Convexity Calculation question-Please Help!!!

Question

Hello,

I've been going through the CFA provided mock exams and their practice questions and have come across an issue with the calculation of convexity when looking at the percentage change in price. There are two questions below, one from the mock exam, one from the practice questions (word for word), both of which seem identical, but are calculated differently, which would give a different answer if you used the same calculation on each question.. could someone help me understand when and why to use the portion of the formula for convexity where you multiply it by 0.5? Thank you!!

Question 1.The duration and convexity of an option-free bond priced at $90.25 are 10.34 and 151.60, respectively. If yields increase by 200 bps, the percentage price change is closest to:

A: -23.71%
B: -17.65%
C: -20.68%

It is calculated as duration effect:
-10.34*(+0.02)=-20.68%

and convexity effect:
 1/2*(151.6)*(0.02^2)=3.03%

Total perentage change is the sum of duration effect and convexity effect:
 -20.68%+3.03%=-17.65%

Question 2: The duration and convexity of an option-free bond priced at $90.25 are 10.34 and 75.80 respectively. If yields increase by 200bps, the percentage change of the price is closest to:

A: -17.65%
B: -20.68%
C: -23.71%

Ther percantage change in price is calculated as follows:
Duration effect:
-10.34*(+0.02)=-20.68%

and convexity effect:
(75.80)*(0.02^2)=3.03%

Total perentage change is the sum of duration effect and convexity effect:
 -20.68%+3.03%=-17.65%

I realize that the convexity they list in the second question is half, but how is one supposed to know whether or not to multiply it by 1/2 in the calculation. You obviously wont have another question to compare it to on the test...

Thank you for any help!!
Paul

pcweldon · Answer

Just as an FYI if anyone is questioning as well, it looks like CFAI made a mistake in their question. Here is the response I receieved from them:

Hello,

It looks like they did not show the step in the second question explanation, rather they justed halved the given convexity.  We will make the necessary adjustments.  Thank you for bringing this to our attention

CFAcharterwannabe · Answer

alright so there has been a lot of confusion about this. The 0.5 was basically not used in the previous curriculums. That said, to use 0.5 depends on how convexity is calculated. there is a whole formula on it. Since CFAI is giving you questions in the topic exams that 0.5 in the formula, we are probably going to be given questions based on the new formula that use 0.5. So relax and use 0.5.