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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

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  • $\begingroup$ Depending on the amount of missing data points in the yields for UK government bonds, you could do interpolation to reconstruct the full amount of data. If you have too much missing data, then interpolation is not ideal. $\endgroup$ – Pleb Dec 31 '20 at 12:41
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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

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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

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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.

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