# Qbank #28631

Hey all, busy going through the QBank and came across this question which I don’t understand the answer for: Question 30 - #28631 For a plain-vanilla interest-rate swap with annual reset and one year to maturity, which of the following is the swap’s duration? A) 1. B) 0.5. C) 0.25. D) zero. Your answer: B was incorrect. The correct answer was D) zero. Since this is an annual pay swap with 1 year left the durations of both the fixed and floating side are both 1 thus they cancel each other out so the overall duration of the swap to either side would be zero. This question tested from Session 13, Reading 40, LOS b I would assume that if you held the receive fixed you would have a duration of slightly less than 1 and if you held the pay fixed you would have a duration of slightly more than -1. Are they asking for the sum of those two values (-1 and 1) and if so, is the overall duration of a swap not always zero?

No duration of a swap is not always zero. You have two streams one fixed one floating. You receive one, pay the other. The duration of the swap is the sum of the durations of these two streams, not the one that you receive.

That makes sense, my heads a bit fried. I don’t understand why the duration of both the fixed side and the floating side are 1 though.

You have 1 year to maturity, rate reset is annual, so actually both the floating and fixed are fixed at that point.

ah, thank you.

Hiya Turkiya Wrote: ------------------------------------------------------- > You have 1 year to maturity, rate reset is annual, > so actually both the floating and fixed are fixed > at that point. Not according to the CFAI text. The duration of the Floating side is 1/2 the time to next payment. So in this case it would be 0.5. For a semiannual swap the duration of floating becomes 0.25 and so on. Don’t rely totally on Shweser it has many differences with the actual text.

yes, Mo you’re right but in this case the floating is essentially a synthetic zero coupon bond (and the fixed IS a zero coupon). and we know that zero coupon bonds have a duration equal to its maturity date.

The whole maturity of the swap is 1 year. You already know what you are going to pay and receive. It is not the case that it will reset one year later and you will have another payment 2 years later.

Hiya Turkiya Wrote: ------------------------------------------------------- > The whole maturity of the swap is 1 year. You > already know what you are going to pay and > receive. It is not the case that it will reset one > year later and you will have another payment 2 > years later. I missed the part where it said " one year left" … you’re right the floating rate has already been set. But if it had One year + 1 day left to maturity you would have to assume the duration of the floating side is 0.5 … agree ?

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mo34, No. I think in that case duration would be 1.

Actually I take my word back, it was correct. I think it should be 0.5

wow, so semi-annual reset it is 0.25, annual reset is 0.5 – I am not sure what I;m missing - I doubt schweser’s answer…i think the correct answer is C ==> 0.75(fixed) - 0.5(floating) = 0.25

trymybest - what you missed was the post above explaining why the answer isn’t c.

mo34 Wrote: ------------------------------------------------------- > Hiya Turkiya Wrote: > -------------------------------------------------- > ----- > > The whole maturity of the swap is 1 year. You > > already know what you are going to pay and > > receive. It is not the case that it will reset > one > > year later and you will have another payment 2 > > years later. > > > I missed the part where it said " one year left" > … you’re right the floating rate has already been > set. But if it had One year + 1 day left to > maturity you would have to assume the duration of > the floating side is 0.5 … agree ? I won’t say so. If you have one year + 1 day to maturity, that means you have 1 day to reset. Assuming the fixed part’s duration is (1 + 1/365). Now that the duration of the float part is 1/365, the duration of the swap should be (1 + 1/365) - 1/365 = 1. - sticky