CFAI vol. 5, page 486 To calculate the duration of swap- paying fixed and receiving floating has approximately 75 % of the maturity. 1. For one years swap with semi-annual payments, would have a duration of .25-.75=-.5 2. For 1 year swap with quarterly payments, would have a duration of .125-.75=-.625 My q here is that why the fixed side has the same duration? from semi to quarterly payments, it does change or not, in both these cases, the fixed duration is .75 ?!!! Can anybody answer that?
derswap I am not quite sure i understand your question, considering that you have stated it in the first statement- “paying fixed has approximately 75% of the maturity”. i am going to give it a shot - as you may recall an interest rate swap is analogous to a fixed rate bond and a floating rate bond. Since you have a one year bond, 75% of the maturity is 0.75. Since you are paying fixed it is -0.75.
derswap07, BTON04 is right. As long as both are 1 year swaps, the duration of paying fixed is approximated to be -0.75. The durations (0.25 & 0.125) of receiving floating are different just because the first one is semi-annual payment and the second one is quarterly payment.
Thanks for the help.
This is my take on it: So Fixed side is the equivalent to a fixed rate bond. The value of a bond is determined by the cash flows and the rate at which the cash flows can be reinvested. For simplicity, if you assume a flat yield curve, the number of payments before maturity wont have an effect on the value of the bond because all cash flows will be reinvested at the same rate… therefore the number of coupon payments dont affect the duration of a bond (duration = value sensitivity) Also Effective duration = (V1-V2) / (2*V0* ChngeYield) Since coupons are reinvested at the same rate, V1 & V2 are unaffected by the number of coupon payments. Duration of a floating rate bond is estimated by divding time to next coupon by 2. Because the coupon payments are floating and reinvested at a floating rate, the terminal value is pretty constant, hence a low duration.