Which risk-free rate to use for the UK?

Question

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 1

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 2

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 3

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.