CDO’s (collateralized debt obligations), see this for my introduction to these, depend on underpriced low grade debt. If I can get a 20% discount on debt that has a 10% chance of defaulting, then I should just buy this all day. All I need is enough risky debt (and some confidence in these percentages, but that’s a story for another day). But as CDOs became more and more popular low grade debt was getting used up. Even worse, as demand for it grew its price rose. CDOs were changing the entire ecosystem of low grade debt. There wasn’t enough of it and it was too pricey. There was no profit left. What to do?

One compelling answer was to simply issue more of it. Brokers could persuade people to take on deceptively structured mortgages, that could only get paid back if house prices rose forever. Lousy business plans were funded by people whose sole investment in the debt was they commission they got for issuing it. Dogs were being offered credit cards. These guys made the Glengarry Glenross salesmen seem like saints.

But there’s only so much new low grade debt that this can create and only so low you can go. Enough of it was issued to ruin the economic lives of people who thought they were just buying a house, but not enough to feed the maw.

Alchemy

What there was plenty of was collateralized debt. Some was graded AAA, some graded B. Why not buy these crappy debts and create CDOs? So, we start with $100 of debt that someone was misled into borrowing. We structure that to create $60 worth of grade B debt. Get enough of that and you can create another CDO, with $50 worth of single B tranches, and so on. $100 of crappy debt turns into $300 worth of crappy debt. (I’m making up all these numbers, but the principle is correct.) These were the synthetic CDOs. George Soros (that vicious communist) says pretty much that in April 23rd’s Financial Times.

So why was so much money lost? Why were trillions of dollars needed to prevent an economic meltdown?  It wasn’t because people took out trillions of dollars of mortgages they couldn’t afford. It happened because people got paid, and very well paid, for turning $100 worth of debt into $300 of debt. So they did it again, and again. What did they have to lose?

Given your circumstances, they can produce a curve showing the probability of you dying at any given year from then on.

Here is an hypothetical curve of life expectancy at birth. Babies have a higher risk of dying than older children, then it pretty much rises (though far more complexly than the curve below suggests).

Given your circumstances

Your circumstances, the things that shape your probable mortality curve, are complex. Your sex, your ethnic mixture, your behavior, your age, (not always a negative, in Mediaeval Venice insurance for a 20 year old cost the same as that for a 40 year old, the 40 year old having proved himself immune to the prevailing diseases). These, and  many other dimensions, contribute to the shape of your mortality curve. Think of it as eHarmony calculating your annualized compatibility with death.

If the insurance companies can calculate these curves accurately enough, can sell enough insurance to even out the risks, and have enough capital behind them that they can survive a temporary run of bad luck, then they can charge a little bit above the real risk, and make a tidy, reliable profit. Paying over the odds can be well worth it for the individual, given the effect of catastrophe, and this can be a perfectly reasonable business. That’s what most of AIG did, and did well.

Insurance companies also have a get out of jail free card: the Act of God. Mortality curves can only take so much into account. If the earth’s crust splits, if a meteor strikes and makes half the planet uninhabitable, if the zombie epidemic finally erupts, or if the river floods (different insurance contracts are more or less inclusive in what they count as Acts of God), then all bets are off.

What Insurance Is

Insurance is a way of sharing risk. If we each have a one in a thousand chance of our house burning down, and we all pay two thousandths of the value of our house, then all things being equal, the people whose houses burn down will be paid back, and there’ll be some money left over as recompense to the people who set up the deal.

But insurance can’t reduce risk, it can only share it. And probabilities can only be calculated based on an enormous number of assumptions. The reliability of these assumptions is up for grabs. In the financial world the invisibility of these assumptions can have dire consequences. I shall take this up again in an overdue discussion of Credit Default Swaps.

Bad Debt: 15% Off

Many relatively high risk borrowers need, or would like, credit; many investors would take a small profit provided there’s very little risk; some want to play the odds in the hope of a big payoff.

There isn’t enough high quality debt out there to supply the risk averse, and there’s lots of the dodgy stuff. This is the opportunity. I can buy lots of crappy debt cheap. A percentage of it will fail: some companies and people will not pay off their loans, their mortgages, their credit card debt. But there’s so much of it, that I can get it cheap. I can buy the collateral for much less than what it will actually (probably) pay. Now I can structure a deal.

The Waterfall Model

This is the waterfall:  one group (the equity investors) buy the collateral, and sell a tranche (a bunch of bonds) that will get paid first as that collateral pays off, making its purchasers a small profit. (Whoever is doing all the work of setting up this deal, usually a bank, will take a cut of that.) Then they sell a second tranche that will get paid from the money left after the first lot are paid. These purchasers get a slightly higher profit, and the structurer takes a cut of that. And so on. Maybe. The number, size and profitability of the tranches is where cleverness comes into it. It’s surprising how much high grade debt you can make out of low grade debt, about 80% or more, depending on your assumptions about the percentage of that debt is going to default.

If there’s any money left after all the tranches are paid the equity investors get it all. If the deal goes well and only about the expected percentage of debt used as collateral defaults, then these guys make a tidy profit. Everybody wins.

More dodgy credit can be issued, people who need to buy safe bonds get to do so, and people with lots of money get to take a tilt at a high score.

So far the only objectionable thing would be if the quality of the collateral was misrepresented, or if the bankers’ cut was unreasonably large. Below the diagram (not to scale, but accurately representing my graphic skills) is my explanation of what would be really nasty, possibly illegal, and what the SEC is saying happened. (I’m not a lawyer. Please do not sue me.)

