According to Schweser:
The convention is to treat the duration of the floating rate side of the swap as being half the reset period. For example, for a 6-month reset, the duration would be taken to be 0.25, for a quarterly reset it would be taken to be 0.125, etc.
At inception or just after a settlement for a quarterly reset swap, the duration of the floating payments is 0.25; for a semiannual reset swap, the duration is 0.5; et cetera. Just before the payment is due, however, the duration is 0.0. Hence, the average duration of a floating instrument over the reset period is one-half the length of its settlement periods.
First of all, why is it 0.25 and 0.125 in the first paragraph? Then, why is it 0.25 and 0.5 in the second paragraph? This is confusing…
Second, why is it 0.0 just before the payment is due?