Comparing Yields

CRE-Seattle-CFA · May 21, 2019, 6:22pm

Stuck on this question re: the quarterly pay bond (Bold section below) - why am I multiplying the effective quarterly yield by 4 to get the annual YTM? I sort of understand it but hoping someone can break it down simple for me. Thank you…

“If a 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?”

SemiAnnual EAY = 1.02²-1 = 4.04% to compare against yield on an annual pay-bond.

Annual YTM on quarterly bond - 1.02^1/2-1 = 0.995% x 4 = 3.98% Why do I multiply by 4 here? The quarterly yield of .995% is equal to a yield of 2% per six months…so I can just multiply by 4 and voila?

S2000magician · May 21, 2019, 6:35pm

The annual-pay bond’s yield will be quoted as an EAY because the compounding is once per year, so you want to compute the EAY on the semiannual-pay bond to have a meaningful comparison.

The quarterly-pay bond’s yield will be quoted as a nominal rate with quarterly compounding, so you want to compute the nominal rate with quarterly compounding on the semiannual-pay bond to have a meaningful comparison.