CFAI text V4 P112: Example 10

How come the answer indicates the new bond market value = dollar duration of old bond / DOLLAR DURATION of new bond * 100? Yet the equation above example 10 (on the same page) indicates the new bond market value = dollar duration of old bond / DURATION of new bond * 100. Can anyone tell the why it’s different?

The equation is for new bond “market” (not par) value" and can be mialeading. The new bond shall have a market value of \$4.4M according to this equation. The question asked the new bond’s “par value” and they used DD of 4.5 (\$90x5/100) “per bond” as the duration of the new bond in the equation and get the answer of \$4.889M. I think if the equation shall be applicable to new bond “par” value, it shall be revised to : New bond “par value” = (DD of old bonds/DD “per” new bond) x 100 => (220,000/4,5) x100 = 4.899 (in this example) or New bond “par value” = (DD of old bonds/DD of new bond) x (100/90) => (220,000/5.0) x(100/90) = 4.899 (in this example) Hope this will help.

***Correction*** New bond “par value” = (DD of old bonds/DD “per” new bond) x 100 => (220,000/4,5) x100 = 4.899 (in this example) or New bond “par value” = (DD of old bonds/Duration of new bond) x (PV of new bond/ MV of new bond) => (220,000/5.0) x(100/90) = 4.899 (in this example) PV : Par Value MV : Market Value

thanks, this is very helpful! sometimes the wordings are little bit confusing…

The fixed-income readings are vague and sometime can be misleading ! I spent very much time but still some questions remained.

So, to say “dollar duration of 4.5 per bond” is the same as to say “duration of 4.5”? Sorry to beat to death, but I re-read the passage 3 times & your response and it hasn’t sunk in yet.

The equation on P112 : MV(N) = [DD(O) / D(N)] x 100 since DD(N) pb = D(N) x MV(N)pb x 0.01 => D(N) = DD(N) / [D(N) x MV(N)pb x 0.01] =>D(N) = DD(N) x [100/ MV(N)pb] thus, MV(N) = [DD(O) / D(N)] x 100 = [DD(O) / DD(N)] x [100/ MV(N)pb] DD(O) : Dollar Duration of old bond DD(N) : Dollar Duration of new bond DD(N)pb : Dollar Duration per new bond D(N) : Duration of new bond MV(N)pb : Market value per new bond Hope this will help further !

I am sorry again that I made mistakes again because I am in a hurry. Please double check if I am right in deriving the formula as follows. DD(N)pb = D(N) x MV(N)pb x 0.01 => D(N) = DD(N)pb/ [MV(N)pb x 0.01] => D(N) = [DD(N)pb/ [MV(N)pb] x 100 = [DD(N)pb x 100]/ [MV(N)pb] => MV(N) = [DD(O) / D(N)] x 100 PV(N) = (220.000/4.5) x 100 = 4.899M PV(N) : Total par value of new bond PV(N)pb : par value per new bond It is simplified in the example while actually it is complicated !

Wow… I have to say, impressive deduction. Went way beyond the call of duty. Thanks for the color. I read twice, and it hasn’t fully sunk in but I understand a lot better. I’ll read again tomorrow. Maybe need a fresh set of eyes. Hate doing all this studying after a full workday…