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-D_{Q}) and (.25-D_{S}) and you know that D_{S}>D_{Q }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!