Question about inverse floater, please kindly help

[kin28]

Consider the market environment in which 1-year swaps are yielding 4% and have a duration of approximately 0.95. A 1 year inverse floater with a coupon of 12%-2 LIBOR (3-month) has been just reset and its trading at par. The duration of this inverse floater will be closest to:

The answer is: 0.95x3 - 0.25x2 = 2.35

But why the answer is not 0.95*3=2.85?

is it because the inverse floater is separated into 3 month with 1 year?
I could not get 0.25*2...
Please help

 

[David Harper CFA FRM]

Hi kin,

This would be a great question, except for that difference. I would agree with you and get 2.85. At least in the FRM, the working assumption (to my knowledge) has always been that the duration of a floater = 0, such that, in this case:

1. Solve for leverage, w: 4% = L*(1-w) + w*(12% - 2*L) --> w = 1/3.
2. Equate dollar durations: 0.95 = 1/3*d + 2/3*0 --> d = 0.95*3 = 2.85

By the answer given (2.35), it appears they meant to assign a duration of 0.25 to the floater; i.e.,
2 (implied by answer). Equate dollar durations: 0.95 = 1/3*d + 2/3*0.25 --> d = [0.95 - 2/3*0.25]*3 = 2.35;
the 0.25 would be justified as the duration is ~ time to next coupon, but question would need to specify "next coupon in 3 months and duration of floater is time to next coupon" because the default working assumption on the floater is duration = 0 (rounding down), in my opinion. So, I don't disagree with answer, but rather the question setup. Thanks for sharing interesting question. Can i ask the source?