Recipe for Disaster: The Formula That Killed Wall Street

A snip from this month's WIRED cover story by Felix Salmon about a mathematical formula that played a critical role in the global economic collapse (which is worsening still as I type this blog post). Snip:

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists–even Wall Street quants–have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut–determining correlation, or how seemingly disparate events are related–and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

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. And it became so deeply entrenched–and was making people so much money–that warnings about its limitations were largely ignored.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008–when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

Recipe for Disaster: The Formula That Killed Wall Street (WIRED). BTW, the moral of the story as I see it is that we should STOP MATH NOW! Also: WIRED's other must-read story this month, Dan Roth on the move to bring radical transparency to the SEC. (Via @chr1sa, who I like to refer to as Original Recipe Chris Anderson)

Image above: "The Market Is Not Functioning Properly" by The Joy Of The Mundane, a creative commons licensed image via flickr.

Related Boing Boing blog post: How are you coping with collapse-anxiety?


  1. Seems a bit like blaming Einstein for the atom bomb.
    Anyway, according to the logic of the banking industry, shouldn’t he be given a bonus??

  2. This article was presumably written by hedge funders and other speculators that make up their own currency in IOUs. This creates an economy that can’t be measured effectively, so that any model will fail. Any system that you model without checking it against reality over time will wander away from your cozy “truth”.

    Blaming something concrete and vivid – here’s a simple formula, and look at the curve – is more convincing than the reality of the situation if you haven’t got the time or educational foundation to think it through.

  3. Seems a bit like blaming Einstein for the atom bomb.

    Maybe even a bit like blaming Al Roker for Hurricane Katrina.

  4. It’s stuff like this that seems to lend credence to the “Black Swan” stuff that was posted here a while back. I’m still not convinced either way.

  5. This mess was caused by speculation with borrowed money. Same as in 1929.

    The fault lies not in the math, but in ourselves.

  6. Folks dismissing the blame issue… If you knew the history of the Nobel prize, you’d understand why atoning for one’s sins by actually doing something in real life is admirable. Short story: He felt he had to atone for the wealth he gained from the destructive power he unleashed with dynamite, so he drafted his will to create a prize to award scientific and humanitarian achievements.

    He was a great guy who had a real capacity of understanding the impact his invention had on the world.

    That said, I still think you can blame traders—and not David X. Li—for greed and not understanding tech since anyone who programs or does tech work knows that non-techs often don’t understand or don’t care about tech “quirks”… How many web techs warned about dot-com boom delusions but were ignored, but then blamed when the bubble burst?

  7. Good article. It really helped me understand what caused this whole fucktastrophe (hey look – I made a word!).

  8. Economics is not formulas. Economics is not higher math. Economics is not experimental science. Economics is not even quantitative. Economics is logic applied to the choices that people, and business, make constantly. The logic of marginal value, opportunity cost, uncertainty, and all the rest is as good as it’s ever been — it’s universal as long as time and resources are finite. It’s when you start to say that the demand elasticity of natural gas times the velocity of money, minus the consumer price index, is correlated to the relative humidity in china with r^2=.83, that you’ve fucked up irrevocably.

  9. The story of science: a guy analyzes vast amount of complex data, finds a simple model or a formula – a simlification that fits the data well within specifed limits, regimes, conditions, etc.

    And then people, like the Ohm’s law, start using the sole formula – NOT the theory – as a magical solution wherever they can and wherever they can’t.

    So when the stuff faults, he gets the blame. For trying – successfully – to further our understanding of the world.

    “David X. Li, it’s safe to say, won’t be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li’s Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.”

    It wasn’t his formula that was instrumental, it was the stupidity of the bankers that took the formula as a magical, works-for-all, fool-proof cure for their ilk.

  10. Hi,
    I have been a BoingBoing fan for quite some time although this is the first comment I post. Sorry for my broken english as I have to write this in a hurry.

    I think that the author of the wired article doesn’t know what he’s talking about. The contribution of David X Li is far from groundbreaking. Copula functions have been known for a long time and have been used to model non-independent events way before he formalized the use of a very simple instance of such a function for finance purposes. The problem is in fact that it is too simple. Although this allows market operators to understand the formula and its parameters, it makes the model less realistic, and in the end useless.

    One should not forget that a mathematical model is just a model. Like Newtonian mechanics it can be useful when applied in the correct framework.

    Given how incredibly succesful mathematics is in all sort of aeras, the conclusion of the post strikes me as one of the worst thing ever written on Boing Boing ! Xeni, I assure you math is not the scapegoat here. People like Nicholas Nassim Taleb (who formerly claimed to be a mathematician) are trying to launch this “anti-maths” meme, which I find stupid and dangerous, so I am disapoitned to see it echoed here.

