reverse floater

[aditya]

hi david,

sorry for asking questions all the time despite knowing that u are so busy these days, but i dont have any other option bcoz there is only one david harper in this world..........


this is a question from FRM 2003

Which of the following statements most accurately reflects characteristics of
a reverse floater (with no options attached)?

a. A portfolio of reverse floaters carries a marginally higher duration risk
than a portfolio of similar maturity normal floaters.
b. A holder of a reverse floater can synthetically convert his position into a
fixed rate bond by receiving floating and paying fixed on an interest rate
swap.
c. A reverse floater hedges against rising benchmark yields.
d. A reverse floater’s price changes by as much as that in a similar maturity
fixed rate bond for a given change in yield.

my thoughts regarding options

a ) if this talking about duration then we know that duration of reverse floaters are much greater than normal floaters ( but is it not tgrue always like in the case when

normal floater coupon:libor
reverse floater :12 % - libor

and if libor < 12 % - libor :> that duration of normal floater is greater than that of reverse floater ) correct????


b) the holder of receiver floater is receiving coupon gor it ,but receiving coupons for reverse floater is like paying libor so position of reverse floater can be converted to a fixed rate bond by receiving libor and paying fixed ... so b is true


plz tell is my understanding correct

thanx

adi

 

[David Harper CFA FRM]

Hi adi,

You are very kind, thank you.

First, can i mention that floaters (and questions like this) should not appear on the 2008 FRM exam. I see no justification for this sort of question in the cirriculum; it is nowhere in the assigned readings so it would be "unfair" of GARP to quiz on it, IMO (The FRM handbook is not assigned. Inverse floaters do not appear on the AIMs)

Regarding your (a), I see that refers to Jorion's example 7.6.3, but this will generally *never* be true: "duration of normal floater is greater than that of reverse floater. "

Instead, what you say here is almost true: "position of reverse floater can be converted to a fixed rate bond by receiving libor and paying fixed ... so b is true"

Fabozzi explains this well, see page 90: http://books.google.com/books?id=t61BRhZWbSMC&printsec=frontcover&dq=duration+inverse+floater&source=gbs_summary_s&cad=0

If you look at Jorion's example 7.6.3, he splits $100 fixed income into floater + inverse floater:
$100 MM fixed coupon = $50 MM floater + $50 MM inverse floater, such that
$50 MM inverse floater = $100 MM fixed coupoon [i.e., long position] - $50 MM floater [short position]

So the inverse floater is synthetically the same as long fixed bond plus short floater
This can be inferred directly from the coupon: 12% - LIBOR. Typically the +/- signs will tell you much of what you need! Consider directly:
12% - LIBOR = Receive/long (+) fixed 12% and Pay/short (-) floating LIBOR.

So, given:
$50 MM inverse floater = $100 MM fixed coupoon [i.e., long position] - $50 MM floater [short position]

and knowing that...
Duration of $50 MM floater [short position] is nearly 0 (time to next coupon); this you should know from the Hull's interest rate swap valuation. We do want to understand why a floater has almost zero duration.

Then
Dollar duration of $50 MM inverse floater = Dollar duration $100 MM fixed coupoon [i.e., long position]

such that
Duration of inverse floater = 100/50 * duration of fixed coupon

In this way,
the duration of inverse floater will be some multiple of the duration fixed coupon. It should be at least 1.0 but can go much higher; i.e., that's the 'leverage' in the floater. For example, Jorion's second example is:
$100 MM fixed = $66.67 float + $33.3 inverse float, so
33 inverse float = $100 - 66.67, and
The duration multiple is 100/33 = 3x

I hope that helps!
David