CFA CFA Level 1 Fixed income problem (schweser)

# Fixed income problem (schweser)

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• 4

Hey guys,

Would you agree with me that schweser have made a mistake with the answer to this question?

A bond has an effective duration of 10.5 and convexity of 97.3. The estimated percentage change in price, in response to a decline in yield of 200 bp is:

A 19.05%
B 22.95%
C 24.89%

I got B but the book is saying C. Makes no sense to me. Could someone pls enlighten me? Thanks very much!

• 4

Ah that’s strange @CFAcharterwannabeâ€Œ – during ‘my time’ it was as per my formula. I would advice you to stick to the latest 2014 syllabus’ formulae then, and you should assume that perhaps Schweser forgot to update their answer for this.

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@Sophieâ€Œ yeah I remember someone else raised a doubt on the same question and I spent hours trying to find out if it was an error or something I was doing wrong. @vincenttâ€Œ also answered that question. I went all the way back to the dec 2013 book and I saw that they had the exact same question. So I realised/assumed it must be an error cos of the formula change.

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Hey @PortfolioManagerâ€Œ – the answer is indeed C. That’s because you forgot to take into account the convexity adjustment factor.

Remember that a bond’s duration is a measure of the approximate sensitivity of a (non-callable) bondâ€™s price to changes in interest
rates. This relationship is true for a small % change in interest rate, the relationship is not linear over large changes in interest rates, here’s where convexity comes in. The differences are nicely summarised in the below image, by ignoring convexity, you’ve missed out the area in green below and your calculation underestimates the increase in bond prices:

So to account for convexity, you need to add the convexity adjustment factor in your bond price change calculations.

Total Bond Price change = (-duration x change in yield x 100) + (Convexity x change in yield squared x 100)
= (-10.5 x -0.02 x 100) + (97.3 x (-0.02)^2 x 100)
= 21% + 3.892%
= 24.892%

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@Sophieâ€Œ actually this is a problem a lot of people at Level 1 are facing. I was having the same issue. The formula in the books is :

Total Bond Price change = (-duration x change in yield x 100) + (1/2 Convexity x change in yield squared x 100)

so if you use the half the answer is indeed B. the 2013 books didn’t have the half in them so the answer would turn out to be C. I was very confused myself but I chalked it up to an error and and I am thought I would stick to what the book includes now. What do you think?

• 1

@Sophieâ€Œ @PortfolioManagerâ€Œ I just checked the errata on Schweser:

Page: 107 – Correction
The correct answer for Concept Checker #13 is B. The solution should read:
{[â€“10.5 Ã— â€“0.02] + [(1/2) Ã— 97.3 Ã— (â€“0.02)2]} Ã— 100 = 21.0% + 1.95% = 22.95%. ( Posted: 2013-10-16)

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Thanks a lot guys! I shall be sticking to my answer then.

Gosh fixed income is killing me…