YTM of bonds - semiannual versus quarterly.

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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.
 
S2000magician wrote:
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.
Click to expand...
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
 
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