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!
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