Cuspy Coupon Bonds and Swaptions

So this is from 2 different parts of the curriculum, but I was thinking that this strategy might work:

First, to provide a little color: reading 26 talks about hedging cuspy coupon bonds by taking a short position in 2 & 10 year tresuries + option positions. To make things simple let’s just look at the case if interest rates fall, in this case the hedging securities would be the 2 yr treasury and a long call option. This basically protects the investor from a loss in mkt value of the mortgage security. In the book this addition of the options is close to 7bps.

My question is: What if you were to, instead of buying options to protect the mkt value, you instead purchase a receiver swaption on the interest income that would be lost if rates decline. Would the receiver swaption cost less since it is on the interest and not mkt value loss (basically having a smaller notional)? Would the receiver swaption have effectively the same result, effectively removing the short call option from the mortgage security?

Even though you are getting your principle back on the mortgage security (causing you to have to reinvest at a lower interest rate), the income from the swaption would cause your effective interest income equivalent to the original mortgage security purchased.

I thought about this breifly last night and couldn’t find any holes, maybe the strategy is just outside the scope of the text? Anyone else see any issues with this?

Cuspy coupons is optional material.

You cannot get something for nothing. The swaption would require a notional , which you would set equal to the principal being hedged to be able to effectively hedge. That means it is likely to be as expensive as the two bond hedge for similar coverage

West, Cuspy is not optional - better check your books again

Cuspy coupons aren’t in Schweser material at all…wtf… Neither are FRA’s…

CFAI is KING - if she is in the CFAI texts then she is testable…

Would a swaption cost the same as a regular interest rate option if it is covering the same notional?

I know there is no free lunch, but there are different ways to hedge which may cost more or less depending on the risk you wish to take. (like when deciding whether to hedge with options or futures)

In this case there would be extra risk in using the swaption because if you decide to enter into the swap you are stuck receiving a fixed interest rate. While this is good if rates have declined, it is not if they subsequently rise again. This is why I wonder if the swaption may be cheaper.

however if interest rates rise after entering the swap, I guess the counter argument is that you could enter into an offsetting swap to pay fixed, receive floating. But that might increases transaction costs… I think a larger analysis of expected future interest rates and swaption, option and swap (transaction) costs would be appropriate in this case.

Anyway, none of this is relevant to the test, I was just wondering if this strategy seemed correct. It sounds like it is, but when priced efficiently creates no advantage over the one using only options.

Summary of cuspy coupon MBS:

  • Two-bond hedge doesn’t work (why?)
  • Need to add two options to hedge it properly.

Please feel free to critique me.

the cuspy coupon is on the “cusp” of entering negative convextiry territory, so any small change to rates will put it over the cusp and into negative convexity land…so using an ‘average price change’ ala the two-bond hedge will not suffice, so you also use options to hedge the interest rate risk