# Swap Duration

Below question is from CFAI’s online practice questions, I’m a little confuse on how does a pay fixed/receive floating swap increase interest rate sensitivity. My understanding is that pay fixed swap would reduce the overall duration of the position, but the explanation below is saying otherwise, can anyone explain to me why, thanks.

D(pay fixed) = D(floating) - D(fixed), which should be negative and should reduce the duration of the position.

The question was removed but i know what question you are referring to. It had to do with managing cf risk and interest rate risk right? I got it wrong too. I think the answer has to do with the combination of borrowing with a variable rate and converting that variable rate into fixed, using the swap. The answer doesnt provide ample reasoning imo.

-swap is used to hedge

-when you enter a pay fixed, receive floating swap, it’s assumed that you are currently paying floating rate.

-floating is cancelled out and you’re left with pay fixed obligation.

=increased duration / increased interest rate risk

hope this helps

but isn’t it also true that the duration of the pay fixed/receive floating swap is negative based on the swap duration formula, and when this swap is added to the portfolio, shouldn’t it reduce the duration of the portfolio ?

Yes.

Do we still assume that fixed duration is 75% of the no of years? Found that in an old mock.

Yes.

Also remember that the duration of the floating portion is half of the pay period. So if it’s a semi-annual pay period, the duration of the floating rate leg is 0.5/2 = 0.25.