YTM of bonds - semiannual versus quarterly.

Bond A

YTM: 10.63%

Coupon Rate: 8%

Semiannual

Years to maturity: 5

Price (per 100 par): 90

Current yield: 8.889%

Bond B

YTM: 10.696%

Coupon Rate: 12%

Quarterly

Years to maturity: 5

Price (per 100 par): 105

Current yield: 11.429%

YTM: 10.696%

Bond B is a bit more risky than bond A. How much more compensation in terms of higher YTM does someone need to pick B over A?

I’m a bit confused as how to compare the two yields. I know I need to set bond B to bond A’s YTM but beyond that I am lost. Any help would be greatly appreciated!

By what measure is bond B riskier than bond A? YTM? How about modified duration (bond A’s is higher)?

Assuming that YTM is calculated on the same basis for both bonds – and it should be BEY – the numbers are directly comparable.

I should have been more clear - the question states that B is riskier than A.

I am told to convert B to semi-annual (which = 10.839%) because “A is semi annual and B is quarterly and in order to properly compare, we must convert quarterly to semi-annual”

A couple of quick calculations show that the quoted YTM on bond A is a nominal rate compounded semiannually (i.e., a BEY), whereas the quoted YTM on bond B is a nominal rate compounded quarterly.

Thus, you either have to convert the quarterly YTM to a semiannual YTM, or convert the semiannual YTM to a quarterly YTM.

Using two different (nominal) conventions to quote YTMs isn’t typical, by the way.

to compare YTM to another periodicity you can use this calculation:

(1 + YTMn / n) ^ n = (1 + YTMm / m ) ^ m

(m and n are periodicities, i.e. days in coupon period / days in year)

then rearrange to get YTMm

i.e.

YTMm = m* [(1 + YTMn / n) ^ (n/m) - 1]

so for your question:

2 * [( 1 + 0.10696 / 4 ) ^ (4/2) - 1] = 10.839%


i.e. that is the YTM of a hypothetical semi-annual bond that will give the investor the same compounded annual return at bond B. You can see it’s high than A’s YTM - so yes, the investory is being reward more for taking on the risks of bond B