Yield Compensation for Greater Risk on Bonds

CFA Level I Fixed Income
#1

Question below;

Bond A

  1. Annual Coupon Rate: 10%
  2. Payment Frequency: Semi-Annual
  3. YTM: 10.00%

Bond B

  1. Annual Coupon Rate: 14%
  2. Payment Frequency: Quarterly
  3. YTM: 10.25%

An analyst believes that Bond B is more risky than Bond A. How much additional compensation, in terms of a higher yield ot maturity, would a buyer need for bearing the risk of Bond B compared to Bond A?

A. 0.25%

B. 51 basis points when yields are stated on a quarterly basis.

C. 51 basis points when yields are stated on a semi-annual basis.

The answer is B, which I generally understand without doing any calculations but I am having a hard time understanding the answer reasoning given with the answer. The reasoning says; "The difference in yield is not the 25 basis points. It is essential to compare the yields for the same periodicity.

The 10.00% for a periodicity of two is the same as 9.87% for a periodicity of four.

((1+.10)/2)^2 = ((1+APR4)/4)^4 => APR4 = 9.87%

The 10.25% for a periodicity of four is the same as 10.38% for a periodicity of two.

((1+.1025)/4)^4 = ((1+APR2)/2)^2 => APR2 = 10.38%

Thus, the additional compensation for the increased risk of Bond B is (10.38-9.87%) which is 51 basis points."

From the answer they gave it looks like they are comparing two different periodicitys, Bond A if it was a periodicity of four and Bond B if it was periodicity of two. Is it not? I would have expected to use the Bond A periodicity of four (9.87%) and the Bond B periodicity of four (10.25%) which is a basis point difference of 38.

Let me know your thoughts and if you can explain how I am looking at this incorrectly. Thanks!

#2

Their reasoning is, well, stupid.

You should compare the effective annual rates.

Unfortunately, the information in the question isn’t clear enough to answer the question. When it says that the YTM for bond A is 10%, is that an effective annual yield, or a BEY? (No other possibilities seem reasonable.) When it says that the YTM for bond B is 10.25%, is that an effective annual rate, a BEY, or a nominal rate compounded quarterly? (Again, no other possibilities seem reasonable.)

Without knowing the answers to these questions, it’s impossible to answer the question as posed.

#3

Unfortunately, this is exactly how it was worded. When I did the mock exam I took it as being the annual rate for compounding semi-annually, and compounding quarterly for Bond A and Bond B respectively. Based on their answer this seems to be the most logical answer right?

#4

It’s not a matter of “most logical”; the question is crap.

Don’t give it another thought. The real exam won’t have anything this stupid on it. Remember that you need to compare _ effective annual_ rates, and you’ll be fine.

#5

Thanks, appreciate it!

#6

You’re welcome.