Example: Adjusting yields for periodicity
An Atlas Corporation bond is quoted with a YTM of 4% on a semiannual bond basis. What yields should be used to compare it with a quarterly-pay bond and an annual-pay bond?
Answer:
The first thing to note is that 4% on a semiannual bond basis is an effective yield of 2% per 6-month period.
To compare this with the yield on an annual-pay bond, which is an effective annual yield, we need to calculate the effective annual yield on the semiannual coupon bond, which is 1.022 − 1 = 4.04%.
For the annual YTM on the quarterly-pay bond, we need to calculate the effective quarterly yield and multiply by four. The quarterly yield (yield per quarter) that is equivalent to a yield of 2% per six months is 1.021/2 − 1 = 0.995%. The quoted annual rate for the equivalent yield on a quarterly bond basis is 4 × 0.995 = 3.98%.
Note that we have shown that the effective annual yields are the same for:
An annual coupon bond with a yield of 4.04% on an annual basis (periodicity of one).
A semiannual coupon bond with a yield of 4.0% on a semiannual basis (periodicity of two).
A quarterly coupon bond with a yield of 3.98% on quarterly basis (periodicity of four).