    A much more illuminating piece on the current financial crisis is the two episodes of the podcast “this american life” (giant pool of money and another scary show about the economy) and the blog and podcast “planet money” on NPR.

    Disclosure : I am a practising mathematician. My area of expertise is in probability (random branching structures) but I knoow enough financial math to be teaching it at graduate level.

    Best regards,

  11. Just one word to note that this time it is not the markets that crashed but the banking system. The stock market going down is a consequence of it.

    And one question:
    I’d like for the knowledgeable people here to tell me what would have the banks done with all the money they had to lend if they wouldn’t have gone for the bad risk? Isn’t everybody so loaded with debt right now that there is very little good risk left? Was this crisis even avoidable?

  12. What the story shows is not that mathematics is at fault, but rather the danger of mistaking a model of reality for reality itself – whether this model is religious or scientific.

    There is also a danger when everybody uses the same formula/model, because then they always act in concert, exaggerating any fluctuations.

    – Klaus

  13. Grief, the actual reason is even in the story:

    In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn’t understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.

    Turns out that putting non-technical people in charge of making highly technical decisions is a bad move. Who could have predicted that?

  14. Well, this is weird. I have just been using the same sort of math to try and demosaic images. A raw image from a digital camera has red, green, and blue pixels, but you never have red, green, and blue at one point. You try and work out whether the pixel you are at is brighter than the ones that surround it, and then whether the other colors are correlated with the one you are looking at. You are always working with incomplete data. I have to get something that works for all the pixels in a digital image, and this is really never reliable enough – you have to stir in some model based on a guess on the nature of the underlying image – does it look like we are on an edge or on a texture, or what?

    The problem with the banking model is a bit the same. You are working out correlations on inadequate evidence, and there will be cases where the correlation data will mislead. There is a classic case which they should have prepared for. Most values are not correlated until the market starts crashing, and then all values lock into correlationa with each other, as they are all correlated negatively with time, as everything goes down the plughole together.

    Remember Black & Scholes? That assumed that prices did random walks in value space, and there was no correlation. In such a model, it would be impossibly unlikely for the whole economy to gain or lose value. If I was modelling the economy, that theory would have gone straight in the bin as it clearly no match for reality.

    So, what did they do after the B & S crash? They find some other old and somewhat obscure bit of maths (I agree with JBerest – this is nothing new), but embodying exactly the same flaw as the old stuff. They polish it up. They make some money. They make a religion out of it. It all goes wrong at once, as it clearly had to. They are probably already working on a Mk III theory.

    If you want to get a decent model of the economy, try asking a physicist who has worked with turbulence, or weather prediction, or sea waves or something a bit complicated. I once tried to get a job in a bank, but they wouldn’t take anyone who had ever had a sniff of a real job. I think their ideal candidate would be a single cell raised in a sterile banking environment.

    Which means it’s gonna happen again.

  15. Gaussian? Bah!

    Gaussians are nice because a Gaussian plus a Gaussian is a Gaussian. But there are other distributions that have this property, the whole Levy skew alpha stable family. Gaussian is the prim and proper one in this family. The well behaved one. The one with nice formulae, and a standard deviation that converges. The rest are prone to wild outbursts. Their tails are long, and vicious.

  16. @PFH
    I don’t think that it’s the additive stability property of the Gaussian that makes the Gaussian copula so popular. I think that it’s just the fact that market people “get” Gaussian (and mean, variance and correlation) whereas they don’t “get” alpha stable for instance.

    And anyway you can define a copula function (i.e. a correlation structure) with any marginal distribution you like, you don’t need an additively stable one.

    The idea on market floors, from what I hear, was that they would do a “Black & Scholes” of correlation, i.e. a simplistic model that would allows people to quote and trade correlation.

    It’s interesting to note that some people went as far as filling the correlation matrix of their Gaussian Copulas with a unique value in order to get a single parameter model.

    A great resource on credit and default modelling is

  17. Back in the sixties, it was determined that business school students would benefit from learning calculus. “Take my derivative . . . please!” Applying techniques of calculus to numbers pulled from one’s ass does not cause magical things to happen to money. Repeat after me, “Business Is Not Science.” Yeah, I got an MBA in operations…what a waste.

  18. Ackpht: the fault’s in ourselves, AND our lack of resolution.
    Shapessphere’s line is an arrow aimed at lack of resolution and action.
    Yes, they got the math wrong, but don’t expect the guys who screwed up to be next to you at the bread line.

  19. Business, calculus? WTF!?

    When I got out of college 7 years ago business was either the degree you got when you needed something easy, or it was your 2nd degree…

    I had a suite mate that told us all about how much work he had to do that week. I looked at him, and asked how much. I listened…and then proceeded to tell him of what I had to do. Engineering vs. Business…I won.