The Waterfall of Collateralized Debt.

Suppose I know that the collateral I’m buying is much crappier than I let on. (It’s like the right hand waterfall, while I’m pretending it’s like the left side.) Normally that would be a lousy idea. The amount I get paid selling the various tranches doesn’t cover my equity investment. But suppose I also take out insurance on these thranches failing?

Yes, you can do that. That’s what a CDS (Credit Default Swap) is: insurance against a default. Very clever, and surprisingly legal.

(A future post will try to explain CDSs in a little more detail.)

Since it was decided that it was legal to insure debt, somebody gets to sell that insurance. AIG lost the farm because it sold tons of it, believing it was insuring left hand waterfalls. People bought a tranche and then took out insurance so that if it defaulted they would get paid anyway. AIG sold tons of insurance against things that were much more likely to happen than they (probably, perhaps) realized. It’s a bit like taking someone’s money and pretending to buy their lottery ticket every week. That works really well unless they win the lottery.

I can even take out insurance on debt that I don’t own (no, really), betting on your failure. That’s ungentlemanly at best. But it gets worse.

Suppose I was to structure a deliberately crappy, right hand, deal, sell it as a left hand deal, and take out insurance on it failing? I get the insurance on all the tranches I sell, the people I sell them to get completely screwed, and I get rich. What could possibly be wrong with that?

Well, it might be illegal. Being the bank that takes its cut, knowing the full story, might also be illegal. In both cases it sure as hell should be.

What actually happens with these “structured investments”, legal and illegal alike, is, of course, much more complicated. But that’s the big picture.

The Goldman Sachs case will be worth following.

If you ask them to do a multi-step problem it is an enormous struggle to get them to write down intermediate results. This, of course, makes it much, much harder to get to the final result. Trying to add two numbers together while remembering a third is so much harder than just adding two numbers. Why is this hard to learn?

I suspect it is evolutionary. Externalized memory is evolutionarily recent. As a survival skill it has been of no value until relatively recently (even Socrates despised writing as something that weakened the reason, rather like the current argument that Google rots the brain). Human beings like to take in the whole picture at once.

Given that this is a more or less universal problem in teaching math I think it’s reasonable to assume that this is a reluctance that is genuinely difficult to overcome. There have been plenty of great math teachers (not enough to distribute adequately, of course, but a large number nonetheless). If there was some teachable trick – teachable to teachers, that is – that could convince students, at an early stage, of the value of externalizing intermediate results, then someone would have figured it out. (This is an obvious area for empirical research.)

Instead we have generation after generation of math teachers, themselves all too often under-trained, and unaware of the existence or implications of short term memory limitations trying to browbeat children into following a rule none of them really understand.

Those who go on to advanced mathematics are generally either docile enough to have done what they were told, or had capacious enough short term memories to get by until they finally figured out the value of externalizing intermediate results. An article in the New York Times covered some interesting research on innate number sense and its correlation to achievement in mathematics – about as surprising as a correlation between hand eye coordination and achievement in sports.

Dijkstra, the programming genius, once wrote: “The competent programmer is fully aware of the strictly limited size of his own skull” This awareness generally involves painful experience, and more time than can be fit in a school math curriculum. It certainly involves far more comfort with error than most school boards have.

The Punchline

If I don’t know the answer to the teaching problem I do know an implication of this for the reporting of mathematics in the public sphere: make minimal demands on the reader’s short term memory.

People can compare two charts. They can’t remember one chart while looking at another. In fact most people can compare dozens of charts – as long as they can see them all together.

No one I know of does this better, on a regular basis, than Martin Wolf in the Financial Times. Most of his articles are illustrated by a number of charts, all beside each other, most with multiple lines or bars, often in different scales. (Here is a recent, depressing, but illustrative, example.) These are fairly extreme examples, written for a specialized audience, willing to devote considerable attention, and knowledgeable about the subject matter. But the principle holds for any audience. Teachers should keep trying to get the damn kids to record their intermediate results. Those trying to communicate to the public should know that their audience wont do that. The audience won’t do this work for you. Show them the working yourself.

The original post is design specific – and well worth reading – but it also struck me as completely relevant to programming, which I do professionally, and to a great deal else that I’ve done and tried to do over the years.

Here’s my version of the six suggestions:

1: Original ideas come as solutions to problems, not when you go looking for original ideas. Collect good problems.

2: The goal is not to impress people with the complexity of your ideas, but to stun them with their simplicity. There’s nothing better than an “obvious” solution that no one else has thought of.

3: Ideas are there to be shared. If you can take someone else’s idea to a new place, or someone can take something you’ve done and use it for a new purpose, then everyone wins. Ideas are not used up by being applied. Intellectual Property is Theft©

4: Always be growing your vocabulary and your capabilities – expanding the collection of things you’re confident you know how to do. This opens up new landscapes. If it isn’t in (or close to…) your repertoire then it won’t be in your imagination. You can’t want to do things you don’t know about.

5: Lose the fear of doing the wrong thing by minimizing the cost of doing the wrong thing. Errors are not the problem; expensive errors are the problem. Reduce the cost and increase the rewards of your mistakes. Then make plenty of them. If you don’t fail some (or most) of the time then you’re not trying hard enough.

6: Do something. Actually take the first step and see what the landscape looks like from there.