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Math The Almighty Buck Science

The Math Formula That Lead To the Financial Crash 371

Posted by Soulskill
from the can-we-blame-fermat-for-this dept.
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."
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The Math Formula That Lead To the Financial Crash

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  • by Anonymous Coward on Saturday April 28, 2012 @10:51AM (#39831757)

    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

  • old news (Score:3, Interesting)

    by Anonymous Coward on Saturday April 28, 2012 @10:54AM (#39831773)

    This was covered by the guardian a whole two months back. Link [guardian.co.uk] Partly debunked here [forbes.com]

  • Re:Don't blame math (Score:5, Interesting)

    by Anonymous Coward on Saturday April 28, 2012 @11:12AM (#39831845)

    The real problem is that the "solution" - bailing out of the banks by the governments that were the source of the problem, is no real solution. It creates a delay. And while a delay was certainly necessary once they let it become as bad as it became, it will just repeat. A lot of Hedge funds are going to become rich - again.

    Solving the problem would take a prolonged crash that lasts - well lasts until the system rebalances. That sounds cute in theory but in practice it means that it must last until the baby boomer retirees (a big portion of them) are dead. It also means Obama and the democrats have chosen very close to the worst moment in the nation's history for their national healthcare. It will be a disaster much sooner than even the worst of the republicans projected. It will become a disaster in the next 3 years.

    And nobody can really do anything at this point - well I guess baby boomers could commit suicide in large numbers but ... - it's like watching a ship about to crash from the top of it's deck. There's nothing to do but watch. If you're a hedge fund manager you play a few games betting on the ship crashing while the captain assures everyone everything's fine and the ship is unsinkable.

    This situation also means the real crash hasn't come yet. It will happen not this year but by the end of next year.

  • by circletimessquare (444983) <circletimessquare AT gmail DOT com> on Saturday April 28, 2012 @11:35AM (#39831937) Homepage Journal

    the purpose of a tool has a meaning

    give everyone a toilet brush, toilets will get cleaned. give everyone a hammer, nails will get pounded. give everyone a gun, people will get shot

    the availability and easy access of a tool with an intended purpose and meaning makes certain outcomes easier. it's not complicated

    the tool itself, and the presence of the tool, has significance. we all reach the limits of our temper at various points in our lives. we will confuse our teenage son sneaking into the house in the dark with an intruder. we will be drunk and clumsy. and in those situations, whether or not a gun is in easy reach radically changes the outcome of the situation

    the purpose and presence of the tool matters

    the proper quote is

    "guns don't kill people, people with guns do"

    if you want guns to be legal, fine. but don't depend upon flimsy easily dismantled logic to justify your beliefs

  • by TubeSteak (669689) on Saturday April 28, 2012 @11:39AM (#39831963) Journal

    Deregulation, not models, permitted bad behavior.

    Banks were faking/changing loan documents, lying to customers, and pushing customers into bad (but profitable) loans.
    All the regulation in the world won't help if there's no one enforcing the rules.

  • Complexity theory (Score:5, Interesting)

    by Anonymous Coward on Saturday April 28, 2012 @11:41AM (#39831995)

    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

  • by Futurepower(R) (558542) <MJennings.USA@NOT_any_of_THISgmail.com> on Saturday April 28, 2012 @12:17PM (#39832207) Homepage
    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 [npr.org], 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" [lbo-news.com].

    There are other editions of the book, such as this one published in 1999, Fiasco: The Inside Story of a Wall Street Trader [amazon.com], 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. [pbs.org]

    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. [washingtonpost.com]

    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 [bbc.co.uk] 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.
  • Re:typo in headline (Score:2, Interesting)

    by Anonymous Coward on Saturday April 28, 2012 @12:53PM (#39832397)

    Yup, whenever you misspell a word or write a malformed sentence, it's not a mistake. It's a contribution!

    In fact, you're a genius, on a par with Shakespeare. The language is just too small to contain your brilliance.

    Well done you.

  • Re:economics ? (Score:5, Interesting)

    by MickLinux (579158) on Saturday April 28, 2012 @01:11PM (#39832517) Journal
    The complexity of the system largel invalidates the scientific method's assumptions, thus greatly limiting the applicability of the reasoning. That is why, for sufficiently complex systems such as economics, psychology, sociology, or theology, other assumptions must be used. That doesn't emean that those who study such things are irrational. It just means that the tools and judgement of results must be different. Alchemy was once also at such a stage-- but today it has advanced to a science(except at the University of Utah).
  • Re:Don't blame math (Score:5, Interesting)

    by tqk (413719) <s.keeling@mail.com> on Saturday April 28, 2012 @01:25PM (#39832629)

    These should have been rated as entirely high risk (being a collection of mortgages that, due to the first CDO, were almost guaranteed to fail) but gullible ratings agencies still gave the top tranche a top rating. So investors worldwide were buying crap believing it to be a low risk investment.

    The ratings agencies weren't gullible. They were in on it too. They were paid for their ratings by the people asking for the ratings. If they'd done their jobs and rated them poor, those buying the ratings would go elsewhere for them.

