Understanding Bond Yields

Question

According to Bloomberg, the coupon rate on a 10-year UK government bond is 4.75%.

Bloomberg also states that the yield is currently 0.55%, and the market price £143.51.

But if the following formula is correct:

Then the yield should be $\frac{4.75}{143.51} \approx 3.31$%

Clearly this isn't the case. So what did I do wrong?

Bond yield is ususally always yield to maturity. It gives us information about how much return we can expect over a period of time if we hold the bond until maturity. This yield is usually found with some root solver (Bisection, Newton Raphson or the like). — AKdemy, Oct 07 '22 at 07:38
Does this answer your question? How to Calculate Bond Yields — AKdemy, Jan 01 '23 at 20:00

score 2 · Answer 1 · answered Oct 07 '22 at 09:25

The current yield is just an approximation and it shouldn’t be too surprising that it doesn’t match yield to maturity for a bond which is at a heavy premium or discount. Specifically the current yield ignores the ‘pull to par’ ie the concept that the bond that trades at 143 now, will be at 100 when it matures in 10 years. Thus, on average the bond loses 4.3 every year. Adjusting for this , we get closer to the correct yield :

Adjusted current yield = $$(4.75-4.3)/143.51= 0.31pct $$

Some additional details can be found here, which is the same question. — AKdemy, Oct 07 '22 at 10:50

FreeMarketUnicorn · Answer 2 · 2020-03-22T03:32:35.063

-1

You did not apply your formula correctly.

Your top formula is correct. But in your bottom formula, the numerator on the left side of the equation is a percentage. It should, instead, be a monetary unit of £ in this case.

The annual coupon payment should be denominated in £. Not a percentage. Otherwise, the units don't balance each other and don't match the units of the original equation.

Edit:

I noticed in your comment you include some information that was left out of the original question: that the par value is £100.

That's why I asked for a link to the source of the Bloomberg report. These numbers would make more since if the par value were £1,000

edited Mar 22 '20 at 03:32

answered Mar 21 '20 at 19:30

FreeMarketUnicorn

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But the par value is £100.00, so the coupon rate of 4.75% = £4.75. – Ryan Walter Mar 22 '20 at 00:33
@RyanWalter: That's why I asked for a link to the source of the Bloomberg report. These numbers would make more since if the par value were £1,000. – FreeMarketUnicorn Mar 22 '20 at 03:32
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The Bloomberg link: https://www.bloomberg.com/markets/rates-bonds/government-bonds/uk. Seems highly unlikely to me that 10 year UK government bonds are trading 86% below their par value, so I don't think that the par is £1000. – Ryan Walter Mar 22 '20 at 12:23
"Typically, the par value of a UK bond is 100£, while for a US bond is $1,000." - https://www.theinvestingsite.com/bonds/default.php
"Gilts have a face value, usually £100" - https://www.moneywise.co.uk/investing/beginner-investor/how-do-bonds-work-should-you-invest-them

"Each bond has a fixed nominal value, often £100 for a sterling bond." - https://moneyweek.com/glossary/nominal-value-of-a-bond

All these sources back up the claim that the par value is £100
– Ryan Walter Mar 22 '20 at 12:28

Understanding Bond Yields

2 Answers2