Journalists argue over which math equation killed Wall Street

In the 2009 Wired mag article “Recipe for Disaster: The Formula That Killed Wall Street,” writer Felix Salmon blames the Gaussian Copula Function for the financial meltdown in American markets.

A SciAm article today by Chris Arnade argues that another equation is more to blame, and that it "requires nothing more than middle school algebra to understand and is taught to every new Wall Street employee. It is leveraged return."

In other words, the return on assets using borrowed money.

* NB: Same Chris Arnade whose beautiful photography we've featured on Boing Boing before.


  1. Are you telling me it was merely misapplied maths, and not thievery? I call shennigans! Using Other People’s Money has been an ingrained habit, I am sure they meant well, but things got out of hand, and here we are today.

  2. I can’t determine which equation was responsible for the last economic crisis, but I am certain that this equation will be responsible for the next economic crisis: Number of Wall Street executives prosecuted for financial malfeasance = 0.00

  3. I suspect the return on investments made in political lobbying are the ultimate culprit. In other words, the donations that led to elimination of Glass-Steagall.

    Plus whatever mad-cow disease made anyone think Greenspan was anything more than a delusional hack.

    1. Yeah, it’s pretty clear that Graham-Leach-Bliley gave the Federal Reserve the power to enact the types of controls that Glass-Steagall had in place, but that power was clearly misplaced.  And as you correctly identify, Greenspan’s idea to replace the NASDAQ bubble with a housing bubble makes ‘delusional hack’ a kind description.

      But the root of the problem is all the phony credit that the Federal Reserve enables in the banking system.  None of the banks, even without Glass-Steagall, gambled insured deposits in the investment system.  But they did use those deposits for leverage, and as the article points out, that ratio went up and up (or the requirement down and down).

      Historically speaking, reserves below .2 are unstable and reserves around .25 are considered reasonable (by many but not all).   But the Federal Reserve is complicit in frequently having banks at reserves at or below .1.  Nobody but the banks who get that money and the Federal Reserve (whose board is composed of many of those banks) think it’s a good idea, though (OK, the politicians who get money from those banks agree).

      The problem for ordinary people becomes that the banks can take that 10% and through the central banking system turn it into 100% (or 100% to 1000% depending on perspective) but regular people can’t do that.  So the real value of regular peoples’ savings gets evaporated as the total size of the number of dollars in the economy explodes, but not theirs.  That’s how the banks transfer wealth from the people to the oligarchs – through the central banking system.  Nobody would ever accept risks at that level from a bank that wasn’t guaranteed by the taxman.  But the taxman takes almost all of its taxes from the middle class, so in reality they’re funding their own demise.

      So, yeah, Glass-Steagall is a way to keep a fundamentally volatile and unjust system from eating itself.  And Dodd-Frank and Sarbanes-Oxley try to protect that system too.  But that shouldn’t be our goal.

        1. Nice article – thanks for the link.  Providing more options is definitely the right approach.  I think a public bank can be one of those options, but it would sure be nice if people weren’t forced to use the public bank (like they’re currently forced to use public currency despite what the Fed is doing to it).

          Another aspect towards returning to how banks are supposed to be is taking some personal responsibility.  How many people would walk into a place that looks like a tiny convenience store on a typical city block, with one poorly-dressed clerk, but they have a piece of cardboard from a soda flat written in marker on which it says “& Bank” taped to theTony’s Convenience Store sign, and then they just give Tony $10k to deposit?  Nobody does that.  Tony might not even have a good safe.

          But they will walk into a brick building with glass doors and marble tile and three ladies in pantsuits behind a counter and give them their money eagerly, when by midnight it might be invested in some mortgage-backed derivative securities or on a high-frequency trading account.

          The real trouble is that the FDIC will guarantee the deposits of the latter people so they don’t care and the banks don’t really have to worry about the repercussions of failing as far as customer service goes.  This is how we’ve currently aligned incentives.

          Really, what we should be interested in is having a legitimate insurance company backing those deposits and that insurance company auditing the bank, profiling its investment strategies for risk, and making those risk profiles known to us (like bragging about their risk rating on a radio ad).

