Each coupon strip (C-STRIP) is itself a zero coupon bond, and as such, a single C-STRIP, it seems to me, must have positive duration ...
Then, I guess, the question is: what if you were to package a sequence of C-STRIPS into a bond; i.e., reconstitute to a bond that resembles the Treasury but minus the P-STRIP! (I have no idea if they do that)
...and, on the questin. I do not know because I am unsure of the net impact of the prepayment difference. In regard to MBS IO, a key contributor to negative duration is that higher interest rates imply lower prepayment, but with that factor removed, I am (momentarily) unsure and haven't seen this explained ... I am thinking this still has positive duration but please don't trust that, I am unsure
so C-Strip is just a zero bond, and one couponed treasury bond can be stripped into many C-Strips.
On the other hand, mortgage IO is a packaged bond.. and one pool will be stripped to create just one mortgage IO..
I think your distinction is fair enough: the C-strip is a single zero; e.g., a Treasury strips into *several* different C-strips and one P-strip (one strip for each cash flow)
but the "typical" mortgage IO represents a stream; however there are variations - but i don't think you see an IO itself stripped into zeros (but who knows)
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