Good Math, Bad Math

I've received an amazing number of requests in the short period of time since my last post to explain "Tranching". I mentioned it off-handedly, but a lot of people have heard about its role in the whole sub-prime mess, and wanted to know just what it means. I don't particularly like writing about economics; it's just not my bag. But enough people are asking that I feel like I need to answer the question. But this is it folks - no more of this nonsense after today! There are plenty of other people writing about this, who know more about it, and who are more interested in it, than I am.

It's also a relatively simple idea. You've got a bundle made up of, say, 100 loans. You want to sell at least part of that bundle as a super-safe rated investment. But because it's formed from risky loans, you know that at least some of them are likely to default.

So what you do is divide it into tiers called tranches. Suppose you've got 5 tiers - levels 1 through 5, where 5 is the top tier, and five is the lowest. Each tier covers a part of the bundle. So you might sell 20% of each tier. When the loans are repaid, the way that it works is that tier 1 is repaid first. When tier 1 is fully repaid, then you start paying tier 2, and so on. You can think of it like an overflowing cascade: repayments go to tier one; when it's full, the overflow goes to tier 2; when that's full, the overflow goes to tier 3, and so on. So if anyone doesn't repay the money, the people holding the lowest tier, T5, lose everything before T4 loses anything, and so on up the stack.

Let's look at an example. Suppose you sell $100 million worth of loans. You divide it into 5 tranches. So you sell $200,000 of the value of the loans as tier 1, $200,000 as tier 2, etc.

1. During the first year of the loans, $100,000 is expected to be repaid, and $100,000 is repaid. Each tier gets $20,000.
2. During the second year, $100,000 is expected to be repaid, but repayment falls short. Only $90,000 is repaid. Tiers one, two, three, and four each get their $20,000; tier 4 takes the loss, and only gets $10,000.
3. During the third year, things get worse - only $50,000 gets repaid. Tier one and two each still get $20,000. Tier three loses half of its expected payment, collecting $10,000. Tiers three and four get nothing.

Tranching is a good idea. Once again, it's a good way of dividing risk. Anyone who invests in risky loans is taking a chance, but tranching let you divide the chances up, so that people who want safety can buy the top tranches, get less of a profit, but know that they're not going to get screwed unless things really go seriously bad; people who are willing to take their chances in the lower tranches know that they're taking a significant risk, but they can potentially make a lot more money.

The key, though, is dividing into tranches properly. If, as in the example above, you had five tranches, each taking up 20% of the pie, then the top tranch would be pretty safe: you'd have to lose 80% of the value of the loans before that tranch lost anything - and in mortgage loans, even shitty ones, losing 80% of the value would be quite extraordinary.

But that's not how banks set things up. Remember that you've got investors practically begging to get their grubby little paws onto these high-return, low-risk bonds. But it's really only the upper tranch that people wanted. The lower tranches - especially the lowest - were hard to get rid of. So, what the banks did is, once again, screw around with things. Some bundles of shit loans were divided into tranches where 80% of the value of the loans were sold as tip-top ultra-safe investments. That means that if a package of crappy high-risk loans loses 20% through loan default and foreclosure that the principal of the ultra-safe investments are going to be lost. That's not what any sane person considers "ultra-safe".

And then, they took the bottom tranches, and re-bundled them. Take the bottom tranch from a hundred different packages of shit loans, bundle it into a new set of bonds, and re-tranch it. Then sell the top 80% of that as the top tranch of a bundle. And so on. In many cases, the investors have no clue how many levels of re-bundling are going on to create their top-tranch low-risk bond. And you've got all sorts of people who thought they were buying conservative investments who are now stuck with their money invested in bundles of low-tranch shit loans.