You fixed us all pretty good

I've written several times about the CDO market. Let me begin by saying that I think that the CDO market is a net positive for the economy. Used properly, CDOs can be an effective means of spreading risk around in the economy.

However, the CDO market has played a central role in creating the sub-prime housing quagmire we are currently muddling through. Indeed, I believe the CDO market has a lot to do with the housing bubble itself. Let me talk a little about how the CDO market contributed to the sub-prime problem, as well as some ideas of how we can retain the good elements of the CDO market without the bad.

CDOs basically take a pool of risky credits and divide the credit risk up among different investors. Investors who want less credit risk buy the portions of the deal which get first priority on principal payments. Those who want more potential income choose riskier tranches. For a primer on CDOs, click here. Suffice to say that the concept of a CDO is based on the time tested idea that a diversified pool of risky assets tends to have a relatively predictable return pattern.

So what went wrong? It isn't that diversification of credit risk doesn't work. In my opinion, its more like something akin to the extrapolation problem in regression.

Let's say you are studying the effect of caffeine intake on focus. You get together 500 people, with 25% each drinking 0, 1, 2, and 3 cups of coffee over a 1 hour period. Then you ask each to take a series of tests to measure focus. For the sake of argument, let's say your results look something like this:

I'm completely making this up for an example, so these results look far too clean, but stay on target. I'm getting to my point. Anyway, the blue dots represent the range of results at each level of coffee intake and the red line is the median observation. We see that although each additional cup of coffee does improve focus, the marginal impact of that 3rd cup is pretty limited. So I'm sure those who do any amount of econometric work look at this chart and see a nice quadratic. And of course, that's no coincidence, since I used a quadratic equation to make the chart:

5 + 6C - C^2 + Err

Where C is the number of cups and Err is a random error term.

So let's say you divine that equation from your data. Even if your equation perfectly explains what happens to the average person who ingests 0-3 cups of coffee, the applications of the equation are still limited. For example, it tells you nothing about what happens if you drink 4 cups of coffee. Or if you take more than 1 hour to drink your coffee. Or the effect if you drink 4 cups every day for a year. Before I turn us back to the bond market, let me point out that this is freshman statistics stuff. CFA Level 1 stuff. Anyone who doesn't understand this should be banned from using Excel's regression function.

Now let's look at the sub-prime mortgage market. Remember that CDOs work by owning higher risk securities, then spreading the idiosyncratic (i.e., single security) risk out among many assets. So CDO managers are happy to own higher credit risk securities, so long as they believe they can effectively spread the risk out. Ergo, a CDO manager trying to create an ABS deal would be looking for higher risk/higher yielding residential mortgage deals. Managers started finding that the higher yielding items were pools issued by underwriters viewed as having weaker credit standards. Maybe these pools had a higher percentage of 100% (or higher) LTV and/or stated income loans. But as far as the CDO manager was concerned, that wasn't a problem, because that risk could be spread out in a very large portfolio of bonds.

How did s/he know how much in high LTV or low doc loans was prudent? Well, CDOs always assume some level of defaults will occur, and usually they can perform quite well at default levels a fair bit higher than the assumed level. But what they cannot withstand is a large number of defaults occurring over a short period of time. More on that in a minute. Anyway, if you want to avoid a large number of defaults all at once, you need credits with a low correlation. Fortunately (!?!) correlation was right up the alley of the quant wizards running CDO portfolios. Armed with reams of historical data, they calculated the delinquency correlation of high LTV, low doc, low FICO,etc. etc. loans with each other. What they found was the delinquency correlation was relatively low. So if you had one high LTV, low doc HELOC in Oregon, and another in Virginia, the odds of both defaulting was calculated to be quite low.

The ratings agencies took the same approach. Default probability and correlation are the keystones to CDO ratings. Not surprisingly, the ratings agency quants and the CDO manager quants used the same data and came to the same conclusions. ABS portfolios had fairly low calculated correlation. As far as ratings go, a low correlation suggested that a portfolio's realized default level would be more likely to fall within a small band, and less likely that a large number of defaults would occur in a single year. A quick note on the ratings agencies: notice they don't need to be biased to agree with the CDO managers on the approach. While I think conflict of interest is a major problem at the ratings agencies, I think the problem with the CDO market is deeper.

OK so we've all built highly complicated Monte Carlo simulations with carefully calculated correlation statistics. Meanwhile some of the most creative people on Wall Street were getting involved with the CDO market.They began to pepper the ratings agencies with new ideas, usually with the goal of decreasing the subordination (i.e., increasing the equity's leverage). The ratings agencies basically said "If you can make it pass our tests, you'll get your rating." So CDO managers began monkeying with things like IC and OC tests, PIK toggles, and other fun things. If the test could trigger at higher default rates and allow the deal to perform adequately, that would allow for less actual subordination while still getting the ratings desired. In turn, this meant that if everything went well, the equity return would be much greater.

