Reading the news lately, I’ve come across an amazing example of how ubiquitous bad math can be used. Most of you have probably heard about what’s been called “the sub-prime crisis”. Despite a lot of media hand-wringing about how complicated it all is, the sub-prime crisis is really a very simple phenomenon: basically, you’ve got a lot of banks that have loaned out money without worrying about whether or not it could get paid back, and now those loans aren’t getting paid back, which is causing all sorts of grief to people who invested in them.
In the beginning of the mortgage system, the way it worked was: banks loaned people money to buy
houses. People paid back the loans with interest. The interest was pocketed by the bank as profit. All good so far.
Sometimes people, due to either interest rate changes, employment changes, or other circumstances,
couldn’t afford to pay their mortgages. When this happened, the banks foreclose the mortgages, which is
a fancy way of saying “take possession of the house and resell it to make up the money owed to them.” If the sale of the house after foreclosure didn’t bring in as much money as the bank had loaned, then the bank lost money.
Banks therefore, when asked to make a loan, would assess the borrower, to try to determine whether
or not they would be able to pay back the loan. They sorted people into categories, based on just how
much of a chance they thought there was that they would not be able to pay back the loan. Some people
were a good risk: it looked like there was a minimal possibility that they wouldn’t be able to repay.
These people are “prime” borrowers – the least risky. Beneath them, there are various categories,
ranging from “almost as good as the prime borrowers” to “no way in hell are these bozos going to be able
to repay this loan”. The banks picked some threshold below which they would not make the loan; and above
that threshold, they would assign an interest rate to the loan. The higher the risk – that is, the more likely the borrower is to to fail to repay it – the higher the interest rate. Again, all good: you take
more risk, you might lose more – but if the risk works out, you make more. That’s all nice and fair.
Investors like to get a cut of anything that’s likely to make money. Mortgages are great from their perspective, because people will do almost anything before they let their home get taken away – so it was seen as a safe profit. So investors wanted a cut of the mortgage market. What the banks did then, was grab bunches of mortgages, and sell them as a sort of bond. If you bought $100 worth of mortgage bonds, what you were effectively doing is giving the bank $100 to loan out as a part of some mortgages. Then when the homeowners repaid the loan, you would get back your $100 with interest as it was repaid. This was considered a good thing – for the borrowers, it meant that there was more money available to loan people to buy houses; and for the investors, it was a safe investment that brought in a reliable profit.
Now, we start getting to the tricky part.
There’s another kind of risk in the whole lending scene. The prevailing interest rate on loans fluctuates over time. If the bank gives you a loan at, say, 5% today, and then next week, the interest rate goes up to 10%, then what happens? If the bank can’t change your interest rate, then from their perspective, they’re missing out on the interest that they could have earned had they waited until next week to loan out the money. On the other hand, if the bank can change your interest rate, then your monthly payment on the loan will increase. The bank makes more money, but at an increased risk of
your not being able to pay the loan.
The loaner wants to be able to charge as much interest as possible – because interest is profit. So they want to get borrowers to pay as much interest as they can. But borrowers like to know what they’re going to be paying. So the loaner hedges against the risk. If you don’t want to take a chance on the rate changing, they’ll charge you a higher rate, but guarantee that it won’t change. If you don’t want to pay that higher rate, they’ll give you something lower – but that lower rate can change
over time, so it might go up.
Loaners really want you to take the rate that they can spike if rates go up. So they offer teaser rates – low rates for some period of time, after which the rate will increase to whatever is the current rate on the market. So you get a loan that’s very cheap for the first couple of years, but unpredictable
Still, it’s all fair. Everyone knows what’s going on, and everyone is appropriately paying
for risk. The people with fixed rates are paying a little extra to protect themselves; the banks are paying out money in the form of lower rates to get people to take a loan that might pay more in the future; the borrowers who take out variable rate loans are getting a lower initial rate in exchange for taking some risk. That’s how markets are supposed to work.
So you’ve got all of these different kinds of mortgages out there. And the banks realize that they’re making a hell of a lot of money selling the mortgages. But it’s a whole lot easier to sell the
low-risk mortgage than the higher risk mortgages. So what they do is try to find a way of massaging the risk. The idea is, if you take 10 different medium risk things, and put them together, the risk
is less – because one of them might fail, but you still have the other nine. They’re independent, so the risk of one failing doesn’t increase the risk of the others failing. So what you can do is take those
higher risk mortgage bonds, and wrap them in meta-bonds. Now, when you buy a meta-bond, instead of the money going directly into a bunch of mortgages, your money is used to buy a bunch of different higher risk mortgage bonds, and then those bonds are used to make loans. You get a higher interest rate, because you’re investing in riskier loans, but because you’ve supposedly spread out the risk, they’re as safe as the original low risk bonds.
