## Risk Free Rate for UK and US

Note, finding a risk-free rate is complicated not just by the alternative sources available, but also because the risk-free rate required can depend on the context of its use.

- The most requested is
**3 month Treasury bills**, recommended by Thomson Reuters (Datastream) and many others. There is the most historical data for these. For example the UK, UKGBILL3 (monthly – base date Jan 1972) and UKTBTND (daily – base date 04 Jan 1985). See Risk Free Rates on Datastream (October 2013) for more detail. - Fama French benchmark factors are calculated using
**1 month Treasury bills**, but historical data can be limited. For example, the UK UKTBT1M on Datastream has a base date of 10 Mar 2000.

See also Risk Free Rate and Fama French factors – posted Jan 2013 - Bloomberg uses
**10 year government bond rates**as the risk-free rate in its Country Risk Premium (CRP) and related functions. (This makes it easier to handle countries that do not issue Treasury bills in a consistent fashion.)

(For those interested there is a paper “What is the riskfree rate?” on Damodaran Online.)

The last Risk Free Rate post was Nov 2009. These updates have been prompted by queries and also recent news. With the turmoil about the US credit downgrade at the beginning of this month, there is of course debate about what is the risk-free rate if there is a chance of a country defaulting. For example see:

- http://aswathdamodaran.blogspot.com/2011/07/sovereign-ratings-downgrade-for-us-end.html
- http://www.bbc.co.uk/news/business-14430643 – As the US loses AAA, where is a safe harbour?

So what to choose as a good estimate of the theoretical risk-free rate could get harder rather than easier.

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risk free rate

how to I get Risk free rate and equity risk premium in datastream. I got this data from Bloomberg using CRP function. Please assist.

The risk free rate used by Bloomberg is the yield on a 10 year treasury security (10 year govt bond / gilt ) which is available in Datastream. Many researchers use the yield on a 3 (or 1) month treasury rather that the 10 year one as mentioned above.

The equity risk premium is calculated by Bloomberg as the “Expected Return on Market” -(minus) “Risk Free Rate”. To be honest, I do not fully understand how the “Expected Return on Market” is calculated but it is done with reference to the market index UKX (the FTSE 100). The CRP Help page describes the dividend yield, the growth rate, the payout ratio, and the expected market return but you need more financial knowledge than I have to understand the calculations described.

I don’t think that the “Expected Return on Market” or the “Equity Risk Premium” are directly available on Datastream. You would have to do the calculations to get these from the basic data.

i m working on assignment where i found beta using 10 yr data of a company. now to calculate capm do i need to find 10 yr risk free rate or 3 months? what is risk free rate for uk govt bonds?

The risk free rate is a theoretical rate. For your assignment, you need to choose the rate that is the best approximation to this theoretical rate for your analysis. (This may depend on the availability of the data.) For UK, I’d recommend using the 3 month treasury bill rate unless you have a reason for choosing a different UK govt bond / gilt rate. Various sources are mentioned in the FAQ answer above.

I am currently working on my dissertation, I want to access to the Thomson Reuters Datastream on my own laptop, where can I find the datastream ? as I cannot find it on the Reuters site.

thanks .

Licence and software restrictions mean that Datastream (like Bloomberg Professional) is only available on specific PCs. Thomson One Banker does have a web interface and has similar coverage to Datastream for active companies. See https://bizlib247.wordpress.com/2012/06/28/researching-financial-markets-equities-indicies/ for more details.

I am working on my dissertation and I want to calculate the market risk premium, but I am confused that whether I need to average the market returns using FTSE ALL SHARE and how can I use the daily data of the 3 month treasury bill rate? Is it the annual discount rate? or just 3 months and I need to transfer it into annual rate?

I think that you can use the historical total return of the FTSE All Share index as the expected market rate of return in calculating the UK market risk premium (also called equity risk premium). It would be usual to average over five or more years. The 3 month treasury bill rate is the most common proxy for the risk-free rate – whether this is expressed as an annual rate, or a return over a shorter period, depends on the source that you use – see https://bizlib247.wordpress.com/2013/01/18/risk-free-rate-and-fama-french-factors/

If you want more detail then Aswath Damodaran has several interesting posts on the “Implied Equity Risk Premium” on his blog – for example http://aswathdamodaran.blogspot.co.uk/2013/05/equity-risk-premiums-erp-and-stocks.html

Personally, my knowledge is much more limited – I haven’t yet got the financial knowledge to judge that Wikipedia’s explanation of the CAPM is accurate https://en.wikipedia.org/wiki/Capital_asset_pricing_model#The_formula but it looks correct and is the best that I have found online.

How can I find UK’s risk free rate or risk premium rate please because I need it for my dissertation. Thanks.

Use the UK 3 month Treasury Bill rate as your estimate for the theoretical UK risk free rate. The UK 3 month T-bill rate is available on Bloomberg, Datastream, etc. and from the Bank of England website if you are looking for a free online source. For more information see Where can I find historical rates for UK Government bonds (Gilts, Treasury bills)? in this post.

