Duration question

[john.ophof]

Can you explain the duration used with the non zero coupon bond?

What is the best estimate of the market value of a portfolio of USD 100 million invested in recently issued 6% 10 year bonds and USD 1000 million of long 10 year zero coupon bond if interest rates decline by 0.5 %.

Ansere is 209 Million.

Thanks

 

[David Harper CFA FRM]

Hi John,

The question confuses me. Re: the non coupon bond, its duration varies with yield which does not appear to be given. The answers appears to imply a duration of 38 [sic?]. Even the sentence is grammatically hobbled. I can't decipher this question, can you give the source?

David

 

[john.ophof]

The sentence is correctly typed the last 1000 million was a typo and must be 100 million.

Source is exam 2003 FRM

In the answer I can read The duration of the newly issued 6% bond is 7.802 assuming the price of the bond is par. Given a duratinon of 7.802 the change of the bond equals 7.802 * 0.005 * 100.000.000 which equals 3.91 million.

I was also confused especially about the par assumption, nothing about compounding as well.

 

[David Harper CFA FRM]

I don't know, IMO, the question is a mess. In addition to your points, it does not indicate Macaulay vs. Modified duration. Is the "Answer 209 Million" actually part of the question. Actually, nevermind it is a bad use of time to try and decipeher lame questions. I think maybe it is along the following lines:

if 209 MM is part of the question, then
$200 Million portfolio grows by $9 MM if interest rates decline by 0.5%
In which case, the dollar duration is $9 million
and the MACAULAY DURATION of the zero is 10, therefore the MACAULAY duration of the coupon bond would be 8 because: ($100 * 10 * 0.5%) + ($100 * X * 0.5%) = $9, so X must be 8 Mac duration
And modified of 8 mac is about 7.8 modified (=8/(1+5%/2)), but who knows...

David