# Duration of FLoating and Fixed Swap

Im trying to clarify this, not sure why I have trouble remembering it so thought if I posted it and got some answers it would help.

Duration of the fixed payer in a swap is Term*.75, so if its a 4 eyar swap, it would be .75*4 = 3

Duration of floating is 1/Settlements per year/2, so i its a 4 year semiannual swap, it would be 1/2/2 =.125

Swap duration = 3-.125 = 2.875 (will be + or - depending on which side you are on).

Is this correct? Also, why do we divide the flaoting by 2? Is that the standard procedure - we just assume that the duration is half the length of the settlement period (kind of like assuming that the fixed is .75 the term of the whole swap)? Thanks!

floating rate is divided by two to give you the average time to reset. Remember the floating rate side resets e.g. every 6 months for a semi annual bond. Now at the start it is 0, at the end it is 0.5. Average = 0+0.5/2 = 0.25

and instead of writing 1/2/2 - you are better of (less confusing) to write 0.5 / 2 = 0.25 …

just my thought though.

^ +1

best of luck you deserve the kill the beast this year

great thanks. And yea you are probably right about the way to write it, i just wanted to show it here by breaking it up step by step to see if i was right.

Think of the .75 for fixed maturity and .5 for floating reset period as averages/rules of thumb for quickly calculating a maturity from an instrument with periodic coupons.

For floating rates, the duration ranges between 0 and the time between reset dates. Once the interest rate is reset, the next payment acts like a short-term zero-coupon bond with duration equal to time-to-maturity. If you have a floater with quarterly resets, then immediately after a reset date, the floater’s duration will be .25, and immediately before a reset date, the duration will be zero. So, the average duration for the life of a swap will be the average of the min and max durations.

Seriously if cpk doesn’t pass this test, I have no hope of ever passing it.

cpk is dynamite.

remember this

annual = .5

semi annual = .25

quarterly = .125

Is the 0.75 for fixed just a standard set by CFAI? Or is there a ‘logical’ explanation as in the floating duraction.