How can you use the annualised interest rates of a 3 month T-Bill if I want to examine daily excess returns? I want to have the daily risk free rate and I somehow cannot believe that an annualised interest rate may serve as a daily risk free rate, or am I wrong?

Take a look at https://bizlib247.wordpress.com/2013/01/18/risk-free-rate-and-fama-french-factors/

If you have the daily annualised interest rates for a 3 month T-Bill, you can calculate the equivalent daily return by finding the 250th root (assuming 250 trading days per year).

For an annualised rate of 3.2% you could use the Excel formula – POWER((1 + 3.2/100), 1/250 )

Thanks a lot, Mark! That’s what I thought… I haven’t found too much info about that though!

i am currently working on my thesis. I need to know how to calculate the daily-risk free interest rate with given annualized cut-off yield percentage from RBI site.

I am taking data from april 2003 to March 2013. I have read a paper in that it is written that the yield cut-off rate is converted into daily prices on the basis of date of issue of biil and after that trading period.

This is a little beyond my knowledge. Since treasuries are issued over a short term (lass than 1 year) to get a long time series you need to convert the individual traded treasuries into a generic treasury. Looking at the Reserve Bank of India site I expect that this would be expressed in an annual percentage yield ( http://www.rbi.org.in/scripts/FAQView.aspx?Id=79#26 ).

https://bizlib247.wordpress.com/2013/01/18/risk-free-rate-and-fama-french-factors/ should give some help in converting to a daily rate.

Hi I am looking for 3 months treasury bill rate for Portugal, Netherlands, Germany, Austria and Denmark from 4 quarter 2002 until 2 quarter 2012 can I find it in Bloomberg or in Datastream? Thanks Ana

Hi Ana, You will probably not get a 3 month treasury bill rate for all these countries because they might not all issue 3 month treasury bills. In this case you need another rate as a good proxy for the theoretical risk-free rate.

Following my suggestion for Datastream – https://bizlib247.wordpress.com/2013/10/25/risk-free-rates-on-datastream/ – there is TRPT3MT (Portugal), TRNL3MT (Netherlands), TRBD3MT (Germany), TRDK3MT (Denmark) but nothing for Austria. There is TREU3MT (Euro area) that could be a reasonable proxy for Austria. However some of these don’t have historic data from 2002.

The advice on the Datastream extranet – Thomson Reuters (2009) Risk free interest rates – does not cover all of these countries. You could look up interest rates for Austria and choose ASVIB3M as a resonable proxy for an austrian risk free rate. Another approach would be to look at the short-term interest rate from OECD statistics – following advice from http://researchfinancial.wordpress.com/2014/02/06/risk-free-rate-data-sources/ –

Bloomberg investigation will take some time but you can always ask the nice people on the Bloomberg help desk.

Hi mark,

I found this very useful for my dissertation, however I need to calculate CAPM and I’m wondering if I should use the 3 month risk free rate for the UK that I sourced: 0.39. Or would i have to multiply it by 4 to make it an annual rate ?

sorry I’m a little confused. hopefully you can help me out.

thank you

Jess

Hi Jess,

I am going to assume that you have sourced data for 3 month UK government bonds (treasuries/T-bills) as this is the most common choice as an estimate for the theoretical risk free rate. Unless your source says otherwise a figure of 0.39 for UK 3-month T-bill is the equivalent annual yield (so you don’t multiply it by 4). Annual yields are used so that figures are comparable for government bonds of different maturity dates.

Hi,

i am writing my thesis and i need to estimate my capm model. i am using the 3 month treasury bill for my risk free rate and using historiacal betas, but i dont know how to get the market risk premium? what am i supposed to take for that and how do i find it on datastream? it is not the TOTMKCN right?

thnak you

Karim

You need to choose an estimate for the market risk premium that is appropriate for your research, in the same way that you have chosen the 3 month treasury bill as your estimate for the risk free rate. You can use an average of a historic market return – S&P 500 for UK, FTSE All Share for UK, etc. averaging over 5 years, 10 years or longer depending on your analysis, to get an expected market return and subtract your risk free rate to give the market risk premium (see http://www.investopedia.com/terms/c/capm.asp )

There are other ways of estimating a market risk premium (also called equity risk premium) – see http://aswathdamodaran.blogspot.co.uk/2012/03/equity-risk-premiums-2012-edition.html for details.

Thank you.

My firms have to be publicly listed and my countries are Canada and China so i will have to see which markets i can take for them.

One choice is to use the market index that you used in calculating betas.

Other posts that might help :-

https://bizlib247.wordpress.com/2013/02/20/world-equity-indices-benchmark-key-indices/ gives tips on finding benchmarks for different markets. https://bizlib247.wordpress.com/2014/04/30/market-return-datastream/ mentions China.

Reblogged this on fblfabulous.

if i have a portfolio including stock from us and uk how to estimate the risk free rate to calculate the efficient portfolio

[To the best of my knowledge there is no definitive correct answer]

If your portfolio is being held by a US firm/individual then you could calculate the returns in US dollars and estimate the risk free rate using US Treasury Bills.

If your portfolio is being held by a UK firm/individual then you could calculate the returns in UK pounds and estimate the risk free rate using UK Treasury Bills.