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The Math Formula That Lead To the Financial Crash
New submitter jools33 writes "The BBC has a fascinating story about how a mathematical formula revolutionized the world of finance — and ultimately could have been responsible for its downfall. The Black-Scholes mathematical model, introduced in the '70s, opened up the world of options, futures, and derivatives trading in a way that nothing before or since has accomplished. Its phenomenal success and widespread adoption lead to Myron Scholes winning a Nobel prize in economics. Yet the widespread adoption of the model may have been responsible for the financial crisis of the past few years. It's interesting to ponder how algorithms and formulas that we work on today could fundamentally influence humanity's future."
Nobel prize in economics.
that's Nobel prize in pseudo-science.
It was human stupidity and greed.
"If any question why we died, Tell them because our fathers lied."
Plenty of financial collapses have preceded the current one without the benefit of Black-Scholes. What did they, and the current collapse, all have in common? Excess credit.
The Black-Scholes model is an attempt to apply solved heat flow equations to a financial pricing problem. It requires demonstrably invalid assumptions to be made to make it work (such as markets do not trend). Just because a Nobel prize was awarded does not make the model valid.
Interesting, but really, blaming the seed on Jack looting the giant's castle? I used to write risk analysis software for the traders and market makers at the options exchange in Chicago (CBOE) and am intimately familiar with Black-Scholes algorithm (I've implemented it more than once). In the article, the sub-text to one photo, "Options allow a trader to have a delicious risk-free portfolio", is totally bogus! Options allow a trader to MINIMIZE the risk in their portfolios, and BS (no pun intended) helps traders to do that in a mathematically/statistically rigorous way. Misuse of any tool (using a hammer to kill someone, for example) is not the tool's fault, but the wielder of the tool!
-Rubberman
You're so sure they didn't understand what they were doing? Maybe they didn't care. None of them returned their commissions on all the trades and phony "profits" they took out of the system, and practically nobody went to jail. They won. Furthermore nothing much has changed. It will happen again.
1. Approve $300K mortgages for people earning $35K/yr, falsifying documents as needed
2. Bundle slices of thousands of these mortgages into derivatives along with "insurance" against the mortgages defaulting and "insurance" against the bundles failing, etc, under the direction of math and finance PhD's. Sell these "Triple-A-rated securities" to gullible investors worldwide.
3. ??
4. Profit!
8-figure pay packages for bankers and 7-figure for mortgage brokers, real estate agents, workers in credit rating agencies, etc. until the music stops. But hey, you won't need to defend your resume when you've got enough millions in the bank.
5. Watch housing prices rise by 30-50 percent/yr
6. Goto step 1.
There's more to it than that. The model has developed into a philosophy which has been built out beyond its workable foundation.
It starts with the risk neutral measure. Basically the concept is that you can construct a probability measure (basically a reweighting of probability of events) from market prices. Basically the market prices of a stock, a forward contract (a contract to deliver the stock at a fixed point in the future), a call option (an agreement to offer the option of buying the stock at a given price in the future), a put option (an agreement to offer the option to sell a stock at a given price in the future), and other contracts related to the price of the stock in the future all have to have prices rationally related to each other. If the price of one of these things deviates from the risk neutral measure implied by the others, you can construct arbitrage positions where you can make a profit with negligible risk and executing this arbitrage has the effect of moving the market prices closer toward their theoretical values.
Observably, market prices don't reflect real probabilities. Safe investments such as treasury bonds are disproportionately more expensive than highly rated bonds with a low chance of default based on historical default rates. This is explained due to risk aversion and philosophically, the risk neutral measure is said to reflect the market's assessment of the risk of each investment and also the risk preferences of market participants. This concept is the basis of financial economics, and the school of thought derived from this position has been dominant in economic related disciplines for the past 30 years.
As a means of analyzing for arbitrage opportunities and pricing of marketable securities in a way that avoids offering others arbitrage opportunities, this methodology is largely unassailable. However, where they overextend themselves is that in conjunction with the efficient market hypothesis, they've started to assume that this framework lets you farm out the function of assessing the likelihood of future events to the market and even in some cases they've asserted that it's immoral to use methodologies which imply prices for non-marketable securities which aren't directly comparable to marketable analogues.
It's basically a religion at this point. They honestly believe that the risk neutral measure isn't just a post hoc rationalization imposed on market prices, but a normative guide to upright living and that the market's assessments of the ("risk-adjusted") probability of future events is the best and most rational basis for making all decisions and for framing all policy and regulation.
My only political goal is to see to it that no political party achieves its goals.
The emulsifying you are talking about wasn't the problem so much as was the leverage and the short information horizon. An investor could buy one mortgage and take on binary risk- it pays off, or it fails. That's a lot of risk. So he can pool his money with a bunch of other people and buy 1% of 100 loans. The risk of any loan failing is spread across all the investors. That, in itself, is a good idea, it is just basic diversification.
