#### Super Senioritis

I’ve been perusing the finance blogs lately and I’ve noticed a recent obsession with Synthetic CDOs, specifically the super senior tranches of these transactions. And so I felt it was necessary for me to chime in on the debate, by applying my usual toast-dry analysis to Synthetic CDOs for the second time. This is a huge topic that requires consideration of how Synthetic CDOs function, how they’re rated, and how tranches distribute risk among investors. As a result, I’ve decided to break the article into two parts. This first part deals with the basics of rating the assets contained in CDOs. The next will examine the application of ratings to tranches of CDOs, how that translates into the world of synthetic CDOs, and ultimately, culminate in a discussion of what are known as “super senior tranches.”

#### Required Reading

You are likely to struggle greatly with this article unless you have some familiarity with Synthetic CDOs. And because I am an unabashed self-promoter, I highly recommend you read my introductory article on Synthetic CDOs and my article on Tranches. If you’re going to read only one, then read the one on tranches.

#### Tranches And Structured Products

Payment waterfalls allow the risks of an investment to be allocated among different groups of investors, or *tranches*. For example, in the case of Mortgage Backed Securities, a fixed amount of prepayment risk can be allocated to one tranche by tailoring the rules in the payment waterfall to pass all prepayments of principal to that tranche. But there are risks beyond prepayment risk. One obvious example is *default risk*. In the MBS world, this is the risk that because of defaults in the underlying mortgages the cash flows from the mortgages backing the notes will be inadequate to make payments on those notes. Obviously, default risk will be a primary concern of any investor. The risk that you will not get paid is arguably paramount to all others. So, payment waterfalls have been developed to address this risk and tailor the distribution of default risk in a way that allows each investor to assume a desired default risk level. But before we can understand how investors distinguish between these different levels of default risk, we must understand how rating systems describe these different levels.

#### Rating Systems And Rating Agencies

You have undoubtedly heard terms such as “AAA rated” and “AA rated” thrown somewhere near names like S&P and Moody’s. It’s not necessary to become familiar with the peculiarities of each rating agency’s system to appreciate the general idea: the ranking of default risk. That is, the market wants a short-hand system that both describes the probability of default for a particular financial product and can be compared across a disparate class of financial products. So, *rating agencies* developed models and systems of ratings (using confusingly similar labels like “AAA,” “Baa,” etc.) that purport to do just that.

#### How CDO Ratings Work

#### Part 1: Past Performance And Correlation

The models that rating agencies use to produce their ratings are *backward looking*. That is, the first step in the process is to accumulate data about how financial products have behaved in the past. Rating agencies, and investors, will look to the past and produce charts like this:

They will note that in the past, of all bonds that Moody’s deemed Aaa, less than 1% of such bonds defaulted within 10 years of issuance. People then assume, quite reasonably, that this data provides probabilities of default across time for the various ratings. That is, they assume that if we wish to know the probability that a B rated bond will default in year three, we simply look to the above chart and discover that it is .1977 or 19.77%. Examination of this assumption is beyond the scope of this article. But for a great article on that topic (containing the above table and more!) go here.

A CDO is in essence a portfolio of bonds. So in order to model the cash flows of the portfolio, rating agencies turn to charts like the one above and examine the past performance of bonds similar to those in the portfolio. They also look at the *correlation *of default between the bonds in the CDO portfolio. Correlation, in this context, is a very precise term. And it’s impossible to do justice to the concept in a few sentences. That said, in layman’s terms, when considering the correlation of default between two bonds, rating agencies are looking for a connection between the bonds defaulting. That is, if bond 1 defaults, how does that change our expectation of the probability that bond 2 will default? Exactly how this is done is also well beyond the scope of this article. For those of you who are interested, you can read all about this and more here.

#### Part 2: Scenario Analysis

So after we have all of our data, we can begin to construct a chart of how likely a given level of loss is. This is done through scenario analysis. That is, the models are run hundreds of thousands of times (and possibly more) using different inputs. In each of these simulations, some bonds might “default.” That is, the model predicts that given a particular set of inputs, certain bonds will default. After each of these simulations, an amount of *loss *will be calculated, which is based on the estimated recovery values for the bonds in the pool that “defaulted” during that particular simulation. We can then ask, out of all of the simulations, how many times did the loss go above X? So if we ran our simulation 500,000 times, and if the loss was greater than $1 million in only 5,000 of these simulations, then we could say that the probability of the loss being greater than $1 million is .01, or 1%.

I had a feeling you were out there, but I didn’t want to keep requesting that you do this work. It was beginning to seem presumptuous. However, one question on the Alphaville Graph:

How can it not be apparent that it’s a ladder of risk, with the riskiest at the bottom? I’m still not so sure what’s complicated about reading that graph. It might be complicated to create the levels of risk, tranches, but the graph doesn’t seem that unclear.

Take care, and thanks, as always, Don

3 December 2008at10pmIt’s not complicated. You are indeed correct. It should be evident that tranches form a ladder of risk. Subordinated AAA notes (those with something above them) though very safe investments, should be riskier than AAA notes that are senior to all other tranches.

3 December 2008at10pmSince you discuss payment waterfalls and super senior, you may be able to answer this question: It appears that policymakers are trying to delay mortgage defaults, so that the process of default gets drawn out over a longer period of time (e.g. foreclosure moratoria). Doesn’t this process, increase the likelihood that the supersenior tranches will face losses. Or more specifically, doesn’t this allow mortgage prepayments to be directed to lower level tranches for a longer period of time — before the defaults are realized — and thus reduce the recovery available to the super senior?

4 December 2008at2pm[…] only one payment at maturity. Further, assume that we have conducted several hundred thousand simulations for our CDO and constructed the chart […]

4 December 2008at11pm[…] the previous articles (part 1 and part 2), we discussed both the modeling and rating of CDOs and their tranches. In this […]

8 December 2008at9pm[…] that cash is generated, it gets funneled to and split up among the investors. For more on CDOs, go here and […]

31 March 2009at10amI just wanted to point out that the above Moody’s default chart contains default probabilities, not marginal default probabilities, so that the probability that a B rated bond will default in year three is actually 6.92% (19.77%-12.85%), not 19.77%.

3 April 2009at4pmJohn,

I must disagree with you here. What YOU are describing are marginal default probabilities, i.e., the increase in the probability of default from year to year. This table gives the actual distribution of defaults in the past, which we then interpret as descriptive of the probabilities of default.

3 April 2009at4pm[…] model to price distressed CDOs since early 2008. And not just any part of those CDOs, the infamous super senior tranches. He’s got an update of his model in the July issue of Risk: In 2008 and 2009, the calibration […]

25 June 2010at4am