I got an email from my friend Todd yesterday, saying that despite my best efforts, he still doesn't understand CDOs. This puzzled me: Todd's a very clever chap, and he even works at an investment bank. CDOs are easy to understand, I replied: "if you understand the concept of overcollateralization, you can understand a CDO."

And that, it turns out, is where the problem lies. It didn't take long for Todd to reply:

Overcollateralization? Huh? I think you've got a topic for tomorrow.

OK, Todd – this one's for you (bet you didn't think your offhand comment was going to turn into a 2,658-word blog entry), and for people like my commenter yesterday, who wrote this:

How exactly did ratings agencies get away with giving CDOs AAA ratings even though they were filled with near junk assets?

The answer is that through the alchemy of overcollateralization, just about any old base metal can be turned into gold.

It's a relatively intuitive concept, actually: it's a bit like what happens when tons of flowers are turned into a single bottle of perfume, or when rotten grapes become fine dessert wine. If you have a lot of something mediocre, you can often transform it into something much more desirable.

But enough of the metaphors: they're likely to confuse more than illuminate. Let's stick to finance, and the concept of collateral. If I trust you, I'll lend money to you unsecured: I give you $10 today, in the hope and expectation that you'll give me my $10 back on Tuesday. But let's say I don't trust you, or I want more certainty that I'll get my money back, or you don't want $10 but rather $10,000. In that case, I might well ask for security, or collateral. Sure, I'll write you a check for $10,000. But just to be on the safe side, I'm going to ask you to leave your diamond engagement ring with me for the weekend. When you pay me back, you can have your ring back.

Lord knows I don't want, or expect, to sell your ring: what I want is for you to pay me my money back, as agreed. But if you don't, at least I'm not out of pocket. If push comes to shove, I can take that ring down to 46th Street and get more than $10,000 for it. And since I'm an honest soul, I'll both bargain for the highest price I can get, and also give you back anything I get over $10,000. After all, the ring was never mine: it was always yours. You just agreed to let me sell it in the event that you were unable to pay me my money back. Once I did sell it, and I did get my money back, all the rest of the proceeds belong to you.

But what happens when you want to borrow $100,000? Your engagement ring ain't worth that much, and in fact there's no way that you're going to be able to come up with the money by next Tuesday, either – it's going to take much longer than that. I'm going to have to start charging interest, and you are going to have to come up with something rather more valuable than a piece of jewelry in order to set my mind at rest that I'm not going to lose my hard-earned savings.

What you give me is a legally-binding promise that although you're engaged, you're not going to get married until you've repaid the loan. This is valuable to me, because until you get married, you will still get a steady stream of alimony payments from your first husband, a publicity-shy hedge fund manager who traded you in for a younger model. You've been getting $15,000 on the first of every month, like clockwork, and so we come to a simple agreement: I'll take that $15,000 for seven months, and then we're even (and you can get married). You get your up-front $100,000, I get my money back over the course of seven months plus $5,000 in interest, and everybody's happy.

In each of these cases, you've borrowed money, which means you have a debt. In the financial markets, debts can be bought and sold – they're called bonds and loans. In each of these cases, I'm the lender. So in the first case I have (I own) a $10 unsecured loan. In the second case, I have a $10,000 loan secured by a diamond ring. And in the third case, I have a $100,000 loan secured by an income stream: your ex-husband's alimony payments. (In any given month you could just pay me the $15,000 directly and hold on to the alimony payment yourself, but that would be a bit silly, so I end up taking the security in full.)

In the case of the secured loans, the size of the security (a diamond ring, seven months of alimony payments) is commensurate with the size of the loan. But it doesn't need to be that way. In theory, I could ask you to post your diamond ring against the $10 you owe me on Tuesday. And in practice, it's not at all uncommon for people who own their houses outright to take out a relatively small home equity line of credit, if they want to do some home improvements, say. That line of credit would then be secured against the whole house: you could have a $1 million security collateralizing a $20,000 loan.

That's an extreme example of overcollateralization. But in fact it happens every day. Let's say your niece, who's just turned 18, wants to borrow $2,000 to buy a new computer. She doesn't want anybody's charity, she wants to buy it herself. But she was brought up well, and she doesn't want to pay the exorbitant interest rates being offered on the credit-card solicitations that are finding their way through her mailbox. What's more, she doesn't have any credit history, so her bank is very wary about offering her an unsecured loan (although it has to be noted that her bank doesn't seem to have the same compunctions about offering her an unsecured credit card).

You want to help your niece out, but not by lending her the money yourself. Instead, you'll guarantee the loan. You and your niece walk into her local bank, and explain what you want to do: your niece will take out a 2-year $2,000 loan, which she will personally repay over the course of 24 equal monthly installments. By doing so, she will get valuable history of credit repayment, as well as the valuable experience of owing money to the bank. You, meanwhile, will guarantee the loan by posting collateral: you'll buy a 2-year certificate of deposit, and if your niece fails to repay her loan for whatever reason, you give the bank the right to reclaim the shortfall out of your CD.

Now you might think that a $2,000 CD would suffice, in this case. After all, the loan amount is only going down, not up, while the value of the CD (which is earning interest) is only going up and not down. But banks, it turns out, don't work like that – they generally lend on a secured basis only up to 95% of the value of the collateral, even if they're holding that collateral themselves in the form of their own CD. In order for your niece to be able to borrow $2,000, you are going to have to buy a CD for $2,106.

That extra $106 is known as overcollateralization.

And just as a lump sum can be overcollateralized, so can an income stream. Not all income streams are sure things: the income stream from an ice-cream shop, for instance, goes up on hot days and down on cold days. And the income stream from subprime borrowers is also uncertain, because some of them have a nasty habit of defaulting.

