Gilt yield calcs

aroominyork

I cannot align nominal gilt yields with the BoE’s yield curve. The yield curve on the top graph at this link shows 15 year gilts yielding close to 5%. TR38 is trading at 107.53 which, using Excel’s formula =YIELD(TODAY(),[redemption date],[coupon],[price],100,2) gives a YTM of 4.10%. Why the disparity please?

waveyjane

At a guess I'd say it's because the BoE sets a nominal (as in theoretical) yield, while the market sets the actual yield based on whatever interpretation of the market you have (rational expectations, etc.). But I have no real idea.

GeoffTF

aroominyork said:

I cannot align nominal gilt yields with the BoE’s yield curve. The yield curve on the top graph at this link shows 15 year gilts yielding close to 5%. TR38 is trading at 107.53 which, using Excel’s formula =YIELD(TODAY(),[redemption date],[coupon],[price],100,2) gives a YTM of 4.10%. Why the disparity please?

Tradeweb gives the YTM:

https://reports.tradeweb.com/account/login/

Johnjdc

In simplistic terms it's because the Bank of England Forward Yield Curve is the implied cost of borrowing at that point in the future, whereas the yield to maturity on gilts currently in issue is the cost of borrowing from now until that point in the future.

coastline

List of various bonds gilts etc...decent bookmark

Bonds | Investing | Digital Look - Sharecast.com

Gross redemption yield showing at 4.09%

4¾% Treasury Stock 2038 : The latest Government Bond price - Sharecast.com

I'll guess what the central banks publish and what the markets think are two different things.

Latest bond rates, interest rates, Libor and interbank rates - FT.com

In six months the UK 10 year has moved between 4.5% and 3%

United Kingdom Government Bond 10Y - 2023 Data - 1980-2022 Historical - 2024 Forecast (tradingeconomics.com)

In the US the FED funds rate is 5% 

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Looking out 2 years the market thinks different  because there's a real possibility of a recession . Rates will be cut is the message.

United States 2 Year Note Yield - 2023 Data - 1976-2022 Historical - 2024 Forecast (tradingeconomics.com)

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aroominyork

Johnjdc said:

In simplistic terms it's because the Bank of England Forward Yield Curve is the implied cost of borrowing at that point in the future, whereas the yield to maturity on gilts currently in issue is the cost of borrowing from now until that point in the future.

Interesting. If that is so, it is the cost of borrowing what? In 40 years it will yield 3% to buy a gilt of what duration?

Johnjdc

aroominyork said:

Johnjdc said:

In simplistic terms it's because the Bank of England Forward Yield Curve is the implied cost of borrowing at that point in the future, whereas the yield to maturity on gilts currently in issue is the cost of borrowing from now until that point in the future.

Interesting. If that is so, it is the cost of borrowing what? In 40 years it will yield 3% to buy a gilt of what duration?

In theory, 24 hours (3% would be the annualised compounded rate, i.e. it would cost 0.000821% to borrow for a day).

To work out what the curve predicts a gilt of x duration would yield in 40 years, you need to average (ish) the curve for the period between 40 and 40+x.

aroominyork

Johnjdc said:

aroominyork said:

Johnjdc said:

In simplistic terms it's because the Bank of England Forward Yield Curve is the implied cost of borrowing at that point in the future, whereas the yield to maturity on gilts currently in issue is the cost of borrowing from now until that point in the future.

Interesting. If that is so, it is the cost of borrowing what? In 40 years it will yield 3% to buy a gilt of what duration?

In theory, 24 hours (3% would be the annualised compounded rate, i.e. it would cost 0.000821% to borrow for a day).

To work out what the curve predicts a gilt of x duration would yield in 40 years, you need to average (ish) the curve for the period between 40 and 40+x.

Curious. What use it is to know the cost of overnight govt borrowing in 40 years' time, and how can it possibly be predicted with any kind of accuracy?

EthicsGradient

I think it's predicted from the prices of the various gilts, such as the one you linked to. It seems that knowing the market's estimate of the future of government borrowing would be extremely useful to those who have to plan long-term borrowing or lending, such as banks, pension funds, insurance companies etc.

The "latest yield curve data" link on the BofE page you gave has a spreadsheet with what should match with the gilt price - "spot curve" in "GLC Nominal daily data current month.xlsx". For 15.5 years - closest to the maturity date of that gilt - it has 4.13%.

aroominyork

Thanks All, very useful. I'll set a reminder for 2063 to check that gilts are returning just a fraction over 3%.

Johnjdc

They almost certainly won't be, just as the weather forecast for 1st June is probably wrong. The point is that if you knew for a fact that you (as the government) needed to borrow for a year in 2063, you could do so today, for about 3% in 2063, by borrowing until 2064 today, and using the proceeds. today, to redeem debt currently due for repayment in 2063.