          But that takes some trivial level of thought which we want to avoid, so we let the government “handle it” and tune in for the next episode of “Banks Gone Wild” on the nightly news, which never mentions that WE are going to be paying for all those bailouts for the next hundred years in the way of impossibly high taxation and a low standard of living.  “Maybe we should have paid attention” might be the new catch-phrase in another few years.

    1. I’d say that greed and stupidity are co-factors. Look at Bernie Madoff. Would you have gotten yourself into that situation?

      1. Madoff had nothing to do with the housing bubble.  The basic point behind the housing bubble is the question of whether a bank that gives out a loan it knows can’t/won’t be repaid is liable for fraud, which it is under the law, which is not being enforced.  That is the sad joke.  There are literally hundreds of laws we could’ve used to prosecute these loan-fraudsters but we simply don’t.   Because the prosecutors are buddies and colleagues of the criminals, and they all drink from the same money spout.

        Its the corruption:  of the law, the courts, the lawyers and of course, fractional reserve banking (but that’s always been corrupt and gamed).

        Those who make loans in bad faith should be prosecuted extremely harshly, as the root of the ongoing economic crisis in the west is the direct result of that activity.  Clear due diligence rules and common sense must be imposed on lending decisions.

    1. Well, however greedy wall street executives may or may not have been, it wasn’t in their self interest to kill the economy / drive down the market. That hurt everyone — it hurt the already-wealthy much less than it hurt others but it was hardly a win. So in that sense you could argue that the math failed. No one actually wants to destroy the world. That’s a cartoony, Captain Planet view of evil. So if these guys were evil geniuses, they were failed evil geniuses who got the calculations wrong.

      1. I’d be willing to chalk up the collapse to incompetance, since you’re insisting that it couldn’t have been malice. 

        1. I’m chalking it up to people with their priorities wrong. They valued their personal/corporate income over the stability of the financial system.

          1. Everyone values their personal income above the “stability of the financial system”. WTF does that even mean, in practical terms, and how would it affect your personal decisions?

            Would deep concern for the stability of the financial system stop anyone try to get a mortgage for their dream home if they can just about wangle it now; you know, you can get the figures worked out with a financial advisor and it looks okay.  What happens if you have kids or one of you gets laid off?  Better not worry about that….

            It’s the same rules that apply on Wall Street. If you’re looking to apportion blame, blame the people who over-leveraged themselves as much as the people who lent them the money. No one put a gun to their head and told them to borrow… in fact, if anything, the coercion is worse in Wall Street: Try telling your boss you should get out of the market while all your competitors are long and raking in money. You’ll have a very understanding boss if you last more than a quarter. 
            The quote goes – “The market can remain irrational longer than you can stay solvent” – – the market certainly can stay wrong longer than your boss will put up with you losing money while your competitors are raking it in.

            The same applies, of course, to personal finance.  You can apply sound arguments to the overpricing of the housing market all you like, but if your friends are makings lottery money on their leverage property portfolio, even if it’s unrealised, your spouse is only going to listen for a limited time.

      2.  Another possibility is the greedy executives in question actually realized that much of the economy’s value was illusory and that the economy seizing up and deflating a bit was inevitable.  In this case, their best move wouldn’t be to try to prevent such a seizure but to use the confusion as an opportunity to funnel as much real value into their coffers as possible before the train went off the rails.

        If that’s the case then they were evil geniuses who got the calculations right.

        I don’t think many people really believe people in that sort of position go out of their way to be evil.  I think it’s mostly pretty obvious that such people are selfish and fool themselves into believing their selfishness is a virtue.  It’s all part of the “banality of evil.”  Mussolini didn’t consider himself evil, he considered himself the savior of Italy (as did many Americans prior to WWII).

        1. OMG. I need to go to bed, but there’s someone wrong on the internet…..


          For starters, “no man is a villain in his own eyes”.

          Of course Mussolini didn’t consider himself evil. He thought, probably with all sincerity, that he was doing the right thing.  As did Stalin, Hitler, Pol Pot, and the people in Rwanda.