    But I digress..

    I think everyone is spot on here. You just can’t come up with some magic formula that describes things like the market (at least not to enough of a degree to be reliable and useful in the real world). When we have a formula for greed, self interest, and emotions let me know. It’s like the generic supply vs. demand charts you see in Economics 101…that isn’t the real world.

  20. Richard Kirk: In fact many Bank presidents have started their careers as young tellers in their banks – at least, it used to be not uncommon as a career path.
    The thing is ,banking really did not need to get so fancy, now did it?
    And isn’t there a law against using real humans in experiments without their informed consent? Why did Regulators give these “brand new things” an easy green light? For whose benefit?

  21. Economics is an attempt to quantize human behavior patterns with regard to the use of money. Which means the use of Power. Good luck coming up with a formula that does that. Here’s the one that Long Term Capital Management used: I won’t bother translating because there is no point.

    C = SN(d1)- Xe-rt N(d2) Where d1= log (S/X)+ (r + 02/2)T and d2 = d1 – sigma(sqr of T) \ [OVER] sigma(sqr of T)

    This formula won the Quants at LTCM the Nobel Prize in economics and it’s pure bullshit. So much for experts in economics.

  22. The markets are working. Why would anyone say the markets aren’t working? The markets are only a reflection of our economy +/- fear or exuberance. That is the equation.

  23. From the article:

    “Li can’t be blamed,” says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the 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. (Emphasis mine.)

    This is the key to the whole problem. It’s common sense, really. If everybody sells, who’s buying???

  24. I agree with Julien above: Math doesn’t kill markets. People kill markets. The collapse was caused by a huge swath of people who misapplied — with confidence — something they did not understand.

    Don’t hold strong opinions on things you don’t understand.

  25. Even if one were to take the story’s claims literally about how ground-breaking this formula is (Julien above seems to make a fair argument against that), it _still_ doesn’t work to blame the math.

    Whether or not it was the case here, it’s true that Math can be used to obfuscate. Mathematical models may not be understood by those who use them.

    You can obfuscate financial reality through other means as well. By creating obtuse contracts. By using complicated book-keeping schemes.

    Given that there will always be fraudsters out to intentionally delude people, and an even larger group who delude themselves, there’s really only one solution: Sensible regulation that prohibits obfuscation as far as possible.

    The problem isn’t math. The problem is why we’re allowing people to engage in transactions so complicated it takes a maths PhD to model them. The problem is why we’ve allowed financial instruments that serve little purpose other than the obfuscation and hiding of financial risks.

  26. Julien (Jberest): I believe what was missed in Xeni’s post is sarcasm. It’s an obscure humor device utilized by humans from time to time.

    [meaning: she was kidding.]

  27. From an article in the WSJ from 2005:

    “The most
    dangerous part,” Mr. Li himself says of the model, “is when people
    believe everything coming out of it.” Investors who put too much trust
    in it or don’t understand all its subtleties may think they’ve
    eliminated their risks when they haven’t.

    It’s not like he didn’t try to warn people.

  28. Two words: Black Swan. There’s a book by that name, read it. And stop applying the Bell Curve to phenomena with recursive chaos. Then maybe people will learn to stop “picking up nickles in front of steam rollers.”

  29. I can’t say that I’m surprised. Why? This is how much of the modern world and technology function nowadays. What do I mean?

    A brilliant mind creates this wonderful/powerful/useful “thing”. They decide to make it popular, cause it will help people/all mankind. Gives it to people, and people find a way to pervert it/ignore the useage label, and the idiocracy find a way to use it to f&%k up everything.

    Or more properly put, Smart people create things that can help society, but leave their work to be used by everyone else, usually stupider (that’s not a word) than them. Thus, people forget or ignore the creator’s wishes/design for the thing, and bad sh*t happens. Story of humanity.

    Moral of the story- smart people, stop giving useful or complex things to idiots. Especially manipulative greedy ones. Problem solved (?).

    Yes, I know, there are examples against this, but my caustic cynicism compels me. Besides, it’s true often enough.

  30. Mathematical formulas are useful as long as the system being modelled stays exactly the same as it was when you did your analysis and nothing sentient inside the system finds out about your formulas. Neither condition is true for long with economic models of any kind or complexity.

    The classic example outside of finance is one of those “bunnies get eaten by foxes” eco-systems. The number of bunnies is inversely proportional to the number of foxes eating them. The number of foxes is proportional to their food supply of bunnies. So you can set up very accurate equations to model the oscillation of the two populations as the fox population goes down because they’ve eaten too many bunnies but then the bunny population recovers because there are now fewer foxes and so on.

