What is mortgage convexity and why does it matter?

The US is one of the few countries on earth with long-term fixed-rate mortgages that can be refinanced at any time with no penalty. That makes holding mortgages complex. When a mortgage is refinanced the holder of the mortgage gives up a long-term bond and suddenly has cash. The holder has essentially written a perpetual call on the bond.  As interest rates fall the mortgage gets called away.  That means as interest rates fall the long-term bond gets shorter and shorter in maturity until it turns into cash.

The 30-year fixed-rate mortgage market is almost 20TN in size. Depending on where interest rates were over the prior years the fixed rate of each existing mortgage can be different. For obvious reasons, there are very few outstanding high coupon mortgages as most of those have been refinanced. There are a lot of mortgages with coupons around current coupons and at lower coupons. Why does this matter? It matters at a macro level which I will deal with first and then at a technical level which will follow.

Mortgages are by and large safe government-backed fixed income assets with a slightly higher coupon than treasuries to compensate investors for the call they are short to the homeowner. When interest rates fall as I mentioned the expectation is that the mortgage will be refinanced and the expected maturity will be much shorter than before the change. Investors who once had an asset that was comparable to a 10-year treasury (remember 30-year mortgages are different from 30-year bonds because the principal is paid off throughout its life) now they have a two-year bond. That is not what they want. So that leads to holders of mortgages looking to buy lower coupon mortgages to extend their duration. That’s the macro. The technical is about those who hold mortgages and hedge their interest rate risk. For instance, a bank that holds the mortgage as an asset and a deposit as a liability has a long-term asset hedged with an overnight asset. They may not want that amount of interest rate risk. So they short a treasury to hedge the mortgage. When interest rates fall the mortgage becomes less sensitive to changes in interest rates while the treasury hedge short remains sensitive. The hedger needs fewer hedges and buys treasuries to adjust. Then let’s say interest rates rise before the mortgage is refinanced. All of a sudden the mortgage is sensitive to Interest rates again and the hedger needs to sell more hedges. Sell treasuries. So just like any other short option position the mortgage hedger buys high and sells low. They are compensated for this loss-making activity by the excess coupon the mortgage carry’s over treasuries.

Let’s put some size on this. 20TN of mortgages if all are hedged can generate over 1TN of buying when interest rates fall 25bp. See the issue. That’s a whole year of QE in demand. If interest rates then rise by 25 bp 1TN of bond need to be sold. That’s a year of QT. So does this actually happen? No! Though at the macro level it should happen. Most holders of mortgages just let the option play out and don’t dynamically hedge the mortgage. Roughly 10% of mortgages are dynamically hedged. Some mortgage holders buy bond options instead of dynamically hedging their portfolios. But the seller of the option is a dealer who dynamically hedges so that’s just a hot potato. Also, other players have mortgage risks that they hedge. A significant player is the mortgage servicer.  Every mortgage needs to be serviced.

Essentially someone needs to bill and collect from the homeowner and foreclose if they can’t pay and deal with the house. For this service, the mortgage servicer gets a little bit of every interest payment. Mortgage servicers can be independent entities or part of a mortgage department of a bank. Regardless they have an extremely volatile asset to deal with. They only get servicing payments when the mortgage exists. When it is refinanced those payments cease. Because they don’t contain any principal payments they are extremely convex.

That creates lots of dynamic hedging flows. Anyway. The point is that when interest rates move anyone with mortgage risk who hedges needs to buy on the way up and sell on the way down. This flow is large and can extend rallies and dips. Over the last few days, I have mentioned these flows because the sheer size of even 10% of all mortgages hedging dynamically can be a 100BN flow. I will mention swap spreads. Which are footprints left by hedger’s flows but will not go into that because I imagine your head might explode. Another thread perhaps