# LOS 19.d: Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio's objectives

Summary:

The PM’s BPV of Assets < BPV of Liabilities and she much hedge (protect against falling rates). She has three choices:

• 2.5% fixed-rate swap (No premium)
• 3.3% payer swaption (75 bp premium)

The reading says if that a swaption collar is the best choice if she expects rates to be above 2.5% but below 3.3%. WHY?

The collar (buy the 2.3% receiver swaption and sell the 3.3% payer swaption) has no intrinsic value, which is the best choice.

• The right to receive 2.3% when rates are above 2.5% has no value.
• The payer swaption buyer has no rational reason to exercise his right with new SFRs below 3.3%.

I agree with the above that the collar has no value. So if the rates drop from 3.1% to 2.8%, the collar has no value but doesn’t that mean she effectively has no hedge and her liabilities will still go up more than her assets? How does the swaption collar help in this case?

The example’s initial swap rate is 2.5%, thus if it first moves to 3.1% then the duration gap will decrease/become negative - collar is the best solution (no cost). At the point when rate is 3.1% the PM may enter a 3.1% fixed rate receiver swap with expectation of future rate dropping to 2.8%. If the PM chooses no hedge at this point and the rate decreases to 2.8% then the duration gap will increase back up but it still will be smaller than the initial gap (when rate was 2.5%).

Initially “she much hedge (protect against falling rates)” but “she expects rates to be above 2.5% but below 3.3%” => free/cheap protection is needed with this expectation because duration gap will probably decrease => collar is the best choice with given expectation because it is free but still provides protection in case of possible rate decrease below 2.3%(-premium).

I hope my explanation makes any sense to you.

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Thanks. Yes, I think that makes sense. I guess I was confused as to what the initial rate was.