    This is fun and all, until some wolves move into the area and start eating both foxes and bunnies. Or someone sets up a farm nearby and the foxes start getting into the hen-house there. Even worse, the bunnies read your study and start modifying their behaviour when a fox population maximum approaches.

    Also, from my memoirs:
    Being a mathematician, Nadreck knew that any datum secured by extrapolation is of doubtful value. He thus knew that the actual probability of Kandron’s coming was less, by some indeterminable amount, than the mathematical one.
    – Children of the Lens (1953), Chapter 4

    So a large part of the problem was that the people running things didn’t have even a High School knowledge of what mathematics is or how to use it.

  31. My understanding is that the apparent correlation of our mathematics and the physical universe is , well, accidental.
    Why any such correlation obtains, is not clear.
    This applies to physics, never mind economics…

  32. I watched a show on CNBC recently, House of Cards, where they interviewed Greenspan about the CDOs and other crazy things that were being sold. His answer was basically: I looked at some of that stuff and it was pretty complex and I didn’t understand it. We couldn’t regulate it or call anyone on it because then the market would have acted negatively.

    Are you kidding me!? The Treasury Secretary didn’t understand what these people were buying and selling, and he wouldn’t do anything about it because the markets might fall?

  33. greensap is being dis-ingenous: the Repub Congress would not provide the tools to regulate: they would not pass the necessary Laws.

  34. Don’t stop math, Xeni, it’s just back to the good old days of multivariate regression and amortized Bayesian statistics for actuarial work.

  35. To: Ugly Canuck

    I just rewatched the interview with Greenspan CNBC has online. He said almost the same thing as you: Congress wouldn’t go along with regulating or doing anything to slow/pop the housing bubble. But what I got from the interview is that Greenspan didn’t even TRY to “cry wolf” because he “knew” the Congress wouldn’t support him.

    What?! Wasn’t he the top financial/economic guy in the country? Wasn’t his _JOB_ to point out things were not going in a sustainable direction and we were headed for a reckoning/crash?

  36. I think this has been one of the most thoughtful and informative conversation threads I’ve read on boing boing.

    Xeni, I assumed you were being ironic/hyperbolic when you said “stop math now!”, at least I hope you were. Not exactly a good sentiment for a geek blog.

    Though it perhaps goes too far to blame this guy for the mess, and it also goes to far to blame math, I think stories like this need to be heeded as warnings about the limits of math. Sure models have had enormous success in predicting all sorts of crazy things, but there are many things which we don’t yet understand well enough to model. Perhaps we will never understand them well enough, perhaps there is no way to make a good enough model to be useful.

    Finding comfort in improperly applied math is similar to finding comfort in god, it gives you a sense of control over something you have no control over. And humans are susceptible to anything which gives them such a sense of control.

    Even in Mark Twain’s time, there were lies, damn lies, and statistics.

  37. The real problem is that the formula is hugely sensitive to the correlation parameter (gamma), which had to be estimated. My guess is that the point estimate might have given a low AAA-worthy probability of default, but the 95% confidence interval was basically the unit interval.

  38. It’s such a shame that someone smarter than Li didn’t step up and mathmatically prove his theory was BS. But hey…we investors wouldn’t have lost trillions of dollars, had a once in a lifetime math lesson and been able to witness a ten year setback of world economies.

    I feel a bit stupid now, don’t I…. But I am not sure I understand the meaning of Xeni’s Sarcasm. Is it an implied criticism of the wired article?

    Anyway, I reacted maybe a bit strongly, because as a mathematician I feel that a lot of people are making the same kind of comments than Xeni’s but very much first degree, and sometimes with a lot of disingenuity.

    There are a lot of points I could go on discussing here : how a lot of physicists were actually hired on wall street, that B&S didn’t “fail” (anyhow what does that mean for an equation to “fail” ? one could discuss how accurate the model is, but I would argue that it is incredibly useful when properly understood), how and why one should be VERY skeptical of everything Nassim “black swann” Taleb says or write (as a probabilist I can tell you that his “fooled by randomness” is one of the worst book I have ever read, not to mention that its sole purpose seems to be the glorification of Taleb by himself), etc, etc, …

    But I begin to feel like in

    this cartoon.

    But for Ugly Canuck : define mathematics please. Would you say that there is some correlation between our universe and the language we use to describe it.

  40. @Jberest

    Please stick around! Real mathematical knowledge is still in short supply. I can’t Xpeak for Xeni, but I think it’s fair to say that Boingboing is not anti-math. I’m told English is hard for non-natives to master, but internet sarcasm has pitfalls for everyone.

    I’d be particularly interested in your take on the Black Swan thing, which seems to be trendy right now. I mean this without any irony or sarcasm at all.

  41. Thanks! The article is a bit one sided, but the comments pull it back. A reversion to the mean of balance; driven by healthy debate.

