Duration of IO strip in CMO

FRM
#1

Hi,

Could anyone help me?

Schweeser Qbank and study materials says:

  1. duration of IO strip of CMO is NEGATIVE

  2. convexity of IO strip of CMO is NEGATIVE

  3. correlation between price of IO strip and interest rate is POSITIVE.

I can not understant the 1 statement.

Duration=change in price/change in interet rate. IF interest rate rise the price of IO strip also rise. So I think duration of IO strip is POSITIVE.

Am I right? or where is mistake in my logic?

Thanks a lot.

#2

Recall that duration is the negative of the percent price change for a 1% change in YTM: positive duration means that at YTM increases, the price falls.

IO strips can have negative (effective) duration when their YTM is low (the price will rise when YTM rises, and fall when YTM falls), but will have positive (effective) duration when their YTM is high.

#3

Thanks.

Few questions:

  1. YTM? - you mean market interest rate? or yield of IO CMO?

  2. IF CMO traded at par - duration if IO CMOis negative?

#4

My pleasure.

Market rates, but the yield on the IO will have a strong, positive correlation to market rates.

My pleasure.

Not necessarily. The prepayment characteristics of the underlying mortgages will determine whether the effective duration of an IO strip is positive or negative.

#5

Everything is clear now. I just forget “-” in the first equation.

Thats why I got “positive” rather than “negative” in mind.

Simply speaking:

  1. duration= - (change in price)/(change in YTM)

  2. Effective dur = {(BVytm-) minus (BVytm+)} / 2*BV*change in YTM

#6

Fixed that for you.