    The ratings agencies ought to be sort of like Consumer Reports. Instead, they are just another business out to make a quick buck like everyone else. Investors should have seen this coming, but no-one thinks long-term investing anymore. Fundamentals? What are those?

    I agree with those above who say it hasn't finished yet. The bailouts just bought the Too Big To Fails some time. They should have been allowed to fail, but politicians couldn't accept that when their cushy jobs were on the line.

  • by bzipitidoo (647217) <bzipitidoo@yahoo.com> on Saturday April 28, 2012 @02:40PM (#39833025) Journal

    Fraud is a big problem, but not the worst problem. I've grown concerned that we're all engaged in mass delusion. We think the world works a particular way, but we may be wrong. We can produce what seems to be supporting evidence. I am referring to a much more fundamental idea of finance: the formulas for rates. They're neat and simple, and wrong. Implicit in compound interest is exponential growth. The universe doesn't support exponential growth.

    Historically, depending on who you talk to, the stock market has averaged an annual rate of return of 7% or 10% or even more. But that record is only about 100 years long. Can the stock market keep up 7% growth for another 100 years? If it can, how about 1000 years?

  • by micheas (231635) on Sunday April 29, 2012 @12:23AM (#39835519) Homepage Journal

    Does it enter into it that the sales people targeted people likely to have a lack of financial knowledge?

    I know of no DINK (dual income no kids) households that entered into neg-am loans. I know of lots of single women, and people that were have minimal English skills (enough to get by, but not enough to understand a legal contract, whether because of lack of education, or English being a second language that they had not yet mastered.)

    The real idiots are the investment managers that bought the Asset Back Securities. Those people should be barred from managing anyone else's finances under any situation, and probably have their own assets put in a receivership for their own protection, a la Britney Spears.

    Reforming the bankruptcy laws so people can keep their primary residence requires repealing existing law, not creating more law.

  • Re:economics ? (Score:5, Interesting)

    by gadget junkie (618542) <gbponz@libero.it> on Sunday April 29, 2012 @07:24AM (#39836757) Journal
    I may agree that "inability to test hypotheses" is part of the problem, but there a wider issue here: a "political" inability to assess if the price of complexity is less than the advantage it does.
    There's an example here pertaining the US. The Glass-Steagall Act [wikipedia.org], promulgated after the 1929 financial crisis, had a fundamental assumption, which can be broadly stated like this: "while financial markets are essential to an efficient allocation of financial resources, it must be kept by law separated fromthe mechanism of transmission of monetary policy to the real economy. It ensues that no economic player must be allowed to participate in both systems, either as principal or agent"
    . Fast forward to 1987, and the the president of the federal reserve, Alan Greenspan, urges a repeal of the law. what did he know that was unknown in the thirties? why, nothing: he was only convinced that advances in law, mathematics, economy had rendered the safeguards obsolete.
    Guess what? future contracts were known in Roman times, and the first financial contract I've seen printed is in cuneiform on a tablet, circa 2.000 B.C; the only significant innovations in banking since the Hammurabi code had been the supervision of the banking system, including the obligation on the banks to actually have some equity money on the balance sheet, and.... the Glass Steagall act.

    coming back to the topic, the impact of the Black and Scholes formula was not only on the ability to "price" an option, assessing an hypotetical fair value, but on the fact that it provided a toll for big financial houses to "hedge" [wikipedia.org] their exposure dynamically, therein being able to actively propose derivative trades to clients instead of matching opposite client's views. The market expanded greatly, but so did the dependence of the assumptions of the models being right: continuous market access, infinite liquidity, both on the long and the short side. etc.

    Lo and behold, everybody and his uncle played derivatives (Enron anyone? an electric utility, a business slightly less boring than watching grass grow, going belly up?!?!), and it has been impossible to separate the impact of the disaster on the financial markets and on the real economy.
    Think about this: when Long term capital [wikipedia.org] went bust, if you were a shopkeeper in Illinois you had a more than 50% chance of not knowing about it, let alone feeling the heat of the aftermath; now shopkeepers tremble at the sight of the Wall Street Journal.
  • by Grumbleduke (789126) on Sunday April 29, 2012 @03:55PM (#39839133) Journal

    Shortly after acquiring a maths degree I was interviewed for a job in a certain major investment bank, to deal with their "really complex" deals. In preparation, I was given a bundle of notes on the maths behind trading, including the Black-Scholes 'formula'. It was quite interesting, essentially being an application of Brownian motion [wikipedia.org], with some fancy economic terms involved. So basically, the whole financial model is based on the fact that they have absolutely no idea whether stuff will get better or worse, so just add layer and layer of complexity to try to even it all out.

    Of course, that's only half the problem with the financial industries. I then actually went to the interview, and it turned out the job seemed to involve simply keeping an eye on spreadsheets to see what they're doing, rather than any actual maths. The person interviewing me (who would have been my boss's boss) clearly had no clue about any serious maths, or the differential equations underpinning his entire industry, but had a firm handshake and sounded confident.

    Needless to say I didn't get the job, nor want it. But it doesn't surprise me that there was a massive financial crisis - the whole sector seems little more than a confidence scam on the rest of society. "Give us your money and we'll make you more money."

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