The Math Formula That Lead To the Financial Crash 371
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."
economics ? (Score:5, Insightful)
Nobel prize in economics.
that's Nobel prize in pseudo-science.
Don't blame math (Score:5, Insightful)
It was human stupidity and greed.
Guns are don't kill people (Score:5, Insightful)
No need for Black-Scholes to account for things (Score:5, Insightful)
well known in econ circles... (Score:2, Insightful)
The one in 98 (yes there was one there the US gov fixed that one then kept it fairly quiet). Then the one in 2000 and the one in 2003 and the big one in 2008.
Hedge funds are killing us with 'liquidity'. But for a short time they make us boatloads of money!
The way it was explained to me was *IF* the market does not move in one direction or the other much this formula works. If it starts to move in either direction your going to get hit...
Re:No Really (Score:5, Insightful)
Re:No need for Black-Scholes to account for things (Score:3, Insightful)
In this case, Black-Scholes led to the excess credit by creating too much investor confidence in the loans being given. Because it models risk as a thin-tailed distribution, its use systemically encourages risk taking.
Re:Guns are don't kill people (Score:5, Insightful)
People do. The downfall was made by people using tools (like that formula) without understanding all that required or implied.
Quite so. A risk evaluation that says "95% of the time you will lose less than X" implies "5% of the time you will lose a more than X".
With the stinger being that it says nothing of the range and distribution of values of "more than X".
Re:Don't blame math (Score:3, Insightful)
Re:Guns are don't kill people (Score:5, Insightful)
A math model? That must be a fancy name for (Score:5, Insightful)
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 [slashdot.org]. 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.
Re:Don't blame math (Score:3, Insightful)
It was human stupidity and greed.
At least the stupidity part is shared with the slashdot headline. It should be "led" (verb, past tense), not "lead" (noun, heavy metal / verb, present tense).
Re:No Really (Score:5, Insightful)
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.
Re:Don't blame math (Score:5, Insightful)
Not only that, but it also sends a very, very dangerous message to the banks: Playing risky with high stakes is the way to go. If you win, lots of money for you. If you lose, you get bailed out.
That's NOT a sustainable business model. Impending crash notwithstanding, this idiocy alone would already suffice to send the economy down the drain.
Nothing Wrong With the Math (Score:5, Insightful)
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.
Re:Don't blame math (Score:5, Insightful)
Empathy is 100% responsible for the crash. ... It's when those with empathy are given power... that's when feel-good-everyone-can-afford-what-they-can't-afford bubbles happen.
Riiight, because Wall Street traders are known for their empathy above all other qualities.
What color is the sky on your planet?
Re:Don't blame math (Score:4, Insightful)
If I see that you are hungry and I sell you food for a profit, you call that empathy ? Or is it only when my business failed because I didn't calculate my margin properly, that you blame empathy ?
Bankers thought they could make money off people with no money using their clever formula. They were wrong. Some of them maybe thought they were making the world a better place (empathy), but at the end of the day they were in it to make a profit.
Re:economics ? (Score:0, Insightful)
How is that pseudo-science? An economy is a highly complex system. An economist makes observations about that system and forms a hypothesis to explain his observations. In other words, he applies the scientific method to the system just like any other scientist would do when studying other systems.
Re:Don't blame math (Score:5, Insightful)
Except that it's banks making the decisions, and governments writing rules that allow them to do various things, and create environments that cause problems.
Human greed always contributes. It is both what drives our economy forward, and causes it to run into a wall occasionally. We always want something just out of reach. It gives us something to work for, but it also means that if you overestimate, even by a few percent you can cause a 'bust'. When the people doing this are controlling (not necessarily owning, just controlling) 80% of the countries wealth with a relatively small handful of people you can see where this goes badly.
To use the example given, if there's a 10% chance of loans not being paid back, but for the last 5 years I've only had a 3% default rate rather than 10, either
1.The 10% chance of failure estimate is wrong,
2. this is an effect that's longer than 5 years or
3. I should be allowed to change how I count the difference. (the lag effect is long enough I should be able to do something else with the money rather than just sit on it for another 5 years sort of thing)
Enter the government, who, by the way, is largely run by people who have money, and as an institution cares very much about investment returns and interest rates, and they look at your problem. The government probably set the 5 year threshold, it may not have any connection to anything that matters, but it seemed like a good number when someone thought it up. It's possible my estimate is wrong, or worse, the government approved estimation technique is wrong, which means everyones estimate is wrong. Lastly, the government will change how that money can be counted, and what I can do with it. This last point is really the most insidious. Politicians will want to write rules that advantage them when they leave government, and that will advantage their investment portfolios. That means going along with changing how risks are counted, or how to handle the difference between calculated and actual risk in a way that will most benefit themselves personally when they leave. Whatever looks like it will help the bottom line the most right now. And that is very bad policy.
After that, the whole situation is exacerbated by other government policies which aren't directly applicable to what we just talked about. Wealth distribution that has become less equal pushes more money into a smaller number of hands, meaning when they make mistakes they take a larger chunk of the economy with them. The government has written rules (about unions, trade, taxes etc.) that significantly impact wealth distribution.
