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The Math Formula That Lead To the Financial Crash
New submitter jools33 writes "The BBC has a fascinating story about how a mathematical formula revolutionized the world of finance — and ultimately could have been responsible for its downfall. The Black-Scholes mathematical model, introduced in the '70s, opened up the world of options, futures, and derivatives trading in a way that nothing before or since has accomplished. Its phenomenal success and widespread adoption lead to Myron Scholes winning a Nobel prize in economics. Yet the widespread adoption of the model may have been responsible for the financial crisis of the past few years. It's interesting to ponder how algorithms and formulas that we work on today could fundamentally influence humanity's future."
Nobel prize in economics.
that's Nobel prize in pseudo-science.
It was human stupidity and greed.
"If any question why we died, Tell them because our fathers lied."
People do. The downfall was made by people using tools (like that formula) without understanding all that required or implied.
Plenty of financial collapses have preceded the current one without the benefit of Black-Scholes. What did they, and the current collapse, all have in common? Excess credit.
The 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...
The Black-Scholes model is an attempt to apply solved heat flow equations to a financial pricing problem. It requires demonstrably invalid assumptions to be made to make it work (such as markets do not trend). Just because a Nobel prize was awarded does not make the model valid.
1. Approve $300K mortgages for people earning $35K/yr, falsifying documents as needed
2. Bundle slices of thousands of these mortgages into derivatives along with "insurance" against the mortgages defaulting and "insurance" against the bundles failing, etc, under the direction of math and finance PhD's. Sell these "Triple-A-rated securities" to gullible investors worldwide.
3. ??
4. Profit!
8-figure pay packages for bankers and 7-figure for mortgage brokers, real estate agents, workers in credit rating agencies, etc. until the music stops. But hey, you won't need to defend your resume when you've got enough millions in the bank.
5. Watch housing prices rise by 30-50 percent/yr
6. Goto step 1.
There's more to it than that. The model has developed into a philosophy which has been built out beyond its workable foundation.
It starts with the risk neutral measure. Basically the concept is that you can construct a probability measure (basically a reweighting of probability of events) from market prices. Basically the market prices of a stock, a forward contract (a contract to deliver the stock at a fixed point in the future), a call option (an agreement to offer the option of buying the stock at a given price in the future), a put option (an agreement to offer the option to sell a stock at a given price in the future), and other contracts related to the price of the stock in the future all have to have prices rationally related to each other. If the price of one of these things deviates from the risk neutral measure implied by the others, you can construct arbitrage positions where you can make a profit with negligible risk and executing this arbitrage has the effect of moving the market prices closer toward their theoretical values.
Observably, market prices don't reflect real probabilities. Safe investments such as treasury bonds are disproportionately more expensive than highly rated bonds with a low chance of default based on historical default rates. This is explained due to risk aversion and philosophically, the risk neutral measure is said to reflect the market's assessment of the risk of each investment and also the risk preferences of market participants. This concept is the basis of financial economics, and the school of thought derived from this position has been dominant in economic related disciplines for the past 30 years.
As a means of analyzing for arbitrage opportunities and pricing of marketable securities in a way that avoids offering others arbitrage opportunities, this methodology is largely unassailable. However, where they overextend themselves is that in conjunction with the efficient market hypothesis, they've started to assume that this framework lets you farm out the function of assessing the likelihood of future events to the market and even in some cases they've asserted that it's immoral to use methodologies which imply prices for non-marketable securities which aren't directly comparable to marketable analogues.
It's basically a religion at this point. They honestly believe that the risk neutral measure isn't just a post hoc rationalization imposed on market prices, but a normative guide to upright living and that the market's assessments of the ("risk-adjusted") probability of future events is the best and most rational basis for making all decisions and for framing all policy and regulation.
My only political goal is to see to it that no political party achieves its goals.
The 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.
So the book presents a hypothetical derivatives salesman (who doesn't exist), says he used to read Time but now he reads Guns and Ammo, and offers that it's no coincidence. Of course it's no coincidence; the same author made it all up! I do think there's lots wrong with Wall Street, but your book sounds like a bunch of sensationalist junk, frankly.
Breakfast served all day!
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.
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.
Contrary to the popular belief, there indeed is no God.
Actually reading through the BBC story, I feel it's yet another example of the BBC's declining grasp of anything technical. Long term capital management called into question Black-Scholes and demonstrated extreme events in markets, sure. But the elements of the recent crash were also to do with greed, arrogance, mis-selling [of mortgages that were then securitised in un-auditable and therefore un-priceable mixtures] bad-fatih [banks selling both complex derivatives AND insurance for the failure of these complex derivatives] and a general credit-bubble that distorted asset pricing. Michael Lewis' the Big Short: http://www.amazon.com/The-Big-Short-Doomsday-Machine/dp/0393072231 is very good on the detail of this.
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.
On y va, qui mal y pense!
Or, with a different twisted view, derivatives were thought to be helpful by those who have done an otherwise fantastic job of dealing with the complex nightmare of the finance world. That they turned out to cause a catastrophe is more about our collective failure to understand the problem and heed the advice of the few against the resounding successes the stock market gave all of us. We were awash in wealth from the lowly home-owner with a mortgage only sustained by constant economic grow to the financier receiving another multi-million dollar bonus. Only those who had no need for continued success could view the situation with cold logic and real understanding, but they were telling us something we didn't want to hear.
And when they did hold gold, gold wasn't actually useful for much of anything except looking pretty. So it's always been nothing.
Can you be Even More Awesome?!
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.