# What maturity Treasury yield to use for risk free rate to compare against asset typically held for 10 years?

I have a quarterly return in quarter i for an asset which is typically held for 10 years. Which maturity Treasury yield should I use as a risk free rate in this context, and from what period? I initially think quarter i-1, but that thinking may be flawed.

My thinking is I use the 10Y Treasury yield and divide by 4 to make quarterly. I’ve also been told to use the 3M Treasury yield as it’s most often used in literature.

There are mixed answers out there, so I’m hoping to answer this. Typically I’m reading one should use a Treasury yield as a proxy for the RFR with maturity roughly equal to the typical holding period of the asset, but others have different answers. Also getting different answers about whether to use Treasury yield from same quarter, or previous quarter, as RFR rate for quarterly return in quarter i.

Edit: I’ll be using the resulting excess returns for an arithmetic Sharpe ratio (simple excess returns then Sharpe ratio scaled by sqrt(4)) so I am effectively ignoring the effects of compounding for the sake of using the formal Sharpe ratio.

• Don't divide the yield by 4 - don't forget about compounding. Sep 16, 2021 at 18:37
• I’ll be using for Sharpe ratio where I use simple returns and multiply by sqrt(4) to “annualize.” So I’m actually assuming linear returns for the sake of sticking with the arithmetic Sharpe. Does that change your comment? Sep 16, 2021 at 18:38
• Yes, but when you subtract your portfolio return from the risk free rate $r_f$, you should use the quarterly risk free rate, which isn't the same as the arithmetically compounded (divided by 4) yield. Sep 16, 2021 at 19:25
• I think I’m looking for a more detailed answer than that but thank you Sep 16, 2021 at 19:36
• One issue with long term bond yields is that they are IRRs not necessarily actual returns.
– fes
Sep 17, 2021 at 5:39