The government also controls the currency supply, and acts as the insurer of last resort, if it feels like it. Currency supply isn't as much of an issue in this recession compared to the great depression (where the gold standard exacerbated the problem for those still on it). The government has mostly managed to avoid a deflationary spiral, although that's about the only good thing you can say, and it's not even that strong a statement. But the insurer of last resort, if it feels like it is a serious problem. When a company (bank or otherwise) starts to spiral out of control, especially with the CDS situation where there was essentially a bank run, how quickly the government moves to insure banks, how much it's willing to insure etc all can determine how bad the crash is.
If this sounds a lot like the great depression, it's because it is. Other than the gold standard issue* basically all of the same principles and problems and theories apply. There are substantial differences in specific, but: massive overburdening debt on consumers and banks, check. Significant wealth inequality, check. "Austrians" (the economic school of thought) claiming too much money supply previously, check. The same group claiming government policies to help were counter productive, check. Excess production capacity, (now largely driven by production in china rather than electrification and motorization) chec
Re:economics ? (Score:2, Insightful)
Except usually none of that is anywhere close to reality unless market participants agree to listen to economists.
Development of stable self-fulfilling prophecies may qualify as engineering or art but that's definitely not science.
Re:economics ? (Score:5, Insightful)
Posts like this one make me think the /. coders should come up with an "Autism spectrum" filter for posts. Dial it to where you need it.
Re:Quote from the book: (Score:5, Insightful)
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.
Re:Don't blame math (Score:5, Insightful)
It was the greedy preying on the stupid to the detriment of the rest of us. But an unchained wolf will hunt when it sees food, and so will a sociopathic CEO. The blame lies with those who let them run free in the first place by deregulating the financial sector, not on animals following their instincts.
Re:Not economics; theft. (Score:5, Insightful)
It amazes me that some people can see conspiracies everywhere. I've not posted a story before on slashdot - but it seems to me that you are seeing conspiracies where there are none. I have no relationship to the bbc - I don't live in Britain - and I have no interest in finance organizations - as a software engineer I design and write code for a living (and not for financial institutions). This article interested me from the perspective - that making false assumptions - and misuse of a formula or algorithm - can have unforeseen consequences beyond the original authors wildest dreams - which is what I find fascinating and the sole reason why I posted the story. I can guarantee you that I will not receive a single kronor (as I live in Sweden) for this article. I wonder how you think Slashdot editors are going to police the articles that get posted as you suggest. To my mind that kind of heavy editorial censorship would also be heavily criticised.
Re:Complexity theory (Score:4, Insightful)
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.
There is more to science than messing with statistics in artificial environments.
Re:economics ? (Score:5, Insightful)
That is why, for sufficiently complex systems such as economics, psychology, sociology, or theology, other assumptions must be used.
You forgot climatology and cosmology. Or are the objects of these "sciences" not sufficiently complex?
Re:economics ? (Score:5, Insightful)
Mixing things together in the story (Score:4, Insightful)
Then, because the firewalls between speculation and retail banking had been removed, there was a great deal of general contagion and bank to bank movements froze.
However, one can't conclude that all mathematical pricing is wrong from these two separate events. One can reach conclusions regulation, capital adequacy, firewalls etc/ Above all, if the public is well protected and genuine industry is well protected, these idiots [of which I was one once] can do what they like and then suffer the consequences.
Re:economics ? (Score:5, Insightful)
You forgot climatology and cosmology. Or are the objects of these "sciences" not sufficiently complex?
They don't really alter their fundamental behavior as a consequence of you publishing your theory. The problem with the human sciences is that humans read the discoveries and change what they're doing because of them. By comparison, large scale physical systems (the climate, the cosmos) don't give a fig what we think about them; even those changes that we can effect will not fundamentally alter the science itself.
Re:Warren Buffett called derivatives "time bombs". (Score:4, Insightful)
Re:What really happened... (Score:5, Insightful)
And when they did hold gold, gold wasn't actually useful for much of anything except looking pretty. So it's always been nothing.
Re:Warren Buffett called derivatives "time bombs". (Score:5, Insightful)
No one can say the fraud was unknown
It's not fraud as long as the liabilities created by the derivatives are reported on the balance sheet. The liabilities may be difficult to quantify, but as long as they're disclosed the diligent investor can decide for themselves how they're going to respond. What Buffet was saying was that it was very difficult, in his opinion, to estimate the risks in these complex derivatives transactions and Warren Buffet is well known for refusing to invest in things which he either doesn't understand or cannot reliably quantify (his avoidance of high tech investments are another example of this). Just because an investment is high risk or because foolish investors don't or cannot understand the risks that they're really taking doesn't make it fraud. This is an important distinction that's often lost upon the Occupy people and those who decry "preditory lending" or "cutthroat capitalism". Personally, I agree with Buffet and don't invest in futures or derivatives because I don't understand them. Indeed, I suspect that few people, even among professional traders, actually do. So when someone tells me that they fully understand all of the risks associated with their derivatives trade I know that they're either a savant or a liar. However, just because an investment is complex and risky (the two often go hand in glove) doesn't automatically make it fraudulent. As with most things in life, if it sounds too good to be true, it probably is.