Choosing the Risk-Free Rate in CAPM
Summary
The note explains how the risk-free rate enters the standard CAPM as the intercept and as the benchmark subtracted from expected market return. In the standard setup, these roles use one rate; lending and borrowing at different rates can appear in a capital market line framework, but the answer does not treat that as standard CAPM. A negative government bond yield is mathematically usable and does not invalidate the model.
There is no single prescribed instrument or averaging window for estimating the rate. Choices may include short or long government bonds, deposit rates, or other rates, and should reflect the investment horizon and assumptions behind the analysis. The market return input requires similar judgment. The discussion offers no empirical comparison of data frequencies or estimation methods, so it does not establish that a ten-year average, or any particular daily, weekly, monthly, or annual series, is preferable.
Key ideas
- In standard CAPM, one risk-free rate serves as the intercept and benchmark for the market risk premium.
- A negative risk-free rate is mathematically compatible with CAPM.
- The rate proxy and its horizon depend on the investment opportunity and the assumptions of the analysis.
- The expected market return also requires a considered choice of data and estimation approach.
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# Risk-Free Rate In CAPM
# Risk-Free Rate In CAPM
Let's start out with the CAPM equation itself:
$E(R_i) = R_{f1} + \beta_{i}(E(R_m) - R_{f2})$
Are there cases where one should choose a different $R_{f1}$ and $R_{f2}$ (Risk Free Rates Of Interest) or do they always have to be equal?
And what if I had to opt for the Swiss government bonds that now have a negative yield (-0.21%)? Should I just take the mean value over the last 10 years and use this mean value as my $R_{f1}$ & $R_{f2}$? And does it matter what kind of bond yield data (daily, weekly, monthly, yearly) I choose for the "last 10 years"?
## Answer by markowitz (score 1)
https://quant.stackexchange.com/a/45166
The CAPM equation is an straight line and risk free rate ($Rf$) is your intercept. At least in standard version of the CAPM is not possible to have more than 1 risk free rate, in fact in similar case the highest should always preferred in investment point of view. In any case the standard assumption speak about only one risk free rate. In CML framework sometimes is shown the possibility to lend and borrowed at two different rate but I never seen this possibility in CAPM setting.
About the negative $Rf$: is not a problem in mathematical point of view. Maybe this situation affect personal risk aversion but this is another story.
About the data: actually choice of $Rf$ is not obvious. Is possible to choose short term or long term bond but also deposit rate or other. The time horizon and estimation technique are your choices. From "micro" point of view It depend from actual investment possibility and assumptions. From "macro" point of view you have to make more relevant assumptions. Note that for $Rm$ the same is true.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.