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The Formula That Killed Wall Street
We recently discussed the perspective that the harrowing of Wall Street was caused by over-reliance on computer models that produced a single number to characterize risk. Wired has a piece profiling David X. Li, the quant behind the formula that enabled the creation of such simple risk models. "For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels. His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. ... [T]he real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust."
G+R+E+E+D
I want peace on earth and goodwill toward man.
We are the United States Government! We don't do that sort of thing.
Enter Li, a star mathematician who grew up in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo.
He has more degrees than a thermometer!
In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.
Citation? Booms and busts are caused by, respectively, expansion and contraction of the money supply (usually in the form of bank credit), often accompanied by manipulated interest rates. The formulas used by lots of investing firms could cause clusters of errors, but the extent of types of companies (and governments) affected points to a more Austrian-style, systemic boom/bust rather than a single-(important-)sector miscalculation.
There is nothing wrong with using a model. Models are good. They help us simplify the world so that we can understand it. For example, we have hundreds of competing climate change models that explain what is going on and predict what we should expect. We model the weather for forecasts. And so on.
But. And it is a big but. You must know the limitations of your model. By definition, a model is a simplification of a complex phenomenon. That does not make it flawed: that makes it a model. Overreliance on the model is your fault, not the fault of the model.
This game will waste your life. Don't clicky!
Diversity.
Life is not for the lazy.
- Don't spend the money you don't have
- Don't do credit unless you absolutely have to
I know I know, Wall Street are these big finance hotshots who do complicated things that have nothing to do with personal finances, but what is it they do apart from speculating and playing with money they don't have, or other people's money? They just hide that simple fact under abconce financial constructs, but that's all they do in the end.
Bring back some morals sanity in the credit business and there won't be anymore crisis of this magnitude. No need for math here...
"A door is what a dog is perpetually on the wrong side of" - Ogden Nash
It isn't killing Wall Street. Those jokers are getting $billions$ in free money.
It's killing us, the people who work for a living and have to provide all those $billions$ or suffer the inflationary consequences when the Feds just print it.
That Gaussian curves are a poor model for unlikely events has been known for quite some time. This is best explained by Nassim Taleb in the following books:
His main thesis is that the markets are essentially random and are basically impossible to predict in any meaningful way. Further there are unlikely unknown unknowns can cannot be predicted until the they occur, usually with disastrous consequences.
---- It won't be as bad as you fear or as good as you hope, but it will take twice as long as you plan.
An interesting article, for sure. The issue with the Gaussian Copula model for pools of mortgages in CDOs is how sensitive they are to the assumptions of the model. If, for example, the annual growth rate of home prices is 2% instead of 10%, things look tremendously different. If correlations between housing prices in different cities is 50% instead of 10% -- disaster. The lack of stress testing of these models (checking what the results are for different inputs into the model) was a huge issue. Even if a model is decent (which in principle, copula models are), if they are too sensitive to inputs, then the prices it produces are not trustworthy. If the proper uncertainty was taken into consideration, then perhaps everyone would have been a little less gung-ho about CDOs.
Like the (worthless) Value-at-Risk figure, the (also pretty worthless in the end) Gaussian Copula was "easy" to understand. Given that the dynamics of financial markets are not simple and easy to understand, reliance on simple models that are easy to explain to the MBAs is probably not the best idea.
A BIG part of the problem is Washington's tendency to reward economic losers at the expense of the people who know what they're doing, and I'm NOT just talking about the poor. There are plenty of the high-salary types who have some sort of governmental loophole or backing that saves them when they screw a big company up.
It's one reason we don't need to be bailing out bad companies, and instead rewarding or backing up the good ones with incentives and tax cuts so that they can really succeed and push forward.
This brings me to the crucial issue. Unlike the position that exists in the physical sciences, in economics and other disciplines that deal with essentially complex phenomena, the aspects of the events to be accounted for about which we can get quantitative data are necessarily limited and may not include the important ones. While in the physical sciences it is generally assumed, probably with good reason, that any important factor which determines the observed events will itself be directly observable and measurable, in the study of such complex phenomena as the market, which depend on the actions of many individuals, all the circumstances which will determine the outcome of a process, for reasons which I shall explain later, will hardly ever be fully known or measurable. And while in the physical sciences the investigator will be able to measure what, on the basis of a prima facie theory, he thinks important, in the social sciences often that is treated as important which happens to be accessible to measurement. This is sometimes carried to the point where it is demanded that our theories must be formulated in such terms that they refer only to measurable magnitudes.
It can hardly be denied that such a demand quite arbitrarily limits the facts which are to be admitted as possible causes of the events which occur in the real world. This view, which is often quite naively accepted as required by scientific procedure, has some rather paradoxical consequences. We know: of course, with regard to the market and similar social structures, a great many facts which we cannot measure and on which indeed we have only some very imprecise and general information. And because the effects of these facts in any particular instance cannot be confirmed by quantitative evidence, they are simply disregarded by those sworn to admit only what they regard as scientific evidence: they thereupon happily proceed on the fiction that the factors which they can measure are the only ones that are relevant.
Hayek. Nobel Prize Lecture, 1974.
This seems to be a popular story for the past few weeks, but it is a mistake to blame the statistical method used. The problem wasn't that they were all using the equaton, it is that they were all mis-using the equation. All statistical tools can fail to be sensitive to certain aspects which may be critical to an application.
People in finance applied these statistical tools believing that they would be able to master risk with them. Unfortunately, they made assumptions that certain things would continue to be the same in the future, plugged the information into the equation, and now science was telling them that everything would be alright. If everybody on Wall Street was making decisions based on the Magic 8 Ball would we blame the ball or the foolishness of those misapplying it?
The love of money is the square root of all evil.
