I agree that the average duration for the Floating Rate side is 0.25 .
But do not understand why , when computing the duration of a swap, one uses the average duration for the Floating Rate side of the Swap and not the maximum duration
At the begining of the swap, is not the duration for the Floating Rate side 0.5 ?
Are we not interested of the duration at the start of the swap?
There is no “average” duration or “maximum” duration.
We’re talking modified duration here: the sensitivity of the price to changes in the YTM.
As an approximation to the modified duration of the floating rate leg, we use half the time to the next coupon payment. It’s nothing more nor less than an approximation of the true modified duration.