    Here’s my 2 cents.

    Math is just a support tool for decision making. The author is right that Wall St. has its head up its ass and can’t see the big picture (I was an investment banker, I know), but he’s wrong about math being the issue. Math is there to support decision making by experienced business people. It is not a replacement for business experience. Unfortunately, when used by myopic single focused traders with no real world experience who can’t see out of the walls of their cubes… disaster is in the making…

    If you want to play the blame game, look to Wall St. for taking over-sized, immeasurable risk and relying too much on abstract models, look to the government for not regulating parts of the market (or at least requiring the trades to be transparent to investors), look to rating agencies for sticking their head in the sand and continuing to give high ratings to crap assets (realize that companies can choose an agency to use and agencies feared that lower ratings would impact their revenue as companies would choose competitors), look to mark-to-market accounting which requires banks to value assets at their trading value, regardless of the fundamental quality of the underlying asset…. then… look in the mirror… and realize that the world fed at the troth of cheap credit while demanding outsized returns and punishing companies who didn’t generate those returns.

    Here’s a simple bit of math…all systems revert towards a mean. Of course, the mean might shift, but when you push anything to one extreme, you need to duck, because the pendulum will swing back in the other direction quite hard until the new boundaries of normal variation are established. Hopefully we’ll get there before 2010, but it doesn’t look pretty at the moment. Still, the majority of Americans are working (though scared shitless) and while this might be a rough couple of years, it’s nothing like most of the serious poverty and social unrest that exist in much of the world.

  42. This is the part that stuns me:

    You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A.

    How is that possible? Obviously, the formula must predict that bunching these low-rated securities together gave them a cumulative higher rating, but how? This is where I wish I understood the math that would allow you to arrive at such a conclusion.

  43. JBEREST, may I tender my definition?

    Mathematics is a man-made language that attempts to describe the physical universe at some level of abstraction.

    This is a source of confusion in the popular mind; some people think math has substance outsite of mens’ minds and make foolish statements like “the universe runs on math” or “math underlies the universe” (I always ask them if I might borrow the square root of negative one cups of sugar).

    Mathematical formulae are proven or disproven by reducing them to a form where they can be derived logically from empirical observation and deductive reasoning.

    How’s that?

  44. “#36 posted by js7a , February 24, 2009 8:42 AM

    Don’t stop math, Xeni, it’s just back to the good old days of multivariate regression and amortized Bayesian statistics for actuarial work.”

    The problem is that finally business is gambling. The key is information. You can create your information with statistical analysis. You can create information by seeking other people’s wisdom. You make decisions about inventory, personnel, and finance based on what you believe you know. In the end, though, you have to put your money or somebody else’s down on the green felt if you want to play.

  45. While getting my Masters degree at a certain highly regarded Midwest Business school, I took a spreadsheet modeling class. The professor also did a lot of consulting for many industries. He got to see some of the models companies (including AIG and Goldmann) used for the housing market. He told us that the one thing these models did not account for was that the housing market could go down (he is probably one of the foremost experts on excel and spreadsheet modeling so he knows what he is talking about). We were all stupified, these giant corporations were making decisions based on the idea that the Housing market would continually go up and never drop… crazy.

  46. Or maybe it’s just more convenient to blame a mathematical formula than to admit that systemic greed killed the golden goose.

  47. Jberest: here’s a stab:
    Operations upon and using a set of pre-defined elements, such operations being themselves reducible to a smaller set of non-reducible axioms.
    However, I’m not a mathematician.
    But that’s not so important: “my” point as to mathematics and the uncertainty in the application thereof to empirical matters is better set forth in the text ‘Mathematics and the Loss of Certainty’ by Morris kline, 1982. Links:

  48. Comparisons to Einstein are apt. I think the best comparison here, though, would be specifically to Chernobyl.

    You have a very complex system designed by people who are disconnected from the people who will actually use it. The engineers know how it should work — and in their diagrams, everything is perfectly under control; the math makes perfect sense and as long as reality can be assumed to match the model, everything will be fine.

    Then you have a community of people working on this very complex system, all convinced that the system is actually not terribly complex as long as you just follow a few basic rules; after all, the engineers explained the one part they have to use, and by itself that part is pretty easy.

    Finally, you have pervading all of this the sense that there’s no need for fiddly safety procedures or other lame safeguards, because everyone knows what they’re doing, and to add the burden of fail-safes and redundancy would just slow things down.

    A runaway criticality at the reactor core, or a runaway sequence of credit defaults in the markets — take your pick.

  49. The best description i’ve heard about this formula is it was like designing an airbag for a car that works perfectly in every situation except for a crash.

