months?

I have this question so I can apply it to my own studies.

Thanks!

For historical risk-adjusted performance ratios, I personally look at the historical monthly returns of a 10-year T-Bond index over the same time period as the risky asset. I find the geometric mean of each series, deduct the geometric mean of the risk-free asset from the risky asset’s geometric mean, and then divide that by the sample standard deviation (in the case of Sharpe).

Ok. Thanks. I was thinking something similar to that.