Notional Value and Duration relationship

CFA Level III
#1

I read somewhere here that the swap with the smallest notional value has a higher duration.
I am so confused as to why is that?

#2

If you’re trying to adjust the duration of your portfolio a given amount, then you’ll need a certain (i.e., fixed) money duration on the swap you’re using to make the adjustment. Therefore, for a swap with a shorter net duration you’ll need a larger notional amount, and for a swap with a longer net duration you’ll need a smaller notional amount.

#3

you know I still didnt get this relationship

I am trying to find an answer, but i don’t get why its like that

#4

I think I got it, but by looking at the formula

#5

Good to hear.