  50. WMU: I pledge my troth to thee, ye maiden: if thou marriest me, ye shall not ever need feed at the pig’s trough.

  51. WMU: The rest of your comment is very well-taken.
    As a result of mistakes & malfeasance across many players and sectors, everyone’s property is worth a little less, or maybe a lot less: but that hardly makes it all worthless.
    If we all keep throwing stones, all we end up with is more broken windows.

  52. The real Recipe for Disaster is:
    – 10,000 measures of ego
    – Billions and Billons of dollars
    – Dozens of greedy senators and congresspeople for sale
    – Regulations minus good sense
    – Tens of millions of people wanting things that are too good to be true
    – Season with millions of fools to taste

    Mix egos and Billions together. Add in the greedy congresspeople, mix on high. Blend in the greedy senators, mix on low. Pour in the regulations all at once while mixing at the highest speed. Mix the fools with the people wanting something to good to be true separately until well blended. Add the mixed fools mix to the rest slowly, on low speed.

    Add fools until all the fools are gone or the money is gone whichever comes first.

    Serve up to the world as a wonderful thing accomplished by greedy people.

  53. @ITO
    I am not sure I have a very good answer to the question “what is mathematics” beside the nicely circular “it’s what mathematicians do”. But it seems to me that your proposition is a bit like reducing literature to the set of grammatical rules and then saying that therefore it has no relation to the “real” world. Seeing math as a closed language game is a very “Bourbakiste” or Hilbertian view which was very much finished with Goddel, Russel &Co.

    Perhaps what’s happening here is that we are confusing the language of mathematics (i.e. symbols, equations, algebra, etc…) with its substance (i.e. the study of quantity, structure, space, change, and related topics of pattern and form) ?

    What about that ?

  54. jberest@16, didn’t Black & Scholes cause the whole LTCM mess? Again with the Gaussian.

    A simplistic model should yield less certainty than a model of correct complexity. A model should assign some probability to “black swan” events. If it is simplistic, it should overestimate the likelihood of these events, leading to excess caution. Levy distributions would be one way to do this, I’m sure there are others. But fitting Gaussian distributions to economic data is just plain wrong.

    I think that it’s just the fact that market people “get” Gaussian (and mean, variance and correlation) whereas they don’t “get” alpha stable for instance.

    I think that’s exactly it.

  55. @PFH
    Just this and then I really need to stop. Short answer is : no. LTCM did collapse but not “because” of the B&S formula. Things are much more complex than this formula. The B&S formula is merely used in practice to compare the price of hetergenous options through their implied volatility. In itself it is not a strategy for managing a portfolio or making a risky investment (it does give the hedge ration for plain valilla european options).
    What went wrong with LTCM goes wayyyy farther than the B&S formula. What it shows is that you can be very smart and still be a lousy hedge fund manager.

  56. I had a friend on Wall St. dealing with CDO’s, CDS’s, etc. and a few years ago he showed me some models being thrown around the industry and immediately, I told him, “you’re going to regret that Gaussian bit one day.”

    But hey, it made the math easier. It made the math wrong, but easier.

    Sure, plenty of things in the world do seem to hae normal distributions (or to asymptotically approach one), but finance is not one of them. Its a really BIG assumption.

    And then, on top of that, you rely on historical data even though the underlying market stopped resembling the historical market that produced that data. They entirely changed all the rules and practices of the mortgage industry, but still assumed default rates wouldn’t change from what they were before all the rule changes.

    Didn’t it occur to anyone that if you start giving mortgages to people with no jobs, no income, and no assets, that it’d be a bit silly to still assume the historical default rate?

  57. I think we need to see some very greedy people pay. I said this country needed a good enema and that’s what’s needed. The neo-aristos got us in this mess, so now they can lose their heads. Let’s take everything they own and nationalize it. Let’s march on New York and DC. Or maybe not. The second wave of default credit swaps is just about due. Have fun.

  58. Ink mathematics
    Grey mass ecstatics
    Noggin elastics
    Cerebral tactics
    Cranium classics
    Brainium domics
    Grey massmatics
    Quantum pure
    Its plain to feel
    Hard to see
    Fission antics
    Death antiques
    Wrong deductions
    Poor instructions
    Mass destructions
    Peace antiques
    Singing ink mathematics
    Hop along with me
    Ink mathematics
    Moon to a flea
    Ink mathematics
    I breathe black and white
    Day and night
    Grey gymnastics
    Ink math ah ratics
    Ink mathemon to a flea
    Ink mathematics
    Hop along with me
    Ink mathematics
    Moon to a flea

    reprinted without permission (sorry Cap’n)
    from “Captain Beefheart & His Magic Band
    the song “Ink Mathematics”
    from the album Ice Cream for Crow 1981(?)


    Ps Come back out Cap’n, all is forgiven.

