Credit Default Swaps

May 1st, 2010

Credit default swaps are a type of insurance. I buy something that has a small risk of costing me a lot of money, it might get stolen or broken, if it’s a bond or a mortgage it might default. Rather than risk losing my whole $100, I will buy insurance for $5. You promise to pay me if one of these terrible things happens.

Credit

Companies and governments, just like individuals, have a credit rating. The rating is some number on a scale from good to bad. For individuals in the US the scale is in the hundreds, for companies and governments the ratings are on a scale that sounds more like school grades, AAA, AA, A, BBB, BB, etc, with, perhaps, depending on the rating agency (we’ll get to them later), some gradations in between and some differences in nomenclature.

Default

Whatever the scale is, the rating is supposed to be a measure of how good a risk you are. Specifically, what’s the probability is of you defaulting on your debt. Sovereign debt – money borrowed by governments – generally have a very good rating. Until recently the probability of the US government defaulting on its debt was considered to be 0% (it’s still considered very close to that, but some nerves have been frayed and unaskable questions asked). Other governments have been considered a much higher risk. Argentina used to be (reasonably enough) considered a high risk borrower, Greece and Iceland are currently considered as having a decidedly non zero chance of default.

Credit ratings matter because the higher I perceive the risk of you defaulting, the more I’m going to charge you to borrow money from me.

Swap

Suppose we all agree that there’s a 1 in 10 chance of you defaulting: you might lose your job, go bankrupt, go out of business, or be unable to raise enough in taxes to service your debt. (We’re not all going to agree. You’re going to say the odds are 1 in 50, a nervous investor might consider you a 1 in 5 risk. This is where the rating agencies come in. We will get back to them later.)

But suppose we agree. And suppose that I want to lend you money but I don’t want to take a 1 in 10 chance of not getting it back? Well, why not insure it? Insurance on a 1 in 10 risk should a tenth of the amount insured. The “Expected Value” of a 10% chance of making $100 is 10% of $100. That’s really all you need to know. The rest is arithmetic. (How much is a 3% chance of losing $2,500,000 worth, etc. It’s all just proportion. Being able to use proportion is by far the most important mathematical skill beyond simple arithmetic.)

If I insure 10 $10 loans each with a 1 in 10 chance of defaulting, then, on average, one of them can be expected to default. I’ll have to pay $10 to the person who bought the insurance, but I’ve already taken in $1 from each of lenders, so I’ve broken even. Of course I’m trying to make a profit here, so I’ll charge you more than $1. A credit default swap is insurance against a lender defaulting. (More subtly, I can buy insurance to turn a 1 in 10 risk to a 1 in 20, or to turn a A rating into a AAA rating. Once you get the idea of expected value, that a 1 in 10 chance of winning $10 is worth $1, the mathematic is no more complicated.

What Could Possibly Go Wrong?

First off, to human beings, with our finite life spans and our asymmetric financial needs, a 1 in 10 chance of winning $10 is not necessarily worth $1, but that’s another topic. The real question is the reliability of the ratings. How do I know that this company has a 0.1% chance of going bankrupt, and the other company has a 4% chance of doing the same?

We could, in theory, just let the market figure it out. Let some people charge too much for insurance while other underestimate their risks, surprisingly (to me) this might actually work and could be a valuable and legitimate application of CDSs.

Markets can assess risk within reasonable degrees of accuracy and given some fairly reasonable assumptions about what’s likely to happen. GE will probably not go bust because it has been around a long time, and survived some pretty bad economic crises, it seems to adapt well to changing circumstances, all good things. On the other hand, mighty giants have fallen before, so there is some risk. This would be a valid role for Credit Default Swaps – let people bid on the price of guaranteeing a particular debt, and use the market price as a measure of its danger of default. This system is still exposed to serious systemic risk: the danger that the entire thing blows up at once. If I promise to pay if you default, then what happens if I go broke too? If we’re both in the same industry,or country in some cases, then there is likely to be extreme correlation between both our probabilities of defaulting. It’s hard to see a way around this, but if we were looking for a system that’s far worse that, the one we have now answers nicely.

The Ratings Agencies

What we do now is call in the experts.

There is such a thing as expertise in judging risk. The life insurance business has it, But’s that business’s success is built on certain well confirmed assumption. If uncle Earnest gets killed by a giant meteorite, or a war breaks out and he’s hit by a V2 rocket, his insurance company is going to point to the “Acts of God” exemption, and wave goodbye. Events that are so improbable and so cataclysmic that it is impossible to measure their likelihood cannot be insured against.

The rating agencies claim to have similar expertise, but they don’t have an explicit “Acts of God” clause, and they have an inherent incentive to underestimate risk.

