Question about inverse floater, please kindly help

Discussion in 'Fixed Income (P1.T4 or P2.T5)' started by kin28, Apr 12, 2012.

  1. kin28

    kin28 New Member

    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
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  2. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    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?
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