# Risk free rate - short term or long term in CAPM vs Fama French

Is there a hard rule as to when to use the long term vs short term risk free rate? I thought we should match term of the risk free rate to the instrument we’re valuing and typically it’s the long term government bond. However, in one of the CFAI online topic exams, it uses the short term risk free rate. Is this only specific to the Fama French model?

Both long-term govt bonds (FF and CAPM are actually both variations of an APT model). If they only give you the short-term rate, use that one.

This is is weird, I just found the same thing on the online practice exams. And both ST and LT rfrs were given. I guess multifactor models and APT models use the T-bill in the build up, as opposed to CAPM.

The more you know.

The Fama-French model estimate for return on equity is calculated using the formula: , where

ri = Required return on share i

RF = Current expected risk-free return on the short-term government bill

Can we be sure about this MrSmart? I don’t see the point in building the required return on equity using different Rf metrics… when those models are similar equilibrium models

Came in to ask this - I got burned twice so far tonight looking at this - first time I thought it had to be ST because of the instrument we were comparing but the answers said I was wrong. This second time I was like, “Not so fast - can’t get me again” and sure enough I was wrong this time, only going in the opposite direction!

What is the proper instance to use each? This would be a miserable way to lose points on the test.

Scheswer said use st rate for short term investment n LT rate for LT investment…

Use LT govt bond for CAPM and BY methods.

And T-bill for all other multi-factor models

I’m guessing the reason is for CAPM, we use the T-Bonds to derive the ERP.

Here is a 2001 paper by Fama and French, they use the annualized 6-month T-bill to calculate the ERP. for anyone interested.

http://poseidon01.ssrn.com/delivery.php?ID=672090112009086084105123089029083076077025046003043075006118078024101101095110118071000001025090096104086085019064121097030107089100001121097115126088025081013073110096000028028005122097&EXT=pdf&TYPE=2

I just got tripped up on the same problem you were referring to. Naturally I turned to the CFAI currirculum since that supersedes all. CAPM use long term rf rate Fama French use short term rf rate