# Understanding Bond Yields

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?

• Could you please post a link to the Bloomberg report? Mar 21, 2020 at 19:26

## 1 Answer

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

• But the par value is £100.00, so the coupon rate of 4.75% = £4.75. Mar 22, 2020 at 0:33
• @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. Mar 22, 2020 at 3:32
• The Bloomberg link: 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. Mar 22, 2020 at 12:23
• "Typically, the par value of a UK bond is 100£, while for a US bond is \$1,000." - theinvestingsite.com/bonds/default.php "Gilts have a face value, usually £100" - moneywise.co.uk/investing/beginner-investor/… "Each bond has a fixed nominal value, often £100 for a sterling bond." - moneyweek.com/glossary/nominal-value-of-a-bond All these sources back up the claim that the par value is £100 Mar 22, 2020 at 12:28