Swap Duration

I’m reviewing 2013 CFAI’s PM section and there is a question whch asks about the duration of a payer swap strategy:

The answer says that the approximate fixed-rate duration of a bond is 75% of its maturity (with a 3 year matury = (3 x 0.75) = 2.25, while the floating duration is 1/2 it’s semi-snnual pay period (so 0.5 x 0.5 = 0.25). You net these and get +0.25 - 2.25 = -2.0 for the duration of the swap.

Is the 75% duration of the maturity for the fixed side in the 2015 curriculum? I haven’t seen this before, and the Schweser materials only give the duration explicitly in their examples.

Yes, the curriculum uses the 75% rule a lot.

If the duration of a bond with the same term is given, use that instead. But the majority of the time the curriculum doesn’t give you that information and you have to assume it’s 75% of the term.

ya, just go with 75% duration on the fixed end, and then for the floating end, D=.25 if semiannual, and .125 if quarterly. so a 4 year swap pay fix receive float with payments made semi-annually has Duration of:

D swap = .75*4 - .25 = 2.75