Floaters and Inverse Floaters

[notjusttp]

Kindly elaborate on the concept of Floaters and Inverse Floaters and pls clarify on following question

Q)

Suppose you have a position of $100 million in the instruments below. Each one has a maturity of 10 years. Which instrument is most likely to have a DV01 that exceeds the DV01 of a Treasury strip with 10-year maturity?
Choose one answer. a. Perpetual floating-rate notes
b. Convertibles
c. Inverse floating-rate securities
d. Corporate zero coupon notes

The answer is inverse floating rate securities.

Treasury strips have Macaulay duration equal to 10 years. Floating-rate notes have duration close to zero. Inverse floaters (with a leverage of one), have twice the duration of the equivalent coupon bond, so this must be very high.
Corporate notes and convertibles have duration close to 10 years, but are also exposed to other risk factors.

Doubt

1) Pls clarify why does a Floating rate note have duration close to 0 ?
2) Why should an inverse floater have twice the duration of equivalent coupon bond?
3) Since DV01 is just a measure of change of 1bps of interest rate why should it not be the same for corporate 0 coupon notes also.

Thanks

 

[David Harper CFA FRM]

Amit,

It's a good study question...

1. Because at the next coupon the bond will price at par, and at that time, it poses no market risk; the interest rate risk only matters until the next coupon.
So a floating rate note has duration = time to next coupon; e.g., if time to next coupon = six months, then duration = about 0.5
Let me relate this the interest rate swap valuation. Please see:
http://forum.bionicturtle.com/viewthread/1519/
This is Hull's i rate swap valuation by treating as two bonds (fixed for floating), where an important step is our ability to value the floating leg with only one cash flow (the next coupon). For the same reason duration is near to zero: the floating bond will be par at the next coupon.

2. Here is a thread on the duation of an inverse floater @ http://forum.bionicturtle.com/viewthread/1562/
The short version is: an inverse floater is unique in that it's duration can (far) exceed the maturity, depending on implied leverage
I started a learning XLS b/c this has been often asked, work in progress here:
http://sheet.zoho.com/public/btzoho/inverse-float-duration-v1-1

http://learn.bionicturtle.com/images/forum/aug_29_inverse.png

...i've used Jorion's example (handbook 7.6.4)...
if original structure has duration 4.5, and leverage is 1, then inverse floater has duration of 9.0;
e.g., if leverage is 2 (e.g., floater = 18% - 2* LIBOR), then duration = 3*4.5 = 13.5

3. Good point! I agree with you and disagree with the implication in the given aswer. The answer is incorrect to suggest the corporate zero has lower duration due to "other risk factors." For this purpose, corporate and treasury are the same: both have Macaulay duration = 10 years and modified duration < 10.

Key exam tips:
* Macaulay Duration of zero coupon bond = Maturity; e.g., 10 year zero: Macualay duration = 10
* An inverse floater, unique among bonds, has duration greater than maturity of orginal structure (but need leverage to ascertain multiple)
* Because a floating rate note/bond will be priced at par upon payment of next coupon, at that time it poses no further market risk. Therefore (i) duration of floater = "time to next coupon" and (ii) in valuation of interest rate swap, we only need to value the floating leg as a single cash flow

 

[F1mre]

Hi.

I got this question at an exam:

Which of the following bonds has the highest duration if each one has a maturity of 5 years, pay interest once a year(if possible), all are issued by the state and the reference rate is the one-year (let's say) LIBOR?

A: zero coupon
B: inverse floater
(C, D are irrelevant answers)


What is the correct answer? Can we say that the inverse floater's duration is higher 10 out of 10 times?

Edit:
The answer seems to be yes.