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Why IO has negative effective duration?


New Member
I understand IO benefits from rising interest rate, i.e. interest rate increase -> prepayment slow -> IO keeps getting interest. Does it mean when interest rate increases, the value of IO increases? Effective duration is a measure of slope or sensitivity between price and interest rate. So why effective duration is negative?

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi maoxindi,

Your second point is correct and it's the first point of confusion: the SLOPE of the (tangent to) P/Y curve is dollar duration, dP/dy, and it is *truly* a negative (though sometimes expressed as a positive out of convenience), except for the IO where it's a positive.

Then modified duration = -1/P*(dollar duration) = -1/P*dP/dy; hence negative slope becomes positive duration

In regard to IO, can you look at my graphic here @ http://www.bionicturtle.com/forum/threads/negative-convexity.5617/#post-15878
btw, FRM does like to test that IO is the special case of negative duration; e.g., http://www.bionicturtle.com/forum/t...hat-your-remember-here.5923/page-5#post-17678