Choosing a UK Risk-Free Rate for CAPM and Return Horizons
Summary
The discussion considers which UK rate to use as the risk-free input when estimating CAPM beta from market data, with a short investment horizon and gaps in short-maturity government bond yield data. One answer recommends SONIA, identifying it as the UK’s official risk-free rate. Other replies suggest possible proxies, including the UK three-month Treasury bill rate for monthly equity excess returns, scaled to the target horizon, and a longer-maturity government yield as a possible proxy.
The suggestions are not a detailed comparison of rate properties or a definitive prescription for every use. The choice should fit the return frequency and intended horizon, and the document leaves some uncertainty about extrapolation and proxy suitability. It also mentions LIBOR as a candidate in the question, but the replies do not establish it as the preferred benchmark. The examples therefore provide starting points for selecting and scaling a rate rather than evidence that one choice is universally best.
Key ideas
- One answer recommends SONIA as the UK risk-free rate reference.
- A UK three-month Treasury bill rate is suggested as a proxy for monthly UK equity excess returns.
- The suggested proxy rate should be scaled to match the return horizon being analyzed.
- A longer-maturity government yield may serve as a proxy, but the discussion does not assess its suitability in detail.
- The replies do not establish a universal choice for every CAPM application or resolve all proxy limitations.
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Full text
# Which risk-free rate to use for the UK?
# Which risk-free rate to use for the UK?
I am working on an assignment to calculate Beta in the CAPM Model through empirical data on the british market and am still unsure which risk-free rate to use.
Since I have a 1 week investment horizon, my first Idea was to use short term UK government bond yields provided by the Bank of England site (https://www.bankofengland.co.uk/statistics/yield-curves) but their data has many gaps/misses completely after 2013 for bonds under 1 year.
So my question is should I then use a bond with a longer maturity, despite my short investment horizon?
Could I alternatively also use other rates provided like Libor or Sonia? I have found Libor rates whith a matching 1 week maturity and also Sonia rates but I am not very familiar with those.
Any advice on the topic would be greatly appreciated
## Answer by user42108 (score 3)
https://quant.stackexchange.com/a/60267
I would use SONIA. That's the official RFR for the UK. See this BoE link: https://www.bankofengland.co.uk/markets/transition-to-sterling-risk-free-rates-from-libor
## Answer by Preston Lui (score 0)
https://quant.stackexchange.com/a/60306
I have an actuarial background so I am not too sure if using yield extrapolation is a good way.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.soa.org/globalassets/assets/files/resources/research-report/2019/yield-curve-report.pdf&ved=2ahUKEwjt3uyRh4DuAhXSa94KHUnDBYsQFjAMegQIFhAB&usg=AOvVaw2R66gNNIbaW05F9y-blu_J
They may serve as a proxy for the real rate
## Answer by Aaron Kaijser (score 0)
https://quant.stackexchange.com/a/66109
When you are working with monthly returns and you want to calculate monthly excess returns you could also use the U.K. 3-month T-Bill (annualized) rate as a proxy for the risk-free rate of U.K. equities and scale to 1 month. You can download the data via the Federal Reserve's website here.
If you are using R, you could also use the `quantmod` package to retrieve the data directly in R:
```
library(quantmod)
quantmod::getSymbols("IR3TTS01GBM156N", src = "FRED")
```
Then scale every monthly rate by applying the formula: $$(1 + r_{f,3-month})^{\frac{1}{n}}$$ where $n$ is your horizon. For a monthly proxy this would be 12. Weekly would be 52. Daily 252/253.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.