Some readers will be happy to hear that in the overwhelming majority of cases, CDO managers retained some or all of the CDO equity. So when they strove to take on more leverage, they believed they were displaying confidence in their own models and managers. Most were actually putting their money where their model was.

Demand for higher-rated CDO tranches was very strong. Banks could buy insurance on AAA-rated CDO tranches from someone like MBIA at a price slightly less than the LIBOR spread offered on the CDO. The result would be something rated AAA with insurance on top of that at a net spread of, say, 5bps. Someone who can borrow through LIBOR, like a strong bank or someone with a CP program, could basically earn that 5bps for free. Hence the rise of the ABCP programs.

So demand for CDOs was hot and the CDO managers and investment banks were making great fees on creating them. The managers and the investment banks worked together to make sure adequate bonds were issued in order to feed the CDO machine. That meant investment banks were bidding aggressively to underwrite various types of bonds popular in CDOs, including sub-prime mortgage deals. Indirectly, this probably lead to the investment banks proving attractive warehouse lines to sub-prime mortgage originators, or even acquiring mortgage lenders outright. And remember, the CDO manager wants higher risk/higher yielding paper, so the most popular loans were going to be the more risky loans.

But for all the quantitative minds contributing to the CDO market, they seemed to forget Statistics 101. You see, the historical statistics on mortgage delinquencies were computed during a time when loans with over 100% LTV or stated income were rare. The rarity of the loans implied that those loans were only approved because there was a legitimate special situation suggesting the risk inherent in the loan was reasonable. The CDO quants extrapolated this data out, and concluded that no doc, high LTV, etc. were all good risks.

But history turned out to be no guide. Things were different this time. Stated income loans went from a rarity to commonplace. According to Bear Stearns, about half of the sub-prime loans made for home purchases in 2006 were either low or no doc loans. Half. That should have screamed out to everyone in the ABS business that gigantic amounts of fraud was being perpetrated. That half of all sub-prime borrowers had a legitimate reason for not fully documenting their income defies common sense.

Obviously if many borrowers who never should have been financed were getting loans, this caused the demand curve for housing to shift outward. Indeed, there is anecdotal evidence that many were using no doc loans for speculation purposes. Which obviously only fueled the already hot real estate market.

Notice that we don't need to make an assumption about HPA or interest rates to see that these borrowers were highly likely to default. If a banks are underwriting loans that are entirely fraudulent, no amount of HPA or falling rates are going to prevent a much higher default rate. Even if most of the fraudulent borrowers intended to pay off the loan, most fraudulent borrowers are going to be toast. That's just logical.

So it should have been obvious that the default rate on these loans was going to be very high. In fact, there is extensive evidence from other credit-types that when issuance becomes very high, default rates subsequently spike. One could imagine that the quality of potential borrowers never actually improves, so when more loans are being made, the marginal borrower is a weak one.

Anyway, so not only should the ratings agencies have seen that default rates on sub-prime MBS would rise, they should also have seen that the correlation would rise as well. For the same reason. If default rates are related to issuance levels, then when issuance is high, correlation is also high. The loans in Oregon and Virginia became more highly correlated because they were both underwritten with weak credit standards.

And the ratings agencies should have been in the perfect position to see this. They have the world's best databases on historical default rates. They should have used knowledge from other asset classes and applied it to the sub-prime MBS market. We've seen time and time again that huge increases in issuance result in greater defaults. From commercial real estate to manufactured housing to high-yield corporate bonds. Perhaps this is where the conflict of interest reared its ugly head. Maybe they willfully ignored this problem.

So how to improve the CDO market?

• Assume dynamic correlation. Don't just run a bland Monte Carlo. We have the computing power vary the default rate, recovery rate and the correlation within the simulation. Do it.
• Use all information available, not just asset-specific. The financial markets are always inventing new structures, but certain basic principles remain. The ratings agencies know this, and should apply it.
• Ratings should be based on subordination only. A structure relying entirely on subordination for its rating is less reliant on the models working than one that relies on coverage tests and excess spread. By this I mean, if there is 10% of the debt structure junior to my tranche, I know the deal can take about 10% in losses before I'm hit. But if there are a slew of IC/OC tests and other complexities, then that becomes muddled. Then it becomes a matter of how fast the losses come in, which means that the speed of losses needs to be correctly modeled. We need more humility in our modeling!
• Deals should pay sequentially. CDO managers hate this idea, because paying down their most senior tranches also means paying down your lest expensive debt. But here again, a simple sequential pay structure makes gaming the models far more difficult.

I think these simple reforms can restore credibility to the CDO market, which will turn CDOs from a great threat to a powerful ally. We don't want to live in a world where only banks can make mortgage loans. Securitization is a good thing. But we need some culpability. Otherwise it will be a long time before we have a viable sub-prime market again. A long time.