          People don’t go out to commit acts they consider evil (YMMV, IANAL, there are nutcases in the world, etc pp. And there may be a few deranged satanists who try to prove me wrong).  People try to do what they think is right.

          The problem isn’t getting people to do what they think is right. Even psychopathic murderers don’t do things *they* don’t think are right (IMHO, IANADoctor).

          FFS, do you think either of the sides in any war ever fought thought “We are wrong, but let’s have a war anyway”?  

          1. Many criminals, large and small, are completely aware that they’re doing things that are illegal, unethical and immoral.

      3. it wasn’t in their self interest to kill the economy

        Ahh… “rational self interest” such a charming notion…..

        It’s hard to see elite business doing anything else but deliberately extracting wealth because they knew/know they can get away with it. And how again did this hurt them? Their lobbyists and undue influence made sure their companies were bailed out, their bad debts were transferred to the backs of taxpayers, every one of them got record setting bonuses regardless, and not one person brought up on charges.

        Yeah, “cartoonish”… It certainly is…..

        1. What, of course, you don’t get, is that their bonuses would have been even higher if the economy hadn’t tanked.  So where’s the incentive to cause problems?

          It’s hard to see anyone in economics doing anything but work in their own short term interest (mainly because most people can’t see their long term interest).  In London, tube drivers regularly go on strike to increase their already ludicrously inflated salaries – after all, their job largely consists of being alive enough to press a “dead man’s switch”.  A couple of people win; millions lose in inconvenience and higher transport costs; long term, hopefully, someone will have the guts to automate them out of the way.

          Their lobbyists and undue influence made sure their companies were bailed out, their bad debts were transferred to the backs of taxpayers, every one of them got record setting bonuses regardless, and not one person brought up on charges
          As a career banker, I completely agree that bailing out banks is wrong.  There are – tried and tested – mechanisms to kill a bankrupt bank on Friday, and have the good bits of it operating again on Monday, leaving retail depositors unscathed, and equity and bond holders (sophisticated investors, whose job, on the whole, it is to understand the risks) carrying the can.  The fact that this didn’t happen in the US, UK, Ireland is entirely down to the elected politicians in office at the time – don’t blame the banks. If you believe your country will be better off or taking on the debts a private, risk taking organisation misvalued to the extent that they need a government bailout – well, let’s be frank, you’re an idiot. 

          Gee’s, is that the time? I have to wrap up:

          Every economic actor is selfish. Unions, capital….

          Everyone tries to lobby the political powers – but, ultimately, the politicians are responsible for the decisions they make.

          1. What, of course, you don’t get, is that their bonuses would have been even higher if the economy hadn’t tanked.

            There’s no material basis for that claim. Many of them were awarded bonuses in the tens of millions and were quite shocked when popular opinion got the government to intervene. They believe that they deserve all the money in the world and that anything that gets in the way of their greed is an anomaly. And they’re quite right on the latter part.

      4. Well, however greedy wall street executives may or may not have been, it wasn’t in their self interest to kill the economy / drive down the market.

        It wasn’t in the collective self-interest, but the individual decisions that brought down the economy were absolutely made in the individual self-interests of those involved. The system was set up in a way that gambling with other people’s money was all reward and virtually no risk. Otherwise those executives wouldn’t have been getting “bonuses” after the house of cards came tumbling down.

      5. Well, however greedy wall street executives may or may not have been, it wasn’t in their self interest to kill the economy / drive down the market.

        Incorrect. Somebody once said that a depression is when the money returns to its rightful owners – the rich.

        In a good economy, middle class people invest in stocks and property. When the economy goes bad, rich people can afford to sit it out, while middle class people have to sell at a loss in order to survive.

        Economic crises are engineered so that the rich can periodically harvest the resources that have been pumped into the system.

        1. Midas shovelling his workers, along with the ore, into his smelters when there is not enough ore to keep the gold shining.

          Does that work for Midas?

          But that may not stop Midas from trying or, probably more likely, failing to try something that might keep his smelters going and his workers happy at the same time.

          When something is never enough, something is never enough.

      6. Wall Street executives were no greedier than the people who thought they could buy a house they couldn’t afford and sell it in a years time for a profit. 