The leverage problem was that they didn't just split the loans equally like that, they split the loans into tranches, or classes, of investor. The risk averse investor bought the high quality tranche, and for that got a higher guarantee of payment in exchange for a higher price (lower yield). The lower tranches were sold to suckers with the promise of potentially high rates of return. But as the individual loans started failing, the way the package was levered, the higher investors ended up getting paid, and the lower investors got nothing.
A quick example of the information problem was the practice of the 80-15-5 mortgage loans. Conventional wisdom says that when someone takes out a mortgage with zero down, that mortgage is more likely to fail. So again, conventional wisdom says that in order to hedge for that increased potential failure, you need to charge a higher interest rate. For some reason, and I agree it was probably lack of regulation, someone figured out that you could split the mortgage into three portions- standard risk (the 80%), higher risk (the 15%) and highest risk (the 5%). In the documents for the 80% loan, you could then say that this loan had 20% down, and you'd get the good rate. Then you do the same with the 15% loan- "hey, this loan has 5% down, give us the OK rate". Then you would only end up paying the super high risk rate on 5% of the balance of the mortgage instead of the whole thing. The problem there was that the whole loan had the high risk, but the investors in the 80% and the 15% didn't know it.
The same can be said for pretty much advance in science in the last 50 years. If you're truly interested in what can and cannot be predicted - given correct models, there's a science studying that, complexity theory.
But from finance over climate to even whether the planets will keep turning - all are too complex to be predicted, even though science has advanced to the point where individual events can be predicted short times in advance with near-certainty. However there's obvious things that can't be predicted. If the moon decides to crash into the earth, we will know in advance - but only a few weeks at the most. Yes, really.
In some ways this was inevitable. Science has moved from predicting individual events, like say a car collision, or physical changes happening inside an extremely well-described cloud, a single rational decision taken by someone considering a bank loan - to predicting the global effects of an undefined number of such interactions combined. The answer coming out of all this is rather disappointing : it's not working - and it isn't working any better outside of finance either. The mathematician's answer, chaos theory, is thoroughly disappointing : there is no valid way to make useful long-term predictions of any system more complex than X (btw: you want a nobel prize ? find what X is exactly) which does not require omniscience (which for any real world prediction would effectively be all the information that exists anywhere in the universe)
So the real question changes - if you require proof we can essentially predict nothing. If you even require valid inputs to statistical functions we can essentially predict nothing. Barely any recent science follows from first principles, except perhaps in Mathematics. Physics makes a good-hearted attempt, but it has to violate the first-principles - it's attempting to discover new ones. Every other science never even attempts to work from first principles, it just doesn't work.
Finance - the models only work when you assume decisions don't interact in the short term (ie. nobody decides to either sell a house or forestall selling it because of anything that happens that doesn't directly affect that loan. If this is true, then the financial crisis was impossible (yet also inevitable)). And of course the basic economic assumption - that everyone takes the rational course of action immediately - no matter how complex the logic, and irrespective of any personal convictions.
Climate - energy balance only has to sum up if you assume the entropy of the system is negligible, or if you work on infinite time-scales. Needless to say, infinite time scales are a bit long for practical usage. Entropy within our atmosphere is anything but negligible. The second big assumption made in climate science is that small portions of the atmosphere behave identical to large portions of the atmosphere.
Planets - planet's orbits only behave the way you're taught in school if they followed Newton. But that's not the worst assumption. The other assumption necessary to make Kepler work is that planetary orbits are independent, and no objects with mass can possibly cross into orbits (and obviously that orbits don't cross)
All these assumptions can be proven to be wrong - and rather trivially.
In one case this can be shown. Planetary orbits are extremely, extremely regular in the short term. This was useful for sea-faring when it was discovered as it provided a very accurate source of timing. And we still have the books from those days describing how those measurements worked. We still have books describing how to find a ship's position on earth by measuring the orbits of Jupiter's moons ... only they yield incorrect results. You might chalk that up to bad measurements, but that can't be : if the methods were truly useless, they would never have been written down. Plus we can correct the measurements so they work again. No, the reason is much simpler : Jupiter's moons have shifted so much over the course of 300 years that those me
The equation was not at fault: the output is only as good as the inputs. The real problem was the instruments being traded: credit default swaps. These are of dubious merit and much more complicated than more traditional underlying instruments (the thing on which you hold an option contract). For example, suppose you have an option to be 100 shares of Google at a given price. It's easy to evaluate the value of the underlying instrument because there's an efficient market for it: Google is traded on a public exchange and the value is agreed upon within a penny, generally. Black-Scholes works on Google options just fine and you can minimize your risk reasonable well using it.
The credit default swaps were much more difficult to evaluate because of the lack of an efficient market for them. The essential nature of the underlying instrument were very high risk mortgages, not too different in concept from so-called junk bonds. The potential return was high because the interest rate was high. The potential risk was high because the risk of default was high, making the underlying instrument worth very little, much less than face value. So take these risky mortgages and then buy insurance policies for them, this is standard practice. That hedges the risk of the actual mortgage itself. Bundle the mortgage and the insurance policy up into a quasi-mutual fund like product: you have x number of mortgage/insurance policy bundles with average risk of default at y. Getting more difficult to put a value on, especially since there is no regulated exchange for them and little oversight.
