2014 AM Session 9B pg 55 (Swap duration)

The question states that they think rates are going to rise and they want to hedge it w/ a swap. It then gives 4 swaps and says choose the one that minimizes notional principal. Since we think rates are rising we want to choose the swap w/ the lowest duration (highest negative duration).

The 4 options are 3 year quarterly, 3 year semiannually, 5 year quarterly, and 5 year semiannually.

We can obviously remove the two 3 year swaps, but without being given duration this really confused me. Quarterly payments are going to decrease duration on the fixed rate arm relative to semiannual payments which will increase our swap duration, but the floating rate arms duration would be .125 for quarterly and .25 for semiannually. So you have the scenario where you want to choose the minimum of:

(.125-DQ) and (.25-DS) and you know that DS>DQ so this presents a problem. Then I looked at the answer, and CFA just made a simplifying assumption that the fixed-rate arms duration is 75% of the contract length (which obviously isn’t true) and given this my answer is wrong. So my question is moving forward do we just assume fixed rate arm of the swaps duration is 75% of the length? Schweser doesn’t mention this. CFA mentions that they’ll be assuming that moving forward in examples, but doesn’t say that I’ll need to make this assumption on exam day.

Thanks for any clarification here!

3 year quarterly swap = Duration = 0.75 * 3 - 0.25/2 = 2.25 - .125 = 2.125

For 3 year semi annual => 3 * 0.75 - 0.5 * 2 = 2.00

and so on

Those are the swap durations.

(CFA assumes 0.75 times fixed = fixed side and since floating side resets each term period - it is 1/2 of the floating side duration.)

and for minimum notional principal = you would want to select the highest duration swap - because a) it will reduce your notional principal.

and b) because you would have to pay that out a fewer number of times (notionally).

Kaplan didn’t mention 0.75 but anything in the CFA book is a fair game. So I would just remember this. However, in the Kaplan video to this exam. Instructor mentioned this is a 3 minutes question so doing calculation will take more than 3 minutes.

So, he suggested to use reasoning like "swap with the highest absolute duration will require the smallest notional principal which is use Canis. Its 5 year term have higher fixed side duration than the 3 year swap. And its shorter quarterly PMT will product the smallest floating rate side. "

0.75 * (maturity) for fixed leg and 0.5 * (frequency) for floating leg.

If the target is to decrease duration you will chose - pay fixed + receiving floating side and from those you should chose the lowest, the maximum of negative swap duration.

That’s helpful, thanks.