Rating agencies are paid by banks to estimate the risk of things the banks are selling defaulting. That’s right. I’m going to pay you to say how good the second hand car I’m selling is. I’m going to hire the movie critics to say whether my movie is 5 star good or only 3 star good. I could go on, but you see the problem. If car assessors or movie critics were paid by car salesmen and studios then getting people to pay any heed to these ratings would take a pretty serious branding campaign (at least as good as De Beers’ successful persuasion of the public that the diamonds they are buying are rare and valuable).

So the rating agencies are incentivized to give good ratings, because otherwise the banks won’t hire them. An inevitable outcome of this, given that the rating is a proxy for the probability of the debt defaulting, is that these probabilities are systematically underestimated. This bias added another wing to the glorious structure that became the great economic meltdown.

The Debt Guarantors

The risk of a given tranche of a CDO depends entirely on the risk of the debt used as its collateral (and on the size and price of the tranches above it). If that risk is underestimated, or if the correlation between the debts used as collateral is higher than assumed (the probability of a car company’s debt defaulting is one thing, the probability of it defaulting if another two equally large car companies have already done so is significantly higher), if either of these things is true then the rating of the tranche is going to be far, far higher than it should be.

AIG bought it. They really believed that the probability of the AAA tranche of a CDO defaulting was the same as that of the AAA debt issued by some well established, well tested corporation. So they insured it. They took the probabilities at face value. Actually, what may be even worse, is that they looked at them too, and agreed with the rating agencies valuations. After all, they were getting paid to sell insurance. If they said it was too risky they’d miss out on their commission. That was where their incentives lay.

So they insured it on the assumption that there was a given, low, probability of them ever having to pay off. They thought they were getting money for old rope, collecting everyone’s overpriced lottery money and pocketing it. Sure, there was a chance that some low grade debt would default and they’d have to pay out (like someone winning some minor lottery prize), but the chances of any of that AAA stuff defaulting could be ignored. They thought they were selling insurance that there was no chance they’d have to pay out on. So they did it as much as possible.

It all contributed to a beautifully vicious circle. Overvalued debt was used to create CDOs the tranches of which were similarly overvalued, then their valuations was raised again by buying insurance that seriously underestimated the tranches’ riskiness, then synthetic CDOs were created with these overrated tranches as collateral. Lather, rinse and repeat. Every time round the circle everyone gets paid.

At every stage the incentives of those in the game were to keep the game going. In the short term they were getting paid, in the long term, well, they would still have got paid.

The problem is not that people were greedy, selfish and short sighted. There is never going to be a shortage of these things. The problem is that it paid to be greedy, selfish and short sighted.

Synthetic Collateralized Alchemy

April 29th, 2010

What Was Wrought

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?

The Unexpected Cost of Lotteries

April 25th, 2010

By definition, the expected value of a one in five chance of winning $10 dollars is worth $2 ($10/5). But to human beings, with our finite life spans and our asymmetric financial needs, a one in a million chance of $1,000,000 is not necessarily worth $1, it might be worth more.

Lottery tickets cost far, far more than their expected value. The amount you would win times the probability of you winning is pretty close to zero. They are, as far as expected value goes, practically worthless.

But despite what Adam Smith says, buying lottery tickets is not necessarily a bad idea. They’re vastly overpriced, but unless I’m already rich the difference winning $1,000,000 would make to my life is worth far more than the extra $1 I’m getting charged for my ticket.

Given the choice between $2 and a one in a million chance of a million dollars, I know which choice is more exciting. The poorer I am the more enticing that is. (If I’m well off I have many more, and better, opportunities to make money.)

The injustice of lotteries is that they exploit the perfectly natural assumption that if buying one ticket is a good idea buying 20 is 20 times better. But Adam Smith is right again: buying all the tickets would guarantee that you won the lottery and lost a fortune.

Lotteries are not a tax on stupidity, they are a tax on poverty and lack of opportunity that exploits an almost universal miscalculation of the effects of scale on risk and value.

They are a lousy form of taxation. If you want more money for schools, roads or, cultural institutions, then raise taxes, or issue bonds. Don’t fund opera from lotteries, that way poor people pay for things they can’t afford to enjoy.

Insurance and Mortality Curves

April 25th, 2010

The life insurance business is very good at calculating the probability of you dying within the next year. It’s one of these things that we’ve being doing so long that we’re pretty good at it.

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).

morality curve

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.

How Collateralized Debt Works. (And Where It Got Us.)

April 21st, 2010

Collateralized debt sounds like a damn good idea, and it can be. It’s fairly complicated, but it isn’t rocket science, and it’s really worth knowing enough about to make sense of the news these days.

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.

CDOs

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.

Why Every Educational Experiment Works

January 18th, 2010

Assume that charter/experimental schools achieve better results than regular schools, which of the following is true?

1. You should try to send your child to a charter school:

  • True
  • False
  • Impossible to tell with the information given

 

  • 2. Regular schools should become more like charter schools:
  • True
  • False
  • Impossible to tell with the information given

And the answers are, respectively

  • True
  • Impossible to tell, but probably false

Charter/experimental schools work for two related reason

  • What kind of teacher decides to work in some kind of non-standard school?
  • What kind of parent send their child to a non-standard school?