This formula may have and probably did help crash the world's stock markets (yesterday's Dow Jones was HALF of its worth at its high last June), but the reality is that high energy prices drained everyone's wallets.
When Bush took office, gasoiline here in Springfield was $1 per gallon. At Wall Street's high last summer it was nearly $4.50, over four times as high. We talk about elders living on a "fixed income" but the fact is almost all wage earners' incomes are fixed. We can't demand raises or overtime and have to live within our means. But when that $20 per week gasoline budget quadruples to $80 per week, with heating and electric costs going up as well, that takes money out of other aspects of the economy. Sooner or later people are over their heads and behind on bills, and things spiral out of control.
The result of that and other factors is what you see now.
Happy square root day, everyone.
Free Martian Whores!
In China, they're using this slack time to upgrade the infrastructure, closing down old inefficient factories and building new ones with government CASH. Who's winning this round?
Not the millions of migrant chinese workers who have lost their jobs, which will probably also cause civil unrest. Also, the Chinese holding trillions of dollars in U.S. treasuries will also be slightly annoyed when the U.S. government inflates away their debts.
Finally, the vast majority of China's stimulus package was already announced before this major recession. You have the order backwards.
Yeah, "complex mathematical model". Tell it to the judge.
They did indeed use this model, and the work of many other PhD mathematicians, physicists, and other geniuses. But any of the bankers could have looked at this whole class of derivatives from mortgages and seen the basics that make the model a joke. They sold millions of mortgages and other loans to people using artificially low initial interest, to get people to take the loans, but which ballooned to rates they couldn't afford, so they'd have to default. Inevitably, a large percentage would certainly default. A losing bet overall for banks holding those loans. Meanwhile, each bad loan was "good" because the banks could sell many times the number of derivatives on it. Which was "good" because they got paid for the derivatives they sold, but was much more "bad" because the derivatives would cost the issuing bank many times more when it came due. The derivatives came due when the mortgages defaulted. Which was inevitable.
So whatever "gaussian copula" model they use to convince each other it was good, basic business sense would have insisted that the business was bad, horribly bad. These bankers don't get paid for discovering new math, they get paid for their years of experience and business sense. So they should have laughed this model out of the boardroom, even if they didn't understand why it was wrong. They should have known it was wrong, as the past few years proved beyond any doubt. But they embraced it instead, and centuries old banks like Lehman Brothers have gone down, taking us with them (and no end in sight).
Because ultimately, the model was a way to delay the costs of a business that paid some fat revenue up front. Since bankers are paid in huge bonuses for the initial year of revenue, and then leave before the bills come due , they got paid to make those bad deals, because they paid off up front, before costing many times more their benefit a few years later. By which time the bankers are gone with their early bonuses. Which have a lot more buying power when the economy collapses, and everyone else is holding merely the debt they created.
Nice work, if you can get it. Since they ruined the banking system and everything else, no one can get any work at all.
These people are holding the money. Their bonuses often equal the losses that destroy their bank. The government should take back that money to pay for fixing and repairing some of the mess they made. "Fiduciary responsibility" is a requirement of bank execs, and these violated that by the $TRILLIONS. Make them pay for what they did. That's a simple model anyone can understand. Not just a complex conjob to hide behind.
--
make install -not war
There's nothing advanced or innovative about a gaussian copula. It's a very simple mathematical trick, it doesn't say anything about finance in itself. It's a programming trick to go from a uniform distribution on a cube (easy to generate, run rnd() for each coordinate) to a multivariate gaussian with a specific covariance matrix. The way to do it is cholesky decomposition. This is OLD stuff.
Li's paper is a clever way to measure default correlation using correlation matrixes from asset returns. It's quite clever, and yes it's a pretty good model (more on that later)
This is not journalism, this is a bit of shit where the author decided having an "evil formula" would be cool. Look there's an "equal" sign, how can they be so sure... pffffffffffffffff.
I said it was a good model, yet it's been proven wrong hasn't it? Well, first of all, what has been shown to be wrong is the guesstimate of correlation that was input into the model. G.I.G.O
Plus, if you price a fixed income product and it produces higher than market return, you will borrow short term funds to invest them in it. In a free market that quickly drains the pool of saving and raises short term interest rate. Sure you end up losing money but no catastrophe. In a federal reserve system, well the short term rate stays what the fed says it should be and everyone piles on the arbitrage, creating sky high leveraged position.
Yeah the formula can be misleading, but for a true catastrophe, you need a federal reserve.
\u262D = \u5350
Blaming greed for a financial crisis is like blaming gravity in a plane crash.
\u262D = \u5350
Preposterous! Human gullibility is one of the few things that has no limits.
Support Right To Repair Legislation.
It has been broken since 1694.
Credit is an exponential function. Go check the national debt (in any country) for the last couple of centuries. It's an exponential growth curve. Credit has an exponential function built in to to it. When credit is created, it is created with an equivalent amount of debt attached, which pays interest.
So you have : credit on one side | debt + interest on the other.
So in order to work AT ALL, the supply of credit must grow exponentially every year to pay the interest on the previous year's debt. If it doesn't, there is a monetary collapse as the debt consumes the credit.
Li's function simply allowed the process to continue until they ran out of people to lend money to. The problem has been there as long as money lenders.
Deleted
>The managers making the decisions didn't know what it all meant and the guys using the model didn't adequately explain the model's limitations.
Or the managers didn't understand their explanations -- or more likely yet, didn't *want* to understand their explanations.
This doesn't look fundamentally different than the Challenger explosion: the technical staff knows there's a problem, keeps saying that there's a problem, but their upper management is invested in there not being a problem. It's really difficult to explain something to someone whose job depends on ideas that conflict with what you're explaining.
Nostalgia's not what it used to be.