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A CDO (collateralized debt obligation) is nothing more than a redistribution of credit risk, much in the same way a CMO is a redistribution of prepayment risk. This post will quickly go through the basic math of a CDO. For illustration purposes, I'm going to use a real ABS CDO featuring mostly RMBS as the base for the percentages of each tranche. I'm going to make some simplifications to the structure just to keep the example easy to understand. Regardless, this should be a pretty good basic lesson on how a CDO works and where the risks are. I'm going to use an ABS deal as my example, but any credit-risky security could be used. Also, I'm going to use fixed interest rates just for simplicity, but almost all CDOs are floating rate. Just that LIBOR is 5.30% and stays static over time.

We start with a \$100 portfolio of ABS bonds which yield 7%. This is called the collateral portfolio. The collateral portfolio has a average rating of BBB. In order to fund the purchase of this portfolio, 5 different securities are sold. The amount, credit rating and interest rate of the first four are as follows.

\$75 Class A, rated AAA, yields 5.51%
\$10 Class B, rated AA, yields 5.80%
\$5 Class C, rated A, yields 7.20%
\$5 Class D, rated BBB, yields 9.00%

These are called the debt tranches. Some of you may notice that those yields for Class C and D are far in excess of what typical bonds with similar ratings yield.

The fifth security sold is the equity tranche. That is another \$5. We'll get to the equity in a minute.

Why are the tranches rated differently? Because interest and principal are paid sequentially, starting with Class A and ending with the equity tranche. Only once Class A has been paid what its due does Class B get paid, and so on.

So our portfolio of bonds pays \$7 per year in interest. The CDO then owes interest on the debt it sold:

Class A: \$4.13
Class B: \$0.58
Class C: \$0.36
Class D: \$0.45

That makes a total of \$5.52. So there is \$1.48 left over. In a deal like this, the manager probably charges around 0.20%, and there is another 0.05% for admin fees. So net of fees there is \$1.23. That passes through to the equity. Notice the return on the equity is a quite attractive 24.6%. Now many times a portion of the excess spread is held aside to cover losses, but I'll ignore that for now.

So that's how it works if you have zero defaults, but of course, that's not going to happen. Let's say that 2% of the collateral portfolio defaults, and the recovery is 50%. So now there is \$99 in the collateral portfolio with a 7% yield. Instead of having \$7 in interest, we only have \$6.93. So far, everything is fine, because we had \$1.23 which we were paying the equity. Now we only have \$1.16, but that's still over 20% IRR for the equity tranche.

Now let's say that the deal suffers 2% defaults per year for 10-years at which time principal on the debt tranches becomes due. So that's a total of 10% losses (2% x 50% recovery x 10 years). You've been able to cover interest costs all along, because even after \$10 in principal losses, you are still have \$6.30 interest earned vs. \$5.52 interest costs plus \$0.25 in fees. You're still \$0.53 in the black.

But what about paying off the principal on the debt tranches? You only have \$90 in principal left in your portfolio to pay off \$95 in debt. If that were the end of the story, Class A would get paid its \$75, then Class B its \$10, then Class C its \$5, and Class D would default, and get no principal at all.

Now you might say, net-of-recovery losses of 1% doesn't seem too extreme. How the hell would the Class D tranche get an investment grade rating? There are a couple of things that complicate the math, and make the Class D tranche a little safer. First, there are usually two coverage tests which CDO's calculate: interest coverage (IC) and overcollateralization (OC). The IC test has the total interest earned in the numerator, and the total interest cost of a given tranche and all tranches senior as the denominator plus fees. So in our case, the IC on Class B at the onset of the deal would be \$7/(\$0.58+\$4.13+\$0.25)=141%. Some trigger is set for how high that number needs to be for each tranche and if the actual number is lower than the trigger, some remedy is required. For example, it might be that money that would have gone to the equity is used to pay down some of the debt tranches. Since the size of the collateral portfolio is the same but the size of the debt is lower, the IC calculation improves.

The OC test is similar, except the numerator is the principal value of the portfolio and the denominator is the outstanding amount of a given tranche and all bonds senior. So for Class B at the outset, the OC test would be \$100/(\$75+\$10)=118%. Here again, some trigger level is established when the deal is sold, and if the OC falls below that trigger, some remedy is required.

The triggers are usually higher for more senior tranches. So the top tranches aren't just protected by the extra cash flow of the deal, but also by the fact that if anything starts to go wrong, cash flow will be diverted from other tranches. The trigger levels also tend to be higher in deals with riskier collateral. A deal with all BB-rated bank loans will have higher IC and OC tests compared with an investment grade resi ABS deal.

Now you can see how freakin' complicated the cash flow can get. It becomes extremely hard to determine what default level would sink a given tranche. For example, a tranche may be able to survive 5% annual defaults for all 10-years, but might not be able to survive 10% defaults in year 2. A relatively high level of defaults spread out over time is more easily cured through the excess interest the deal collects. But a spike in defaults would usually result in more senior tranches being paid down, and there might not be enough left over to pay principal on more junior classes.

Another complication is the recovery rate. It is often true that the weaker credits in the deal also recovery at a lower rate. For example, you might have a deal that is 50% prime RMBS and 50% B/C Home Equity. That might have an average recovery rate of 50%, because the prime RMBS recovers at 75% and the B/C Home Equity recovers at 25%. But since the B/C stuff is more likely to default, who cares what the "average" recovery is? The only thing that matters is the recovery on the bonds that actually default.

The interest spread is probably uneven as well. For example, if the whole deal yields 7%, it might be that the 50% prime RMBS is at 6.5% and the B/C is at 7.5%. So if a B/C piece defaults, there is a larger decline in overall interest earned than what the straight average yield would imply.

So CDOs can get pretty complicated, and its impossible to say just how many defaults it will take to sink a given tranche. The concern should be with buyers of BBB and A-rated tranches of sub-prime residential deals. If there is a large default spike in 2007-2008, and recovery rates come in much lower than expected, these tranches will likely perform poorly. If you are an equity investor... well... good luck.