Committed, enthusiastic teachers who are willing to learn and experiment.

Parents who’ve given thought to their children’s education.

The simple fact is that that combination will achieve above average results. (The best predictor of children’s education success is parents who care about their children’s education.

That is why educational experiments work, and why they usually don’t scale. There simply  aren’t enough such parents and teachers.

So what works? Improving the quality of teaching, and getting parents more involved in their children’s education, perhaps by giving them some hope that their children have a chance of a decent education in the first place. If you know your child’s school has a low graduation rate, and teachers who’ve given up it feels futile to even try. Just as if the child’s options are minimum wage or crime and prison it’s pretty hard to explain to them why the relevance of colonial history.

My conclusion? Charter schools and experimental schools are wonderful places to try out new ideas, some of which might work in the wild. (The wooden blocks in every kindergarten in New York are a wonderful case of such an example.)  And if you can get your kid into a charter school, then do so.

But this doesn’t mean that making all schools charter schools will improve over-all standards. The keys to that lie outside schools. And if I knew the answer to that I would let you know.

"Show Your Working"

April 4th, 2009

One of the many things that makes math difficult to learn is the seemingly universal reluctance to be comfortable with incomplete thoughts. In math terms this translates to “write down you’re intermediate results”. Kids hate to do this.

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.

Simulation and Modeling

July 30th, 2008

Simulation is a wonderful thing. It’s one of the foundations of mathematics.

Scale models are a good example. If you want to see what the new building will look like make a model. It isn’t going to tell you everything, the architectural models of housing projects usually look wonderful, but it’s a great example of using the external world to think for you, of externalizing your brain. Yes, you can read a description and imagine what something will look like, but making a model, reduces how much of your brain that uses, leaving more brain for other things, like deciding whether any child is really going to want to play under the gaze of a thousand anonymous windows.

The power of modeling is real. From the scale drawings my father used to make before decorating the kitchen, to the simulation that demonstrated that the proposed system for baggage handling at Denver Airport was guaranteed to fail horribly. (Unfortunately the simulation, costing a few thousand dollars, was done after the actual system was built at the cost of hundreds of millions, and then millions more in delays.) Dangerous, lengthy and expensive processes can be evaluated for a fraction of the cost of the actual experiment. Some people’s love this new power, others can’t forget what’s being lost.

What’s lost in any abstraction is the specific, the individual, everything that matters. Some people can’t get over that.

Simulations and models only work because they ignore details, knowing whether they are important details can be difficult. A scale model works fine for the forces on a house or a skyscraper, but is hopeless for a ship. Econometric models are notorious for their spurious certainty.

So the practical fitness of a model to it’s purpose is one question, but there are others. For some people it is impossible to imagine the classic absurdist math problem characters “a man”, or “a woman” without some humanity to hang on to. People differ on this.

I remember some fine junior high level course material on date arithmetic. A drawing of a set of gravestones: name, born, died. The question was: how old was each person when they died. One child faced with “James Brown: March 1823 to June 1839″ confounded his teacher by insisting on knowing why Jim died. I don’t share that need, but I rather like it. I’m glad it’s around. If we want to make more people more mathematically adept, this is the kind of fact we need to acknowledge and deal with.

Physical Data

July 16th, 2008

RDF stores in hardware.

Whatever else it turns out to be, the semantic web has already given us RDF. It’s here, it’s now, it rocks.

RDF says that every data structure can be modeled using three part statements consisting of Subject, Predicate and Object. Each of these being a simple piece of data that can be represented as a string.

This is a surprisingly substantive claim. It means two part statements (Subject/Property, or Name/Value) are not enough, and four part statements unnecessary. It means that in structured data RDF triples play the role that triangles play in graphics. If you can draw triangles you can draw everything. If you optimize your triangle drawing you optimize all your drawing. In networking TCP/IP packets play a similar role. Routers, switches and network cards don’t care what new applications are built on top of packets. Make passing them efficient, and everybody benefits, the cost of switching packets tends to zero.

The completeness property of triangles in graphics makes graphic cards rewarding – custom silicon that solves a specific problem insanely efficiently. RDF has similar potential. RDF can scale in hardware. The memory storing the statement can be smart enough to parse and query it. The structure is so simple, basic filtering so straightforward, that it can be done on a per triple basis in hardware, implemented directly in transistors alongside the non-volatile memory, built scaleable to plug into an RDF bus. As you add data you add processing power. Since one of the sweetest properties of RDF is the fact that it can be munged together indiscriminately – you can always add more triples without compromising what’s already there – this means we can have physical data. Physical data scales really well.

Six Suggestions That Can Make You a Better Maker

June 6th, 2008

A designer friend recently sent me a link to an excellent post by Eric Karjaluto on design.

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.