Not done yet. Add in that deregulation rules passed during the Clinton era allowed the banks that issue the mortgages and buy the insurance policies to also use their assets to trade on their own. This group within a group is called "proprietary trading". So, the prop-trading groups within the banks buy and sell the mortgages and insurance policies to each other in order to generate income for the bank. There are also other groups that buy and sell these instruments that don't actually issue mortgages. These are called speculative traders.
Finally, to put the finishing touches on this pile of doo, have a group create a new instrument: a binary option (it does or it doesn't) on a bundle of high-risk mortgages and their insurance policies. A binary option is essentially a gamble: it pays out if something happens, it does not pay out if something doesn't happen. Now you're buying and selling options contracts which predict whether a group of mortgages will fail or not. There's no regulation, no formal exchange (which helps create market efficiency). There's no reliable way to determine the value of the underlying instrument because it depends on knowing how many of the mortgages will fail. And don't forget that the banks were using their investment customers to create demand for a product they wanted to sell ("I think you should invest in such-and-such") without telling the customers that the banks themselves would be profiting by selling questionable instruments to their own customers.
This is the magic of unregulated capitalism (almost - the banks should have been allowed to fail in a purely unregulated capitalism system). Nothing wrong with Black-Scholes here. The real problem at the core is that the banks involved are so driven by short-term success that there is no room for sanity. Wrap it all up with the fact that the banks know they will be bailed out by the Feds if they fail. There is no penalty for risk and no regulatory oversight. Gotta have one or the other or we just plain deserve this insanity.
FRAUD ALERT: It was not a mathematical model that caused the problem. It was fraud. Financial organizations convinced investors that they had a "mathematical model" so that they could steal. The theft was ENTIRELY deliberate, as is described in detail in the 1997 book F.I.A.S.C.O.: Blood in the Water on Wall Street, by Frank Partnoy. Somehow the issues were kept quiet for 11 more years until the theft could be completed in the 2008 financial crash. Traders called their work "ripping the client's face off" .
There are other editions of the book, such as this one published in 1999, Fiasco: The Inside Story of a Wall Street Trader, and a 2009 I-told-you-so edition of the original name.
Nothing has been done to reform the extremely corrupt financial system in the United States. No one in the SEC, U.S. Securities and Exchange Commission, the government organization that is supposed to police financial fraud, was prosecuted, even though the agency knew of the abuses. See the February 17, 2009 show Frontline: Inside the Meltdown.
Even though the U.S. dollar is experiencing rampant inflation in 2012, U.S. banks give less than 1% interest on savings. Those who would like to invest can't because the system is so corrupt it cannot be trusted. Corporations hold unprecedented amounts of cash. See, for example, the October 7, 2010 Washington Post article, U.S. companies buy back stock in droves as they hold record levels of cash.
F.I.A.S.C.O. stands for "Fixed Income Annual Sporting Clays Outing" (See page 100 of the 2009 edition.), held at a shooting range called "Sandanona, a club in upstate New York" (Page 97 of the 2009 edition). Traders would go there to shoot guns. The idea was to encourage their taste for violence so that they would be even more financially violent toward the customer.
Perhaps the April 27, 2012 BBC article, Black-Scholes: The maths formula linked to the financial crash referenced in this Slashdot story was influenced by public relations agencies trying to get people to believe that the crash was caused by errors in mathematical thinking, and not by fraud, so that the financial industry can continue stealing.
It would be helpful if Slashdot editors signed a statement about each story saying that they know of no conflict of interest, and no one was paid to run the story.
So the book presents a hypothetical derivatives salesman (who doesn't exist), says he used to read Time but now he reads Guns and Ammo, and offers that it's no coincidence. Of course it's no coincidence; the same author made it all up! I do think there's lots wrong with Wall Street, but your book sounds like a bunch of sensationalist junk, frankly.
Breakfast served all day!
In the Berkshire Hathaway 2002 Annual Report (PDF file), Warren Buffett said this on page 13:
"Derivatives
Charlie and I are of one mind in how we feel about derivatives and the trading activities that go with them: We view them as time bombs, both for the parties that deal in them and the economic system."
From page 14:
"I can assure you that the marking errors in the derivatives business have not been symmetrical. Almost invariably, they have favored either the trader who was eyeing a multi-million dollar bonus or the CEO who wanted to report impressive "earnings" (or both). The bonuses were paid, and the CEO profited from his options. Only much later did shareholders learn that the reported earnings were a sham."
On page 15:
"In our view, however, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal." [my emphasis]
Warren Buffett, the world's most famous investor, published that in 2003. It was widely reported. No one can say the fraud was unknown, or that the present severe economic problems are due to a faulty mathematical formula.