Negative Duration-Callable Bond?

[DavidM]

Hi David,
Could you please explain what the testable concepts are on negative duration as they relate to callable bond issues?

I apologise for such an open/vague question but I can't seem to find a clear question on that....I know there are some key issues we need to know about this relationship?

If you could point me to any questions /spreadsheets that illustrate this or highlite what they really want us to know about this I would appreciate it.

Thanks,

David.

 

[David Harper CFA FRM]

David,

no problem. see this question, except for GARP's mistake, it contains the key idea:
http://forum.bionicturtle.com/viewthread/1418/

(I don't have a dynamic XLS for the negative convexity, but i will add that to our to do list...it's a great idea!)

The most testable idea is that a callable bond exhibits negative convexity at low yields. (In my opinion, it would be great to understand the mistake in the sample question above, b/c that reflects a difference between duration and convexity as 1st and 2nd derivative functions.)

Beyond that, I'd know Tuckman's three points about the mortage passthrough (mortgage prepayment option = option to call a bond):

1. the price of the pass-through is above that of the nonprepayable mortgage when rates are relatively high. This phenomenon is due to the fact that housing turnover, defaults, and disasters generate prepayments even when rates are relatively high.
2. the pass-through does not rally as much as its nonprepayable counterpart when rates fall because homeowners prepay at par. Prepayments in a low-rate environment lower the value of mortgages.
3. for the same reason, the pass-through curve exhibits negative convexity. The only way for the pass-through to experience less of a rally than the non-prepayable mortgage is for the interest rate sensitivity of the pass-through to fall as rates fall.

from his chart (again, the most likely question would be about the neg convexity on the left):

http://learn.bionicturtle.com/images/forum/sep21_tuckman21.png

David