FRN and inverse FRN duration

Hi,

I have two questions:

1. suppose that floater’s coupon formula is C = 75 % x 6mLIBOR, and its maturity is 3 years, nominal value = 10 mln USD.

What is its duration? Is it 0,5 or should it be scaled by 0,75, i.e. 0,75 x 0,5 = 0,375?

I wonder, because at the next reset date, the price of the floater won’t be its par value. so the duration- I think- isn’t 0,5 in this case…

1. Suppose the coupon formula for the inverse floater is C= 6 % - 0,75 x 6mLIBOR, maturity- 3 years, par value 10 mio. USD

What’s the duration?

I would divide this bond into 3 bonds: (A) long fixed 6 %, (B) short floater 0,75 x 6mLIBOR and © long zero-coupon 10 mio., compute their durations and the duration of the original bond would be dur(A) - dur(B) + dur©.

Am I right, or do i make a mistake?

Cheers,

Howdy.

As the coupon goes down the duration (Macaulay, modified, effective) goes _ up _, not down. Scaling by 0,75 would be exactly the wrong thing to do. The duration might be 0,6 years instead of 0,5 years.

The inverse floater will have a longer duration than a fixed-rate bond, though exactly how much longer is difficult to say without doing a lot of work (e.g., Monte Carlo simulation).

Dividing it into three bonds as you suggest will definitely not work.

Back atcha!

So, that 0,6 is a guess - does it mean that there is no way to make use of the fact, that the duration of a floater with e.g. C = 6mLIBOR is 0,5 year and we have some parameter k that scales it ( C = k x 6mLIBOR) ?

We have to compute Macaulay Duration traditionally - by hand ?

For that inverse floater - it confuses me much, because such portoflio consisting of above-mentioned bonds A, B and C is exactly the replication of that inverse. I see that i made a mistake, because portfolio’s duration should be weighted duration:

Portf. dur = (Price(A) x Dur(A) - Price(B) x Dur(B) + Price© x Dur©) / (Price(A) + Price(B) + Price©)

But it’s still not that you wrote. I wonder what’s wrong with that reasoning of dividing inverse floater into 3 bonds.

My pleasure.

I’m not sure if there’s a k that will work all the time, but I doubt it. You’ll probably have to do it . . . well, not by hand; use Excel.

Now you’re thinking.

(But note that the denominator should be (Price(A) Price(B) + Price ©); you’re _ short _ bond B, not long.)

Ok, now after the adjustment for a denominator, I believe everything is OK.

Thank you a lot.

It is, indeed.

You’re welcome.

By the way, referring back to post #2, above, it’s an interesting exercise to determine why, exactly, the inverse floater will have a longer duration than the floater; indeed, it will have a longer duration than a fixed-rate bond. (In fact, it could have a duration that is longer than its maturity.)

I just did a couple of quick calculations:

The (effective) duration of the leveraged floater is 0.65 years.

The (effective) duration of the leveraged inverse floater is . . . are you ready for this? . . . 5.08 years.