# Duration of a swap

I understand if you enter a pay fix duration, you long the floating and short the fix. I just don’t understand how the to get the numbers below.

[question removed by moderator]

Duration of Swap = Duration of Float(receive float) - Duration of fixed(pay fixed)

Duration of float = (1/2) * (1/2) -----> Half the frequency and the frequency is Semi-annual. Therefore, 1/4

Duration of fixed = 3*.75 -----> convention is to use .75 the maturity.

You wrote out the solution. Not sure what you’re asking or if the above is where the confusion lies.

I guess the 683 is a incorrect number.

(3.5 - 6.4)*640 / -2 = 928?

with a 4 year swap that kondo suggests

Swap duration = 0.5*0.5 - 0.75*4 = -2.75

and with this

-2.9 * 640 / -2.75 = 675

I have the answer but as I said I couldn’t understand the solution…“why 0.5 for floating, and why 0.75 for fixed” I couldn’t see this on textbook that mention its a “rule” to use these metrics and don’t know why it’s on the practice exam.

Continuing with the assumption (for convenience) that the duration of the fixed-rate bond is approximated as 75 percent of its maturity, we find, for example, that a one-year swap with semi-annual payments would have a duration of 0.25 – 0.75 = –0.50. A one-year swap with quarterly payments would have a duration of 0.125 – 0.75 = –0.625. A two-year swap with semiannual payments would have a duration of 0.25 – 1.50 = –1.25. A two-year swap with quarterly payments would have a duration of 0.125 – 1.50 = –1.375.

(This is from the text).

So Fixed = 0.75 * duration is an assumption that is being made.

Floating = 0.5 * Duration comes - because the bond resets to Par (So Duration=0 at the end, Duration=Duration at the beginning). So on average it is 0.5 * Duration.

That’s better.