A question on the duration of a swap's semi-annual pmt

[streetplay]

Hi,
I’m using a previous year’s curriculum text book and was unable to solve question 24 on page 504 of volume 5.
This question is about finding a notional principal for an interest swap to be used for achieving the bond pf duration target.
In the question, the duration of the swap’s fixed pmt is given as 75% of the swap maturity, which is 6 years.
For the duration of the swap’s floating pmt, which I thought would be 0.5 given that it is a semiannual pmt, was actually 0.25 in the answer.
Could anyone please explain why the duration of the semiannual floating pmt in this case is 0.25?
Thank you.
From Seoul

 

[Swaption11]

It is half of the reset intervals expressed annually. Semiannual = 0.5*0.5 = 0.25

 

[harryy02]

try and work with it my friend. certainly no time for this questioning..

 

[S2000magician]

At the reset date, the price of a floating-rate bond (paying market rate, not market-rate-plus-a-spread) is par. Thus, any price change will occur only between reset dates, and at the next reset date the price returns to par; it’s as if every reset date the bond is paid off and a new bond issued. As an approximation to the duration of a bond that will be paid off as of the next reset date, they use ½ of the time between resets; i.e., ½ of the time between coupon payments. It’s an approximation, but it’s close enough.
For the fixed rate in a swap, the duration will be the duration of the corresponding fixed-rate bond. Again, as an approximation, they use 75% of the time to maturity. It would be better to calculate the duration of that bond from its cash flows, but the approximation is OK for the purposes of the exam.