# duration of the fixed side of a swap

is there a simple way we’re supposed to be able to calculate this, the way that the duration of the floating side is simply one half the payment frequency? what information do we need to be given to figure out the duration of the fixed side of a swap?

dpcfa Wrote: ------------------------------------------------------- > what information do we need to be given to figure > out the duration of the fixed side of a swap? The duration. Not trying to be a smartass, but it’s always given, far as I can tell. They could give you a scenario where interest rates dropped X bps and the value of the fixed payments went up to Y and have you calculate it, but again, I’ve only ever seen it given.

dpcfa Wrote: ------------------------------------------------------- > is there a simple way we’re supposed to be able to > calculate this, the way that the duration of the > floating side is simply one half the payment > frequency? > > what information do we need to be given to figure > out the duration of the fixed side of a swap? CFAI says approximate using 75% of maturity

I don’t think they would ever not give the duration unless the question is very qualitative. If it is, you could assume it is close, but less than the tenor of the swap. Like kurmanal said 75% is good. So for a 4 year swap, duration might be 3ish.

kurmanal Wrote: ------------------------------------------------------- > dpcfa Wrote: > -------------------------------------------------- > ----- > > is there a simple way we’re supposed to be able > to > > calculate this, the way that the duration of > the > > floating side is simply one half the payment > > frequency? > > > > what information do we need to be given to > figure > > out the duration of the fixed side of a swap? > > > CFAI says approximate using 75% of maturity thanks, that’s exactly what was done in a problem on one of the schweser exams and i didnt know where it was coming from. glad to hear there’s a basis for it.

75% huh? News to me!.. Nice, thanks y’all!

Just read this section again: Fixed leg = 75% of maturity Floating leg = 50% of the maturity

Thats not quite right. The floating leg is 50% of the remaining time to the next payment. So, if it’s semi-annual, it may be less then 3 months.

darkstar Wrote: ------------------------------------------------------- > Just read this section again: > > Fixed leg = 75% of maturity > Floating leg = 50% of the maturity OK, I’m an idiot. I meant to say: Floating leg = 50% of the coupon period

well, I’m just saying that you’ll usually get a situation where you are currently part way through the coupon period, therefore its 50% of whatever time is left until payment. So, if your one month into a 6 month period, it would be a duration of 2.5 months.

The 75% thing is news to me. My understanding was that the duration of a swap is equal to the duration of the fixed side minus the duration of the floating side. The duration of the fixed side is equal to the duration of an equivalent coupon bond of the same maturity as the swap’s tenor. You may be able to approximate that with 75% of the time-to-maturity, but that’s a *very* rough approximation. I can’t imagine that they would have you do that, rather than just tell you the duration. The current duration of the floating side is basically equal to the time (in years) until the next floating rate reset. If you don’t know the time until the next reset, you should assume 1/2*( 1/(#resets per year) ), which is 0.25 for a semiannual reset and 0.5 for an annual reset. If you receive fixed, your duration is equal to the swap’s duration. If you receive floating, your duration is equal to the swap’s duration times -1.

GordGekko Wrote: ------------------------------------------------------- > well, I’m just saying that you’ll usually get a > situation where you are currently part way through > the coupon period, therefore its 50% of whatever > time is left until payment. So, if your one month > into a 6 month period, it would be a duration of > 2.5 months. Yes, OK, I agree. I feel sort of brain-dead today. Third time’s a charm, I hope. Floating leg = 50% of the time remaining to the next coupon payment.

bchadwick Wrote: ------------------------------------------------------- > The 75% thing is news to me. > > My understanding was that the duration of a swap > is equal to the duration of the fixed side minus > the duration of the floating side. Yes, that’s correct. For the floating rate payer, the swap duration is equal to the duration of the fixed leg minus the duration of the floating leg - and the opposite for a fixed rate payer. > The duration of the fixed side is equal to the > duration of an equivalent coupon bond of the same > maturity as the swap’s tenor. You may be able to > approximate that with 75% of the time-to-maturity, > but that’s a *very* rough approximation. I can’t > imagine that they would have you do that, rather > than just tell you the duration. Again, I agree. But they do say in the curriculum that the duration of the fixed rate leg of a swap is 75% of the tenor. It’s a horrible approximation, and you’re probably correct that they’ll just give us the duration for the fixed leg rather than making us use an arbitrary approximation. > The current duration of the floating side is > basically equal to the time (in years) until the > next floating rate reset. If you don’t know the > time until the next reset, you should assume 1/2*( > 1/(#resets per year) ), which is 0.25 for a > semiannual reset and 0.5 for an annual reset. I agree. > If you receive fixed, your duration is equal to > the swap’s duration. > > If you receive floating, your duration is equal to > the swap’s duration times -1. I agree.