The risk is considered low, because the loans are backed by the value of the homes. Home prices generally rise pretty reliably. So if the borrower defaults and you foreclose, you can still get back your investment. The only real risk if if home prices start to fall: then people can’t get out of the mortgage by selling their homes, and you can’t make back your investment by foreclosing and selling the property. But you’ve hedged that, by combining mortgages from New York City with mortgages from Cleveland Ohio and Dallas Texas and…. So you’re only really screwed, even on the bundles of not-so-safe loans if the housing markets in Dallas and Cleveland and NYC all crater at the same time – and they’re independent, right? So that can’t happen.
Investors love these higher interest low risk bond packages. So the banks start to put together more of them. And they realize that they can cobble together even higher yield bundles if they cascade them: they take a bundle of 10 different kinds of shit loan bonds, and turn them into high risk loan meta-bonds. Then bundle 10 different high risk loan meta-bonds (which were formed from the shit loans) into medium risk meta-meta-bonds. Then bundle 10 different medium into a low. And so on. So now you’ve got something labeled as “high quality, low risk” which is formed completely from a collection of shit. But, by golly, it’s marketed as high quality, and it’s got a nice rate of return! And it’s really low risk, because you’ve distributed the risk into a bunch of independent places, and you’re only in trouble if they all fail. (This is bad math point number one: false independence. This scheme only works if there is truly no connection between the failures of the components.)
You bundle them together according to a complicated scheme called tranching to make them look like they’re really, truly safe. And you take out insurance, so that if something goes wrong, it’s all insured.
Investors love it. They’re buying things that they were told are really low risk, and they’re paying a great return. And they investors are happy, because it’s low risk and it’s insured! But the banks have to make lots and lots of shit loans in order to satisfy the demand from investors. So they start to make loans to pretty much anyone who asks. Hey, want to borrow a million dollars? No problem! The bank will happily make the loan, so long as you promise them that you’ve got a salary of $200,000/year. Just promise – the bank doesn’t need to see any proof, you’re clearly a trustworthy fellow!
This creates a feedback cycle. People can borrow pretty much whatever they want, so they can pay
more to buy a more expensive house. This means housing prices go up. Rising housing prices mean that
the risk of a loan is smaller – because if the value of the house increases, you can make more by
selling it on foreclosure. And because the prices are going up, people see houses as a good investment, and decide to borrow more to buy a house. It’s a nice cycle, up to a point.
The problem comes about when the prices get to the point where they’re totally disconnected from
anything resembling the real value of a house. Then when interest rates go up, you’ve got a lot of people who can’t afford to make their mortgage payments – and they paid so much for the house that
there’s no way to sell it for enough money to pay back the loan. And that happens not just in NYC, but
all over the country. Suddenly the shit bonds are worth, well, shit. And the supposedly safe bonds formed from bundles of bundles of bundles of shit bonds? They’re worth shit too.
That’s the current situation. There are who knows how many billions or trillions of dollars tied up in what are, quite likely, bundles of shit. The economy is slowing down, interest rates are going up,
and most importantly, housing prices are falling. So you’ve got tons of loans where people borrowed more that the house is currently worth. And tons upon tons upon tons of fancy bonds which are supposed to be safe, but which are ultimately based the values of houses that aren’t worth what their owners borrowed to buy them.
So what happens next? Well, the bonds are worth shit. But they’re insured! The insurance companies
will take the hit, and cover the loss, right? Well, that’s where we get to the specific bit of bad math that inspired this here rant. The insurance companies based their calculations on the same ideas of “safety by distribution”
that the banks used when they bundled things together! So the people who are
guaranteeing the safety of the loans are relying on exactly the same assumption
of safety that they’re supposedly insuring. If the insurance is ever needed, it’s
because the assumption of safety was wrong. But because the insurance company
used that same assumption, they’re not going to be able to pay it back. (This is big bad math point number two.) So that didn’t work out. So the insurance companies are crashing and burning. And when the insurance on your bond that allows you to rate it low-risk disappears, because the insurance company failed, then you’re in deep trouble. Your bond is no longer considered low-risk. And that means that a shitload of investors are going to get out and sell your bonds. But no one wants to buy them – because they know that they’re a pile of shit, and no one is really sure what they’re worth, because no one knows how many mortgages under the umbrella of that piece of shit are going to fail. So the prices of the “safe” bonds totally collapse. And all of the other investments that relied on those bonds – those start to fall apart too.
So – the banks know that they need to stop the insurance companies from collapsing. How can they do that? Here’s a truly brilliant idea, which was floating yesterday by a bunch of big banks like Merrill Lynch and Bear Stearns: loan money to the insurance company.
So – the insurance company is guaranteeing the value of the banks mortgage loans, using money that it borrowed from the bank, which the bank had to borrow because it’s got these bundles of leans insured by the insurance company. In other words, the banks are insuring their loans themselves, using the loans to pay for the losses on the loans. It’s circularity on circularity on circularity – cycles within cycles of stupidity, relying on stupidity to prop it up.
And there are people – lots and lots of them – who are falling for this as a scheme
to save the banks from the bad loans.