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CFAI Question - Reading 23 - Example 7 - Hedging with Swap/Swaptions


the question if from the CFAI book, Fixed Income, study session 11, reading 23, example 7, pg 84.

I’m confused about the answer to question 2 which is “Indicate the plan manager’s likely view on future 30-year swap fixed rates given the decision to choose the swap rather than the purchased receiver swaption or the swaption collar.

After some discussions with the rates desk at the commercial bank and a conversation with the bank’s strategy group, the plan manager instructs the QPAM to select the 3.80% receive-fixed interest rate swap. Moreover, the manager chooses a hedging ratio of 75%”

Background:The QPAM has negotiated three interest rate derivatives with the commercial bank. The first is a 30-year, 3.80% receive-fixed swap referencing three-month Libor. The second is a receiver swaption having a strike rate of 3.60%. The plan pays a premium of 145 bps upfront to buy the right to enter a 30-year swap as the fixed-rate receiver. The third is a swaption collar, the combination of buying the 3.60% receiver swaption and writing a 4.25% payer swaption. The premiums on the two swaptions offset, so this is a “zero-cost” collar.

The answer states: The plan manager’s likely view is that the 30-year swap rate will be less than 3.80%. Then the gain on the swap exceeds that of the purchased receiver swaption having a strike rate of 3.60%. If the view is that the swap rate will exceed 3.80%, the swaption collar would be preferred. The purchased receiver swaption will be preferred only if the swap rate is expected to be somewhat above 4.25%, the strike rate on the written payer swaption.

My understanding is buy the swap if rates are expected to be below 3.8%. Buy the receiver swaption when rates are expected to fall below 3.6% and buy the collar if you expect rates to fall but offset the premium of a receiver swaption by writing a payer swaption at a higher swap rate. The answer says “the purchased receive swaption is preferred if the swap rate is expected to be somewhat above 4.25%” This is the part I don’t understand, if rates go up you underhedge the liability, why would I purchase a receiver option when I expect rates to go up? Is it to protect against my uncertainty of rates falling (or my lack of confidence in rates rising) and therefore receiving a lower i/r on my assets whilst the value of my liabilities go up?


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apologies for the long winded question, just wanted to provide context. the question was basically which strategy is optimal (with a swap based hedged)

1. receiver swap

2. receiver swaption

3. zero cost collar

going back to the text, it seems option 2 is optimal as rates rise above a certain point where the other two strategies are providing negative payoffs, beyond what was paid for the premium for the receiver swaption and due to larger payments on the swap based on higher floating rates.

but i think I guess the investor just want to hedge against falling rates and will not both with the collar if they think rates could rise about the SFR that creates a zero cost collar. I guess I found the answer, kind of

I was reading that a couple days ago and yes, it’s difficult to understand.

My take is you have to do 1 of the 3 options, so you take whichever is best - even though the best option would be to do nothing because doing nothing is not an option.

You pick the option based on your interest rate view. If you think its going up or down.

- The collar is free but has limited upside and downside.

- The swaption costs money and has lower downside protection, but if rates go up, you can just keep upside.

- The swap is the general choice the view is rates are going down but then you’re locked in

There is a graph in the text that shows the break even points on each of the 3 choices.