## Duration

Finance Junkie
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Joined: Sat Apr 07, 2012 10:24 am

### Duration

Pls explain:

With LIBOR at 4%, a manager wants to increase the duration of his portfolio. Which of the following securities should he acquire to increase the duration of his portfolio the most?
a. A 10-year reverse floater that pays 8%- LIBOR, payable annually
b. A 10-year reverse floater that pays 12%- 2×LIBOR, payable annually
c. A 10-year floater that pays LIBOR, payable annually
d. A 10-year fixed rate bond carrying a coupon of 4% payable annually

Pristine Solution: The answer is a 10-year reverse floater that pays 12%- 2×LIBOR, payable annually. The duration of a floater is about zero. The duration of a 10-year regular bond is about 9 years. The first reverse floater has a duration of about 2 × 9 = 18 years, the second, 3 × 9 = 27 years.

My qn: How the duration is calculated for 10 year reverse floater?

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Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

### Re: Duration

I got the ans that Inverse floaters with leverage of 1 is having twice the duration of the equivalent coupon bond.

However Thanks!

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: Duration

Hi Suresh,

A) Consider a regular coupon bond. Say its maturity is 10 years and it has a coupon of 8%. Lets say that its duration is 9 (a measure of risk).

This bond can be decomposed into 2 parts: LIBOR and 8%-LIBOR for half the face value each and sold separately.
Basically a floater and a reverse floater.
Now, the floater has a duration of Zero.
Lets say that the inverse floater has a duration of 'X'.
Now, the risk of the sum of the two bonds should equal to that of the fixed coupon bond
To find X:
9 = 0/2 + X/2
X=18.
The duration of this inverse floater is 18 years.

B) Now lets take another bond, say a 10 year bond with a 12% coupon. Lets say its duration is again 9 years.

This bond can be decomposed into 3 bonds, with each bond having 1/3 of the original bond's face value:
i) LIBOR (duration 0)
ii) LIBOR (duration 0)
iii) 12%-2*LIBOR (duration Y)

Now, 9 = 0/3+0/3+Y/3
Y=3*9=27
The duration of this inverse floater is 27 years

I hope this helps

Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

### Re: Duration

Awesome explanation.

You made things very clear and easy

Thanks a lot!