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?
Why IO has negative effective duration?
- Thread starter maoxindi
- Start date
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://forum.bionicturtle.com/threads/negative-convexity.5617/#post-15878
btw, FRM does like to test that IO is the special case of negative duration; e.g., http://forum.bionicturtle.com/threads/level-2-post-what-your-remember-here.5923/page-5#post-17678
Thanks,
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://forum.bionicturtle.com/threads/negative-convexity.5617/#post-15878
btw, FRM does like to test that IO is the special case of negative duration; e.g., http://forum.bionicturtle.com/threads/level-2-post-what-your-remember-here.5923/page-5#post-17678
Thanks,
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