If you were lending money to the ice-cream shop and wanted to be sure of getting your money back, you would lend only as much as could be repaid from the store's cold-day revenues. You know that not every day will be a cold day, so the shop will make more money than that – another form of overcollateralization.

But if you're lending money to a subprime mortgage borrower, you can't be sure of getting your money back at all, because if the borrower defaults you get nothing. So the trick is to take a few hundred or a few thousand subprime borrowers, and look not at what each borrower pays individually, but rather only at what the whole group of them pay in aggregate. Let's say that if you add up all of their mortgage repayments, they come to $1 million per month. Then anybody counting on getting the full $1 million every month is being foolish: you know for a fact that in a group of that size there will be some delinquencies. On the other hand, you also know that the vast majority of subprime borrowers do, in fact, pay their mortgages every month. So if you only count on receiving $500,000 a month, you're safe: so safe, indeed, that ratings agencies are happy to come along and slap a triple-A credit rating on your debt. It's all because of overcollateralization: your low expectations of getting just half the contractually-mandated  cashflow mean that you can have very high expectations that all of your repayments will arrive in full and on time.

So what happens to the remainder of the money, which might be as much as another $500,000? That gets pledged too – but only on the understanding that you have first dibs on any mortgage payments from any borrower in the group. Only after you've received all your money in full does the next person in line get anything. The next person might opt to receive the next $300,000 that arrives after your $500,000. The probability that the $1 million of scheduled cashflow will be reduced through default and delinquency to less than $800,000 is extremely small, so the ratings agencies will assign a double-A credit rating to that tranche, as it's known. But still, there's no doubt that you, standing first in line, have a better credit, with more overcollateralization, than the next person, standing second in line. And so to make up for that, he'll receive a higher rate of interest on his $300,000 than you will on your $500,000.

And so on down the line: the third guy in line will have a single-A bond, while the guy behind him (let's call him Fred) will only have a triple-B bond, and the guy behind him has what's known as "equity" – it's not equity as in stocks-and-shares, but the cashflows at that level are certainly very volatile and unpredictable.

The key is that you can take a group of weak credits, like subprime mortgage borrowers, and through the magic of overcollateralization, you can still manage to construct a triple-A security from them. You can't do that with only one loan, of course: you need the law of large numbers to help you out. But if you have a lot of weak credits, you can always bundle them up together and then sell off only a fraction of the aggregate cashflows. The result will be a stronger credit.

Which brings us to CDOs. A weak credit needn't be a subprime mortgage; it can just as easily be a bond with a triple-B credit rating. Any one bond with a triple-B credit rating has a meaningful (if not enormous) default probability. But if it doesn't default, it has a perfectly predictable cashflow: it pays its coupon payment every six months.

So let's say you want to create a security with a triple-A credit rating. One way of doing that would be to buy up a few hundred different triple-B-rated bonds, each of which has its own cashflow. You know that one or two might default, but you can be sure that they won't all default at once: it's the law of large numbers again, which is also known as diversification. If it's BBB-rated bonds, rather than subprime morgtage borrowers, which are paying out $1 million a month, it doesn't make any difference to the logic of overcollateralization. You don't know for sure that all of them will pay, but you can be quite sure that most of them will pay. And so, again, if all you want is the first $500,000 of that $1 million, then that's a sure enough thing to get you your coveted AAA rating.

Once again, there's nothing wrong with this. CDOs have been around a long time, and they've generally behaved very well. You take a few financial-industry bonds here, a few manufacturers there, some technology issuers from California, maybe some emerging-market sovereigns like Mexico or Russia. You mix them all up in a big cauldron, call it a CDO, and sell off AAA-rated tranches to investors who can be quite sure that there's no chance all of those different borrowers are going to default simultaneously.

But what happened over the past few years was that demand for those AAA-rated CDO tranches went through the roof, and it became harder and harder to find a nice diverse universe of BBB-rated bonds to throw into the cauldron. As a result, the ingredients getting thrown into the cauldron started getting less and less diverse, until it reached the point that all, or nearly all, of them were, in some way or another, ultimately reliant on subprime mortgage payments.

Now remember Fred? He was fourth or fifth in line for subprime mortgage payments, holding a BBB-rated security. And although a triple-B rating is indeed "investment grade", it turns out that Fred's investment wasn't a very good one. The default rate on subprime bonds spiked much more than anybody anticipated, and Fred, standing as he was at the back of the queue, ended up with no money at all.

Now that's bad for Fred. Or, rather, it would be bad for Fred if he had held on to his bond. But he didn't: he simply turned around and sold it to a CDO which was desperate for BBB-rated paper. As did Frank, and Fergus, and Fraser, and even Ferdinand, whom you might think would have been a bit more bullish. All of them bought BBB-rated subprime debt, and all of them sold it to a CDO, which reckoned that since it was buying lots of different bonds from all over the country, it was thereby diversified.

Oops.

Of course, it wasn't just Fred's bond which defaulted. Frank's did too, and Fergus's, and Fraser's, and, yes, Ferdianand's as well: subprime default rates went up nationwide, at exactly the same time. Suddenly, all of these bonds, which were meant to be paying a million dollars a month, were paying, in aggregate, zero. The CDO cauldron had run dry. And the investors who bought the CDO's triple-A-rated paper found that they, too, were left with nothing and had lost all their money. All the overcollateralization in the world does you no good if the value of your collateral goes to zero.

So when investors in CDOs take losses, that's essentially what happened. It's as though they lent money to an ice-cream shop based on its cold-day sales, but then the shop burned down, and sales went to zero. Or it's as though I lent $10 against a diamond ring, only to find out that it came from a Cracker Jack box. Overcollateralization is always a good thing, but it isn't everything. Which is something that many CDO investors are now finding out the hard way.