# Negative Key Rate Duration

HI

Can someone please tell me that - “by saying negative key rate duration, it actually means positive relationship between Bond Price and key rates”. I was going through the last reading of Fixed Income and got confused with this. thankyou guys !!!

when rates fall - duration falls, when rates rise - duration rises.

that is negative convexity on the bond - and that is a positive relationship for you. both rates and the duration move in the same direction together.

cpk - Doesn’t your duration increases when rates fall? I am confused now.

for a negative convex bond this above relation is what is true.

for a positive convex bond - your rates rise - duration falls, when rates fall - duration rises.

I am trying to confuse nobody.

I agree with your statements. Just confirm me one more thing - Can we say “Non callable bonds have +ve duration (all rates) and Interest Only strips has -ve duration (long term rates)” or should we say it other way round.

For an MBS security, when Interest rates decreases, Prepayment increases which leads to reduction in duration.

Maybe better to think convexity for positive and

concavity for negative?

I think we are confusing ourselves. @Psahni, does the question relates to MBS? As this is a amortizing bond with prepayment option it will behave differently from a normal option free bond ? So how does the sentence fit in the context?

I think we are confusing ourselves. @Psahni, does the question relates to MBS? As this is a amortizing bond with prepayment option it will behave differently from a normal option free bond ? So how does the sentence fit in the context?

Hello.

The normal situation for a bond is that the price falls when interest rates rise, and vice-versa; this corresponds to a positive duration (Macaulay, modified, effective, key rate, whatever). If a bond’s price rises when interest rates rise and falls when interest rates fall, that corresponds to a negative (effective, or key rate) duration. (Macaulay duration and modified duration cannot be negative.) The common example of this is an IO strip in a CMO when interest rates are low: such a bond has a negative effective duration.

So, a negative key rate duration means that when that key rate rises the bond’s price rises, and when that key rate falls the bond’s price falls: a positive relationship between the bond price and the key rate.

My pleasure.

@S2000magician: You understood my query more than I could and you not only resolved it perfectly but also provided me added info that Macaulay and modified duration can’t be negative. Please find below a dedicated thanks for you.

thankyou S2000magician !!!

My pleasure.

Best of luck on the exam!