  59. Just as an example that this banking/investment stuff need not be rocket science (and that finance has been ticking over in the USA quite well for an awful long time, crashes and wars be damned), here’s an item about some bonds NYC issued just after the Civil War that are just now about to come due for repayment:

    Moral: if your counterparty is solid, there is no reason at all to panic and sell out.

  60. I think the economic meltdown can be attributed to these three major factors:

    1) The United States simultaneously serving the role as global economic superpower, while somehow still managing to run trade deficits for DECADES.

    2) Innovation in financial markets that added a layer of complexity that ultimately made regulation or measurement of the health of the system impossible. The government wasn’t able to see into the opaque system and all the players operated in a myopic world, looking only to beat the market… No serious questions were being asked as to whether new strategies were instilling new structural instabilities in the market itself.

    3) The Internet started to completely rearrange the way society does business. I really think a lot of people tend to seriously underestimate the effects of it. It has touched every industry, and in many cases has transferred business way from large existing structures to new large structures or structures that have yet to be determined. A strong and healthy system would have difficulty coping with this, our structurally fractured system has been driven to the brink by it. The end result is not necessarily bad, but the transition sure is.

    What’s the solution? O-man needs to toss billions, and I mean billions, like 100 billion+ into academic research and lending to venture capitalists for alternative energy research.

    Everybody wants a new energy source, everybody needs a new energy source (without it, there WILL be a third World War) and this country needs to have something to sell to the world again. (It would be bonus points for the US if the technology also were something that started out labor intensive with a few decade time horizon before real efficiency.)

  61. What gets me laughing, because I’d rather not cry, is how many want to blame this whole thing on poor people: poor people bought homes they couldn’t afford; poor people signed mortgages they couldn’t afford; and poor people defaulted on mortgages they couldn’t afford. If it wasn’t for those damned poor people this never would have happened.

    I hate, yes, a very un-Zen like hatred, for any despicable bastard or bitch who blames any of this on poor people, as our wonderful President of and for the people just did moments ago.

  62. The United States simultaneously serving the role as global economic superpower, while somehow still managing to run trade deficits for DECADES.

    That “somehow” is called dollar hegemony. The USD is a reserve currency, so it was being bought up by banks to underwrite other global currencies, which kept the dollar artificially scarce, which made it seem more valuable than it really was, which created the illusion of continuing purchasing power of the dollar for decades of spending.

  63. #48 You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A.

    How is that possible?

    Well the IDEA (pretty well explained in the article) is that if the default risk of the underlying assets is poorly corelated, you can pool and tranche them so that you can create a bond that is safer. Take 100 crappy mortgages, where chance of default on any one is 10% and put them together in a pool. If there is NO correlation between them, you can be pretty sure that the chance of more than 50 of them going bad is small. So if those were all 100k mortgages, you can sell $5,000,000 (50% x 100 x $100,000)dollars worth of bonds that are rated much more highly than the underlying assets, because they are not affected by default rates of less than 50% overall.

  64. foetusnail – What gets me laughing, because I’d rather not cry, is how many want to blame this whole thing on poor people:

    I know. The pirates let some ninja’s into the marketplace as a diversion.

    I think President Obama said it best last night, which I will now mangle through my paraphrasing: The surplus we had 8 years ago was pocketed, and not by poor people.

  65. This thread makes me want to hug a mathematician… and then go trade my English degree for a few higher math classes so I can play in the pond, too.
    Anyone got any recommendations?

    Even aside from that, I am pleased to see the reasonable and rational (who’d expect less from math geeks, really?) discussion, even through disagreement, of this issue.

    I feel something akin to the quietly-close-the-door pride of a soccer mom, watching her kids play a video game of which she has an incomplete understanding, but they are playing quietly and nicely together.

  66. MDH, yes, my wife corrected me and I owe the big guy an apology. What I heard early, as I was typing that comment, was people bought homes who couldn’t afford them, which could mean anyone. Wealthy people bought over their ability to pay too.

    However, what happened to the days when a lender would not lend unless there was a high probability of the debt being repaid? What happened, was the brokers who wrote these instruments never had to accept responsibility, and the institutions the brokers used didn’t give a damn because they sold them as fast as they were written.

    Therefore, I place the blame for this fiasco; first, on Alan Greenspan and friends who refused to recognize the looming disaster and tighten the money supply; secondly, on the brokers who would have lent anything to anyone for a commission; thirdly, on the lenders, who also turned a blind eye and held their noses while selling these rotten tomatoes; and fourth, on the mainly wealthy or upper middle class speculators, the flippers, who swept through communities pocketing the equity and driving the bubble; and last, but not least, our non-existent regulators, the foxes’ friends watching the hen house.

