# Proper Way To Price a Bond Paying a Semi-Annual Coupon

Let's say you have a 10-year bond with a \$100 face value that with a coupon rate of 10%, paid semi annually. The bond is currently price at \$105. Which is the proper way of calculating the yield to maturity?

Option 1:

`105 = 100/(1+ y)^10 + sum of x from 1 to 20 of (5)/(1+y)^(x/2)`

Giving a YTM of 9.43%

Option 2:

`105 = 100/(1+ y/2)^20 + sum of x from 1 to 20 of (5)/(1+y/2)^(x)`

Giving a YTM of 9.22%

I understand these differences are due to the effects of compounding. In Option 2, if we were to account for compounding:

`(1+.0922/2)(1+.0922/2) - 1`

It gives a YTM of 9.43%, just as in option 1.

But what is the correct convention? How are bond yield to maturities typically quoted? Using Option 1 or Option 2?

## 1 Answer

Semi-annual yield (your option 2) is the most common convention in major markets since most government and corporate bonds pay interest semi-annually. It's also only applied to bonds with a maturity of one year or more (e.g. it's not used for Treasury Bills and Commercial Paper)

It's important, though, to make sure that yield quotes are using the same frequency when comparing, as it can make non-trivial differences as you have seen.