Negative duration and positive duration positions in swaps and MBS

Question

Hi there,

very Confused about negative and positive duration positions where they show up in 1) Risk Mgt of swap strategies  and in 2) MBS...:-(

Negative duration: does it mean to 'reduce duration' ? - or hold a position that moves directly with interest rates - eg wanting to add a negative duration position like a pay-fixed swap, receive floating to the fixed income portfolio: pay fixed side -0.75 and receive floating side  + 0.125,  = -0.625 
does this mean simply that a fixed rate borrower gains (+) when int rates rise (+) ?

Positive duration: does it mean to 'increase duration' ? - or hold a position that moves inversely to int rates - eg wanting to add a positive duration position like a pay-floating -0.125 and receive-fixed +0.75, swap, to the fixed income portfolio  = +0.625
Does this simply mean that a floating rate borrower gains (+)  when int rates fall, (neg) ?

In MBSs: Principal Only notes have a positive duration and Interest-Only notes have a negative duration.

I thought that POs dur incr, as when int rates rise, prepayments slower, and POs life/duration gets longer, bad, so their price falls, as underlying mortgage pool duration longer: does 'positive' mean a longer life of the PO ?

IOs have negative duration as when int rates fall, faster prepymts terminate the underlying interest-only pool, and the value of the IO falls - what is the negative position, the shorter life of the IO ?

Head is swimming..............feel faint    ;-) !!

Thanks v much for all the moral and mental support !

adossa3 · Answer

Thanks very much Zee! Awesome, was so confused. :-) 
want to learn formulas over the next week and go over the stuff am finding hard. Extr tired today and progress is v slow....Thank you, thank you thank you Zee and Sophie for the moral support also !

Zee Tan · Answer

Hi @adossa3 - positive duration definitely means a position or valuation that moves inversely to interest rates, and negative duration meaning moving directly with interest rates.

For principal-only and interest-only MBS, here's the conceptual reasoning:

Declining interest rates increase PO repayment speed, lowering the discount rate and increasing the PO price. Hence +ve duration.
Declining interest rates mean that repayments speed up, so there's less interest paid (lower principal, plus lower interest rates), so IO value decreases. Hence -ve duration.

Hope that helps!