  67. #70:

    Yes, that comment about the interNets changing everything is very true. Especially the parts that hooked up every dummy with connection directly up to the markets. It used to be that you had to physically go to a brokers office where there were people who (presumably) knew what they were doing. There even used to be a requirement (at least in Canada) that the brokers there had to actually know you and your financial situation before letting you place orders through them.

    Now it’s just Mob Rule. Now stock prices are determined pretty much by the same on-line voting systems that pick winners on “American Idol”. So, to a large degree, there are no more “investors” just a mob of day-traders. It’s a waste of time looking into a companies track-record or market prospects because these things are unrelated to its share price: only the rumour-mill matters. What a lot of these Quant were doing was pumping that rumour-mill with stories of Magic Math Formulas that indicated that “A” or “B” was a good buy.

    As an example, I used to speculate in Bio-Tech stocks. I wouldn’t invest in anything if I didn’t understand the chemistry and biology of their proposed products to the point of being able to write out and manipulate formulae and liked what I saw. But that was highly naive of me. People poured money into the stocks (all at once) if they thought that the new technology would raise the dead so that they could dance into the shareholders banks with bags of buried treasure. Anything that hinted at anything even slightly less than that caused a instant panic and a run. After all, thousands of “investors” needed their capital back at the end of the month for their rent so their risk aversion was high.

    Egalitarianism is not a good thing in financial markets. In the current system Ignorance is just another point of view and it gets equal weighting with every other point of view through on-line discount brokerages. If one good thing comes from the current meltdown it could be that the people who, in their aggregate millions, pour incredible amounts of money into Nigerian Letter scams get burned enough to keep them out of the systems that manage our economy.

  68. BTW, the moral of the story as I see it is that we should STOP THE IRRESPONSIBLE USE OF MATH NOW!

    There, fixed that for you.

    I’ve always wondered about MBAs–and business majors in general–getting away with light, even ersatz courses in math, statistics, and programming. We could really stand to have more meat on the neurons before this nanotechnology thing starts working. See also “The Sorcerer’s Apprentice.”

  69. Nadreck: The market is anti-inductive.

    Adam Weiss: Third world war? Will we first agree not to use the nukes/bio-war that we know can destroy all human life?

    Oh, and here’s a youtube vid of “Ink Mathematics”, the lyrics to which I posted above – I keep forgetting that this is the internet:

    It sounds better than it reads.

  70. Anti-inductive, in the mathematical sense. More on this notion:

    I know that you know that they know that you think that I think that they think that I know that they know that you think that the price is going….[up OR down]…tomorrow, and they will invest their money accordingly.
    What the Market will do in the future is not inductive a la knowing whether or not the sun will rise tomorrow: the past has not the same weight in the calculation.
    Particularly so, if one considers the role of the knowledge of the past, compared to the role which the weight of real money, plays in the Market. That is , it plays no role at all: the money is the force: the bid and the ask must meet, or there is no Market.
    It is a completely and utterly a question of price. And most importantly, where it will be in the future, although all we can know is the present and the past: math cannot get past this present unknowability of futurity.
    And what is investment, if not a view taken of the future?

  71. JBEREST, I am sorry, I missed your reply weeks ago.

    As you noted, I usually think of mathematics not as “what mathematicians do” but as “the language that mathematicians use”. Like so: an axeman does not axe, he uses an axe.

    I have presumed that what mathematicians do is study the nature of reality and attempt to model it in ways that will allow greater understanding than can be obtained by directly experiencing real phenomena.

    It seems to me that when you say mathematics is what mathematicians do you simultaneously trivialise your work and unneccessarily elevate the toolset.

    But I am not a mathematician, so unless an outsider view is beneficial here my words will have little worth.

  72. Dr GIZMO says…as easy as pi…
    Yes, what a mess… how did this happen…
    All you math guys think of this … make a circle look inside it you see finite area right… but it is impossible to have or even know the area inside…to a mathematical certainty…because of pi… now that is nature…most things natural (alive) are made from curves and circles…they use pi.

    Nature does not fit…it does not do math very well…a lot of uncertainty in natural things Understanding nature is a guess all the time…like the weather…like global warming.

    Now …look a square… that is about the same size look at the area inside that area…it is also finite, but now we can know to a mathematical certainty the area… unlike a circle cause we do not deal with pi.

    Man makes squares, because we like to deal with certainty… but, natural living things makes circles and curves … because uncertainty is the best way to survive in a mean and harsh world of reality.

    Look at an economy is it not a natural thing… made of living human actions … human wants and desires, ecology, decisions and of course time…

    Is there any wonder why it is so hard to predict with certainty what a economy will or will not do…it is natural it is and always will be a guess…the area inside a circle… it is pi…if you doubt this you are either a fool, or ignorant, or ID10T…or perhaps Keynesian economist which my view are all of them.

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