## Duration Of Inverse Floater

swarnendupathak
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### Duration Of Inverse Floater

Suppose that coupon & modified duration of a 10-year bond prices to par is 6% & 7.5 respectively. What is the appropriate modified duration of a 10-year inverse floater priced to par with a coupon of 18%-2xLIBOR (1-Month)??
a) 7.5
b) 15
c) 22.5
d) 0.00

Swarnendu

content.pristine
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### Re: Duration Of Inverse Floater

Swarnendu,

Take a look at this post:
post1199.html?sid=9dd03b1bdd5ecaa83a7c83b550a1df25#p1199

Lemme know if this solves your question

swarnendupathak
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### Re: Duration Of Inverse Floater

Then, that 3 year bond can be splitted into 3 seperate bond with coupon of (a) LIBOR (duration zero, as it become floater bond) (b) same as (a). (c) bond with coupon of 18%-LIBOR. Then the total duration euation would be:
7.5 = 0/3 + 0/3 + Duration of 3rd bond/3
then duration of 3rd is comming as 7.5*3 = 22.50.

Think i got it...if i made it wrong then please guide me.
Very lucid explanation in the post u mentioned.

Thanks
Swarnendu

content.pristine
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### Re: Duration Of Inverse Floater

Yup! You got it!

swarnendupathak
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### Re: Duration Of Inverse Floater

Hey, Thanks, but have some doubt,
here the existing bond is with coupon 6% with duaration of 7.5. And we need to calculate the duration of inverse floter bond with coupon of 18-2XLIBOR (1-month). So, can we split this inverse floater into 2 FRN of 6& each & third one with (6-2XLIBOR)??
If this is true, this could mean, long position in 3 FRN of 6% each & 2 short position in Floater linked with LOBOR???
Then the duration of 3 FRN could be (7.5*3) = 22.5 Less duration of 0.25*2 = 0.5 (Short position in LIBOR - Floater), Net effect = 22 as duration of inverse floater.
Now, here is one confussion, we are consiering short position in floater with duration of 0.50, so i want to know whether floater duration would be ZREO or 0.50???? and also please guide to state which is the correct process & right answer.

Please guide me to clear the confussion......

Swarnendu

content.pristine
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### Re: Duration Of Inverse Floater

Yup! You got it!

swarnendupathak
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### Re: Duration Of Inverse Floater

Thanks, But answer is not tallying with 22.50, as the now the answer is 22.5-0.5 = 22.00.
So, please let me know the correct process.

Swarnendu

content.pristine
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### Re: Duration Of Inverse Floater

The Duration depends on the frequency of reset dates of the FRB.
If it is daily, then duration is 1/365. If it is semiannual, then it is 0.5.
In the question, the frequency is given as 1 month. Hence, duration = 1/12.

"here the existing bond is with coupon 6% with duaration of 7.5. And we need to calculate the duration of inverse floter bond with coupon of 18-2XLIBOR (1-month). So, can we split this inverse floater into 2 FRN of 6& each & third one with (6-2XLIBOR)??"

This is correct..

"If this is true, this could mean, long position in 3 FRN of 6% each & 2 short position in Floater linked with LOBOR???"

I'm not sure what you mean by this but, the object here is that we know the duration of a fixed rate bond. So we can strike an equation. If I didnt solve your query, can you be a bit more specific?

swarnendupathak
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Posts: 119
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### Re: Duration Of Inverse Floater

"If this is true, this could mean, long position in 3 FRN of 6% each & 2 short position in Floater linked with LOBOR???"

We can structured the inverse floater as long position in 3 Fixed Rate Bond i.e. 6*3 = 18 plus short position in 2 FRN linked with LIBOR i.e. 2*L, by consolidating we get 6*3 + -2*L = 18-2L (which is required here) as the negative sign denotes the short position in LIBOR, so don't we need to deduct duration of that from duration of long position??? to get the net duration of inverse floater, i.e. 3*7.5-0.25*2 = 22 (0.25 as it is a 1month LIBOR)

Swarnendu