Tuesday, July 24, 2007

How does a CMO work?

In response to some questions I've received, here is a quick explanation of how a CMO (collateralized mortgage obligation) works. I'll also talk about the difference between a CMO and a CDO.

In many ways, they are quite similar. A CMO takes a portfolio of MBS (mortgage-backed securities) and divies up the principal payments. A CDO takes a portfolio of credit-risky bonds and divies up the credit losses.

A CMO starts life as a portfolio of MBS. I'm going to use agency MBS in this example (REMIC is a term sometimes used), but whole loans are used also. Anyway, say its a portfolio of $100 million in Fannie Mae 30-year 6% MBS. The number of underlying pools could be anywhere from 1 to 1,000. The problem with MBS is that you never know when you are going to get your principal back, and in fact, you are going to get most of it back when interest rates turn against you. This is the primary reason why agency MBS offer such high yields vs. straight agency debentures.

Sometime in the mid-80's, investment banks realized that they could package MBS into a new set of securities with much more principal certainty. The initial CMO's were what's now called sequentials. In this structure, the entire portfolio of MBS would be divided into various tranches. As principal came in from prepayments, it would first go to pay down the A tranche. After the A tranche was completely paid off, the B tranche would start getting principal. Once B was completely paid off, C would start paying down. And so on.

The result was that the A tranche had a very low duration, while the C or D or E tranche was much longer. This worked because some buyers wanted low duration to protect principal, and were willing to pay up for it. Others wanted more reinvestment risk protection, and they were willing to pay up for the longer term bonds. In grand total, every one paid up a little over the MBS portfolios value by itself. CMO creation is therefore an arbitrage for dealers.

But that wasn't good enough. The longer tranches didn't always stay long-term. If there was a prepayment spike, what was advertised as a 10-year average life might become a 2-year average life. This was a problem since people who want long-term bonds usually want to lock in their rate, and the prepayment spike would only be happening if rates were low. So the bonds would be shortening exactly when you didn't want it to shorten.

So the CMO guys created stuff like "PAC" and "TAC" (Planned Amortization Class and Targeted Amortization Class). With the PAC structure, a tranche was created that would pay principal on a defined schedule as long as prepayments stayed within a pre-defined band. Of course, somebody has to get any prepayments that come in. So in order to make the PAC work, some other tranche had to absorb the difference between the "planned" principal due to the PAC holder and the actual principal that came into the deal. The tranches that absorb the differences are called "support." The deal is modeled such that the support bond can absorb all prepayment differentials so long as prepayments aren't faster or slower than the band.

Bear in mind that the total prepayment risk of a portfolio of MBS cannot be reduced. So if someone gets less risk, someone must have more. In fact, in the ultra-simple case of a PAC with a single support bond matched up with it, if the PAC has only half the prepayment risk of the total portfolio, the support bond must have double the risk.

The CMO is still an arbitrage, but under the support bond system, the support buyer must be paid a ton of yield. The PAC buyer on the other hand has to pay up significantly for his prepayment protection.

The PACs tend to break down as well, however, when you go through a prepayment spike. When speeds get very fast, the support bond gets paid off. Once there is no support bond, then the PAC is absorbing all the prepayment variability of the MBS portfolio. So the PAC buyer pays up for reduced prepayment variance, but takes the risk that the support is eaten away and the bond winds up highly variable anyway. In other words, the PAC buyer pays up ahead of time and hopes that he gets what he paid for.

The key to understanding the CMO is understanding the arbitrage, so I'll go through it in a bit more detail. Let's say that Fannie Mae 30-year 6% MBS are at par. Let's say someone will pay $102 for a bond that has a 2-year average life with virtually no risk of it going longer. Now the dealer trying to create the CMO has $2 with which to create a support bond. If he can create the support at $98.25 (or costing the deal $1.75) then there is an arbitrage, and the CMO deal will be created.

Let's say we are using a portfolio of Fannie Mae 6.5% MBS. Let's assume these are trading at $103. So there might be someone who isn't so much worried about prepayment variability, but doesn't want to pay $103 and have the bond prepay away at $100. So they buy a CMO that has a stripped down coupon of, say 5.75% and pay $100 for it. In order to make that work, they need someone to pay them the extra $3 up front, and they have 75bps of extra yield to pay that person, but no principal.

So they create a tranche that in fact pays interest only (IO). Consider what this means. If the bond pays slow, the interest only buyer keeps getting interest. But if the bond pays fast, there won't be any interest to pay to the IO holder. IO's have very low dollar prices, like maybe $20, depending on the reference coupon. And the yield is usually very large, like 10%. But every time principal payments come in, the interest available declines. So in essence, the IO holder benefits from rising rates (rising rates=slow prepays). Hence IO's have negative duration (in the -20 area) and can be used for hedging purposes. Obviously the price/yield situation depends greatly on the coupon of the underlying MBS. If its a steep discount, the IO is worth more and yields less.

The opposite is a principal only, or PO, which has ginormously high duration. There are zillions of other types of CMO tranches, and the means by which support is created varies greatly.

A CMO is fundamentally similar to a CDO, in that the risk of a portfolio of bonds has been redistributed such that some buyers have far less risk and some have far more. The only difference is that the CMO is designed to redistribute prepayment risk, whereas the CDO is designed to redistribute default risk.


F. said...
This comment has been removed by the author.
MS said...

Great article!

I’d like to dive more into the mathematics of CMOs and recreate the cash flows in Excel based on the rules from the prospectus.
Do you have such a model or do you know anybody who has such an Excel?
I’ve built the Excel for Passthroughs (Pools) and I want to understand how to incorporate the tranche payment rules for CMOs.



D Matthew Stewart said...

What a great, straight forward explanation. I just plugged MBS and CMO into google and your page was one of the first ones to pop up. Im glad I came here first--thanks

Anonymous said...

Really good article , very well explained difference between CDO and CMO .
Sachin Dandale

Anonymous said...

interesting article...glad i could find something which goes in detail like this and covers each and every aspect of MBS and CMO...Thank you..!