CFA CFA Level 1 Understanding Fixed-Income Risk and Return “Concept Checkers” Question

# Understanding Fixed-Income Risk and Return “Concept Checkers” Question

• Author
Posts
• 6

All,

I’m taking Level 1 in June and came across the below gem (question #13) on page 104 of Schweser’s Fixed Income, Derivatives, and Alternative Investments book:

13. Assume a bond has an effective duration of 10.5 and a convexity of 97.3. Using the both of these measures, the estimated percent change in price for this bond, in response to a decline in yield of 200 basis points, is closest to:

A. 19.05%
B. 22.95%
C. 24.89%

In the Schweser book, it gives the appropriate formula as: -duration(change in YTM) + 0.5(annual convexity){(change in YTM)^2}

Using the above formula, I calculate the answer as “B”; however, Schweser says that the correct answer is “C”. Our difference in answers comes from the second half of the formula (the convexity effect). In explaining their answer, Schweser lists the convexity effect calculation as [97.3 x (-0.02)2)], but they do not multiply the 3.89% result by the 0.5 given in the original formula. Is there a reason you would leave out the 0.5 in this question?

Any help is greatly appreciated!

• vincentt
Participant
• CFA Level 3
5

@CFAcharterwannabeâ€Œ it would be better if you can take a screenshot of the page as I’m currently doing L3 wouldn’t have an updated version of L1.

However, looking back at my notes (might not be complete), would it be possible that you might have mixed up the “% change in price” formula with the effective duration formula? That’s the only formula in the fixed income topic that has 1/2.

• 5

@vincenttâ€Œ
formula for % change in price is:

= {[-duration * (y)] + [convexity * ( y)^2]} like i mentioned earlier i have serious issues so i went back to 2013 book 5 and checked. the formula has changed. it is now -duration(change in YTM) + 0.5(annual convexity){(change in YTM)^2} the question is just copied and pasted without considering the change in the formula so it is an error i am assuming.

• 4

@ vincentt pg 96 of the schweser does include 0.5 in the formula. I just completed the reading myself and so I am really confused myself now.

• 4

@Pranavâ€Œ yeah I think I am quite behind. Lots of studying to do. Lots of things need to be stuffed into my brain. Yeah even I am not bothering with the formulae ATM. I just want to get the studying out of the e way first. Hoping the question bank will help me retain the formulas. Good luck yeah.

• 3

@vincenttâ€Œ yep i got it now after going through the 2013 books. the formulas have all been changed. the whole section for Fixed Income has been changed quite a bit. And thanks a lot for the link and all your input. I have already spend a lot of time today following this trail. I have to let this go and get back to my studies now finally phew!

• 3

@Pranavâ€Œ well then I am glad my lack of speed makes someone feel good lol i never realised fixed income was going to be so time consuming!

• 3

@CFAcharterwannabeâ€Œ i am hoping the same too ðŸ˜€
practice questions, memorize the forgotten formulas identified during the question bank and hope that is sufficient…
only time will tell…yep, all the best to you too mate!

• vincentt
Participant
• CFA Level 3
2

@CFAcharterwannabeâ€Œ yes the V_ V+ should have a 2 * in the denominator which would be equivalent to 0.5 or 1/2 if you extract it out.

Looking at this http://www.elanguides.com/free-cfa-materials/free-cfa-books/L1-2012J-FS.pdf (page 68), I can’t see any 0.5 there, so the best is to check with schweser’s errata or take a picture of the formula and post it here.

• vincentt
Participant
• CFA Level 3
2

I think it’s the same formula just down to how you calculate the convexity. As far as I can see the second comment make sense:

http://www.analystforum.com/forum/s/cfa-forums/cfa-level-ii-forum/91328038

So the difference is how you calculate the convexity, prior to 2014 at least the convexity calculation was:
(V_ + V+ – 2V0) / (2 * V0 * yield change ^2) <- which is the same as 1/2 But in 2014 it seems to be: (V_ + V+ - 2V0) / (V0 * yield change ^2) Hence, the discrepancy in the formula. Hope that helps.

• vincentt
Participant
• CFA Level 3
1

Hi @EastCoast3â€Œ, I just checked my L1 notes and I don’t think there’s a “0.5” in the formula.

• 1

@vincenttâ€Œ there is no formula mentioned for effective duration besides the one using the V_ and V+ i.e. changes in price due to changes in the YTM. the only formula mentioned is the % change in price. I even checked out the CFAI book. The formula mentioned on the link you pasted above isn’t mentioned in the book. Man I am already confused. This is really not good.

• 1

@vincenttâ€Œ i have a serious mental problem that I cant let go of a problem. So i actually went back and checked the schweser 2013 book 5:
percentage change in price = duration effect+ convexity effect
= {[-duration x (

• 1

@vincentt i figured out the problem. the curriculum has been updated!

• vincentt
Participant
• CFA Level 3
1

maybe there isn’t much to change this year hence CFAI is trying to make some changes to stop candidates from using older version of the books? You never know haha.

No problem at all, happy to help ðŸ™‚

• 1

feels so nice to be studying the same topic as someone else and not feeling left behind #:-S

• 1

@CFAcharterwannabeâ€Œ ðŸ™‚ actually i am running through it faster than i imagined…i started on 30th march and am done with reading 55…expected to complete the book by friday…although i am not memorizing the formulae at this point of time, it’s pointless…understanding and solving the eoc from shweser is all i am doing at present…how about you?

• 1

@leeblevyâ€Œ you have to go through the comments to see how @vincenttâ€Œ and I spend so much time on this and reached a conclusion.

• vincentt
Participant
• CFA Level 3
0

As far as I’m aware the formula for % change in price is:

= {[-duration * (y)] + [convexity * ( y)^2]}

y = change in yield in decimals

stick to that you’ll be fine.

• 0

Which is why I advice candidates to always get the latest books – it’s one of those things where I get paranoid about where 1 question makes the difference between a pass and Band 10…

• 0

@EastCoast3 I made myself the same question ! I assumed it’s a mistake…. Is it?