Duration of floating rate bond

CFA Level III
#1

Hi,

What is the duration of floating rate bond in a swap?

The proposed answer in the question I am doing, is it would be equal to 1/2 of payment interval.

i.e 4-year swap with quarterly payments --> duration of floating bond would be 1/2 of 0.25 = 0.125

I recall somewhere that the duration of floating rate bond should be 0

Thanks for your explanation

#2

the float side is = 0.125

the fixed side is 0.75X4 = 3

so the net amount is 3-0.125 = 2.875

From the past years, we assumed 0 duration since it was under 1 year but for these swaps, esp when used to adjust portfolio durations, you must be more exact.

#3

Thanks for your explanation!

#4

On the reset date, the duration of a floating rate bond is 0.

Immediately after the reset rate, the floating rate bond has a duration equal to the time to the next reset date. If it is a quarterly reset, the duration is 1/4.

So at one extreme (reset date) the duration is 0 and at the other extreme (just after reset) the duration is 1/f , where f is the reset frequency.

Averaging the two extremes, (1/2) * (0 + 1/f) = 1/(2f). Therefore, the floating rate side is 1/2f = 1/(2*4) = 1/8 in your example.

#5

As far as why it’s 1/2 the payment interval instead of just the payment interval, the key is that it’s the average duration. The duration will decrease from a maximum of the payment interval after each payment to 0 just before the next payment. Therefore, on average the duration is 1/2 * [payment interval]

#6

its becomes 0 just before payment

#7

some tricks for solving all swap duration questions, and some detail so you could understand it conceptually…

1. duration of fixed = 0.75 X maturity of the bond (i.e 3yr fixed… 0.75 x 3 = 2.25)

duration of floating = 0.50 x pmt interval (i.e. semiannual pmts… 0.50 x 0.50 = 0.25)

2. the equation is Duration(swap) = D(fixed or floating) - D(floating or fixed). Whatever the swap is (fixed or floating) will go SECOND in the equation. For example, if it is a FIXED swap, you will line it up as Duration(fixed swap) = Duration(floating) - Duration(fixed), and vice versa.

3. when calculating the duration of the swap, you want to first figure out what YOU will be RECEIVING (think “asset - liability”). if you are receiving fixed, it will go first… if you are receiving floating, it will go first.

4. the key to figuring out what TYPE of swap you need (fixed or floating) depends on your interest rate expecations and/or if you want to increase or decrease duration. Obviously, if you want to increase your duration, that means you think interest rates will decline, so you would want to RECEIVE fixed rates and pay floating (think asset - liability, so you will want a swap that is fixed - floating, which is a FLOATING rate swap).

hopefully this helps. after doing tons of questions, it seems more likely that you will need to know this in depth (i.e. see question in CFAI 2014 AM session) as opposed to just calculating the duration of a fixed swap… let me know if you have any questions