        But absolutely, no one set out to destroy the economy, any more than heavy metal bands in the 80s (OMG I’m old!!:) encoded suicide messages in their songs to get their fans to kill themselves.

      7. Wrong.  The banksters who ran the banks made tens/hundreds of millions in bonuses by destroying the banks they worked for.  They didn’t care about the future, of the economy, of the banks they worked for, of anything but their bonuses.  They had a term for it:  “IBGYBG”  (I’ll be gone, you’ll be gone).

  4. Math caused me to shoplift a video game once! The game cost $45. I did some calculations and realized that $45 > $0. Therefore, I had to steal the game to minimize my losses. If only the linear ordering of the real numbers had never been taught to me! I might never have committed that felony. 

  5. The only way to stop a bad guy with math is a good guy with math, but I’m no good at math, so anyone with math must be a bad guy.

    1. I suppose even a math dummy could keep a guillotine blade sharp and release it at the appropriate time.

  6. The failure was pure fraud/greed (read Michael Lewis’s “The Big Short”).  I wrote an article defending the Copula math (but not the application!) at the time:

  7. I think the most revealing formula wasn’t calculating leveraged return, but demanding that next year’s profits must exceed this year’s profits, and this year’s profits must exceed last year’s. It’s a demand to suck more and more out of the real economy, to create worse and worse bubbles, to destroy more and more out of the environment, and to leave less and less for the people.

  8. I think math is a bigger problem than greed, because math affects people.  But the universe limits what we can do about math, while Congress limits what we can do about greed.  So I’m gonna wait and see…

  9. Go back a couple of crashes to the junk bond LBO bubble, and compare the insights from Michael Lewis’ book /Liar’s Poker/ with the testimony in Michael Milken’s trial.

    Lewis pointed out the huge cultural divide between quantitative analysts and salesmen. A salesman is, not just on Wall Street but everywhere, someone you can tell “I need this to sell for $x” who will, then, take personal responsibility for convincing himself that the item is *actually worth* $x. One he does that, he can tell customers in all sincerity that the item is worth $x, and selling for $(x-y), which makes it a bargain. And since humans lean hard on rhetorical proof, and since the standard for rhetorical proof is “if the speaker is confident and sincere then the proposition must be true,” it works every time.

    A quant is someone who works long hours to try to determine what, exactly, the item is actually worth. This information is of almost no use to the salesman. So the only use a salesman has for a quant is that he will read the quants reports, or listen to the quant’s lectures, letting all of it wash over him until he gets to the one or two sentences that he needs to convince himself that the thing is actually worth $x. Imagine a quant explaining that a certain narrow subset of items is, under narrowly drawn circumstances, worth a range from $z to $x, assuming that the dataset that the calculation was drawn for is correct, and assuming that outside conditions don’t change. What the salesman hears or reads is “Unimportant blah blah blah item blah blah blah is worth blah blah $x blah blah who cares about the rest of this drivel.”

    Which is why everybody remembers and villainizes Michael Milken, who corruptly sold junk bonds, not Ivan Boesky, the quantitative analyst who told him that under historical conditions (that no longer applied) junk bonds were under-priced.

    *That’s* the role that the copula function played in the subprime mortgage collateralized debt obligation bubble. Buried in it was the couple of out-of-context phrases that the salesmen needed in order to convince themselves that it wasn’t a bubble, that it wasn’t fools overpaying for assets and counting on a greater fool to come along and take it off their hands before the crash.

    So, if anything, the crash was caused not so much by any mathematical equation but by one simple nearly-universal legal principle: “caveat emptor” (let the buyer beware). Without a contradictory legal principle of “caveat lector” (let the seller beware), without a legal system that holds sellers liable for selling things that are not suitable to the buyer’s stated needs, all of the incentives will still be in place to reward salesmen who sell things for what they can convince themselves it’s worth, not what things are actually worth. You can’t make the salesman listen to the quantitative analyst’s quibbles and qualifiers as long as he’s not going to be the one taking the loss, or even the blame, if what he says turns out not to be true.

  10. A very easy and simplified equation: business is done with immediate profit in mind = Lorng term is effects are overlooked or dismissed as irrelevant.

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