 # Hedging MBS

Hi all,

I’m being tripped up by an aspect of this topic that I’m hoping someone can assist me with. I was always working under the understanding that you can’t effectively hedge an MBS with a single treasury (duration hedge) because of the negative convexity of the MBS, which would result in: as rates rise, the hedged MBS port would experience a LOSS, because the single treasury’s (the instrument you’re hedging with) price would decline in value more than the MBS, creating a loss on the overall hedged position. And vice versa (I thought you’d experience a gain for a decrease in rates using the same logic.)

CFA book 4 page 180 seems to indicate my understanding is off…saying when rates rise, you’ll have a profit on the hedged position.

Anyone have a good understanding of this and can explain how I’m missing this?

Thanks.

do not have my books with me.

but is the hedge on pg 180 a single treasury bond hedge - or is it the 2 bond hedge scenario?

It’s not a two bond hedge. It’s referring to a duration hedge, which I take to be a traditional treasury hedge.

Generally MBS’s display negative convexity when int rates FALL and positive convexity when interest rates RISE. So when interest rates rise, your MBS mkt value falls less than your hedge giving you a profit - when int rates rise.

The opposite holds true if int rates fall. In this situation the MBS mkt value will rise less than your hedge, giving you a loss in this situation.

It sounds like you may be confusing where negative convexity appears on the MBS curve.

will need to go back and look at my books

will post when I see what is being talked about …

FinNinja, doesn’t the treasury hedge also display positive convexity? If that’s the case, why does the MBS mrkt value fall less than the hedge when int. rates rise? They both have positive convexity in that scenario.

you are hedging an increase in rates which will result in loss on a bond, so when rates rise the gain from the hedge will be more than the loss on the MBS(positive convexity) so net gain . when rates fall the gain on the MBS will be more than offset by the loss on the hedge(negative convexity) so net loss

Yes they both display positive convexity, but if I remember correctly the MBS has more positive convexity than the Treasury and so falls less when int rates rise. Can someone confirm?

1, If the rate falls, the futures price rises faster than MBS’s price. Since you short the treasury futures, the net value is negative.

2, If the rate rises, the futures price falls faster than MBS’s price. Since you short the treasury futures, the net value is positive.

In the above discussion, I assume the convexity of MBS is negative and the convexity of Treasuries is postive. I don’t know what will be the conclusion if the rate rises and both have postive convexities.

Again, the graph on P167 is misleading…MBS and treasuries may be two tangent curves sometimes, but they can’t be tangent on every point.

ofc the stupid MBS has a different convexity than the treasury you are hedging with. the MBS has an option embeddd in it. the treasury does not.

less derp pls.