1/x: Okay, so we want to understand how to rate the credit risk of a CLO. First, let's start from the basics: What does a CLO mean? As shown in this very helpful diagram courtesy of the SEC, a CLO is a type of ABS backed by secured corporate loans (usually of junk rating): 
2/x: The portfolio of loans is packaged into an entity that issues bonds to investors, mostly with significantly higher ratings than the loans in the underlying portfolio. Now, how do we analyze this thing? Seems very complicated, right?
3/x: Well, not so much. The key to rating a CLO is to come up with a default distribution for the underlying portfolio. Namely, to answer the question "What is the probability that x% of the portfolio defaults?". Once we have that, the rest is a piece of cake.
4/x: Given the default distribution, we can run scenarios through a cash flow model to see which tranches of the CLO get hit from x% default, and knowing the probability of each scenario, we can come up with an Expected Loss (and thus rating) for each CLO bond. Easy peasy!
5/x: Now, how do we get the default distribution? That's the interesting part, but for most CLO ratings, it's done using only a basic concept from high-school stat: The Binomial Distribution.
6/x: To quickly refresh people who (like me) forgot their stats class, the Binomial Distribution tells us the probability of flipping x heads in y flips of a coin (or x defaults in a portfolio of y loans, if we consider defaults random like coin flips).
7/x: It would be nice if we could model loan defaults as coin flips, but in reality they are not entirely independent. If a portfolio is exposed to mostly energy loans, for example, we can clearly see that a default in one loan would mean a higher chance of default in another.
8/x: The beauty of the most common way of modeling CLOs, called the Binomial Expansion Technique (BET), is that it allows us to bypass all this complexity and still use a simple binomial probability for estimating loan defaults!
9/x: The way we do this is through a single number called the Diversity Score (DS), which allows us to look at a portfolio as if it was composed of a smaller number of truly independent bundles of loans. For example, a poorly diversified portfolio of 100 loans might have DS = 20.
10/x: This means that we would be looking at the portfolio as made up of 20 bundles of 5 loans each, with each bundle defaulting as a unit. Then we can use fixed coin-toss probabilities based on the underlying credit rating to get something like the default distributions below:
11/x: Note that having a higher DS means each bundle is a smaller fraction of the portfolio, and since the coin-toss probability is taken as depending only on the loan credit rating (not the DS), this means that higher DS implies a lower probability of losses. Cool!
12/x: Now, how do we calculate this magical number called the Diversity Score? Well, it's more an art than a science, so let's do an example! Here's a very simple (and unrealistic) CLO backed by $3.7B in 10 loans across 4 industries (average loan size of $370M):
13/x: First, we assign a "Unit Score" to each loan, which is the ratio of the loan amount to $370M up to a max of 1. This step is to penalize above average sized loans since there is no way to get a Unit Score larger than 1:
14/x: Then we will just sum up these "Unit Scores" by industry to tell us the "Total Industry Unit Score", which is basically how many loans are in each industry after handicapping the larger loans a bit:
15/x: Now we come to the part of bundling the loans. How do we know how many bundles we have in the Materials industry given that we started with 4 loans and handicapped it down to 3 because 2 of them were rather large? Simple, we use this handy chart!
16/x: The above is the actual chart used by Moody's to do this step, and like I mentioned, this is not really a rigorous science. If you have 20 "Units" in the same industry, you just read off the chart to get 5 bundles in that industry. For our example, it would look like this:
17/x: Finally, we add everything up and round down to the nearest whole number to get 6 bundles for our simple 10 loan CLO. This means we will treat this loan portfolio as 6 independent $616M assets (instead of 10) all defaulting randomly according to the Binomial Distribution.
18/x: Great! Now we understand the basics of how to analyze a CLO. See, it wasn't rocket science😉 Now, for some conclusions. Firstly, I hope this illustrates how some things in finance we think are complicated are actually based on simple algebra and rule-of-thumb, not PhD math.
19/x: Secondly, I hope that seeing how a complex problem can be solved elegantly through some educated approximations can help in other parts of financial analysis. Not everything needs a 50 tab Excel model!
20/x: Thirdly, on the flip side, I hope this instills some healthy skepticism in some analysis people see in the mainstream. The exercise we just did is used to rate 100s of billions of $ of securities, but it is definitely an over-simplification of reality and not bulletproof.
21/x: Finally, I hope you enjoyed the thread and learned some stuff if you made it all the way to the end! I enjoy writing these and will keep doing so as long as people like reading them. Cheers!🙂
