Very high dollar duration question

CFA Level I
#1

Hi! It is stated that bond A has a dd of 747 which I find extremely high, aren’t duration values usually like from 1-10? Or what am I missing here?

I don’t know how to approach this problem.

Bond A is a 25-year/6% bond selling at 70.3570. Bond A has a dollar duration of 747.2009. Bond B is a 20-year/5% bond selling at 70.3570. Bond B has a modified duration of 10.62. When the market interest rate increases from 9% to 9.1%? Which of the following is incorrect?

A. the approximate dollar price change of Bond A is $ -0.0747
B. the approximate percentage price change of Bond A is -0.106%
C. the approximate percentage price change of Bond B is -1.062%
D. the approximate percentage price change of Bond B is -10.62%

Old kaplan question I found on the internet.

#2

You seem to be missing the dollar part of dollar duration.

Dollar duration is (usually modified) duration times market value.

#3

Can answer options C and D be true at the same time?? :bulb:

1 Like
#4

What do you mean? The dollar duration is 747,2009 for bond A, but sure, there isen’t a dollar duration for bond B only a MD of 10,62

#5

No, just one unfortunately.

1 Like
#6

10.62 years is a reasonable modified duration for a 20-year, 5% coupon bond yielding 8%.

You can check it in Excel.

#7

damn, if C and D had both been true, that would have told us the wrong answer would have had to be either A or B

#8

But the dollar duration is very high? No?

#9

Can you explain please?

#10

Exactly one of A,B,C, and D is incorrect.

#11

Now I’m thinking the question should have said
Which of the following is correct?

#12

and 10.62\times 70.3570=747.2009 so both bonds have a modified duration of 10.62 and both bonds have a dollar duration of 747.2009

since the modified duration is the same for both bonds, at most 1 (and possibly none) of B,C, and D can be true.
I’ll leave that as an exercise for @gneger:
if the modified duration is 10.62, what is the approximate percentage price change of the bonds in response to a 0.1% rise in interest rate?

#13

Hi gneger,

The high dollar duration for Bond A is due to its long term (25 years). To calculate the price change:

For Bond A: Price change ≈ -747.2009 × 0.001 = -$0.0747 (Option A is correct).
For Bond B: Percentage change ≈ -10.62 × 0.001 = -1.062% (Option C is correct).

Option D is incorrect because the percentage change for Bond B is -1.062%, not -10.62%.

Hope this helps!

#14

you might want to check your math: -747.2009 × 0.001 = -$0.747, not -$0.0747

As I said 3 posts up, I think there’s a typo (either in the original question or gneger’s transcription) and the question should have said
Which of the following is correct?

#15

Yeah I can’t find a solution to it now somehow for some reason but anyways thanks for your input once more.