Slashdot Mirror
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."
The past tense of lead is "led", not "lead". When "lead" is pronounced like "led", it's a metal. This mistake pops up everywhere. Correcting it here won't fix anything, but when someone on the internet is wrong, duty calls.
Disclaimer: It's All Been Said Before.
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 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.
Deregulation, not models, permitted bad behavior. Banks that guarantee loans simply should not be emulsifying them into packaged trades, and then hedging their own equity on the loan derivatives. It's like taking a tulip bulb, selling interest in a tenth of the bulb with 1000:1 equity, and then saying it's more stable. Once it goes the wrong way you are screwed and you know it (but you just don't want to believe it could ever happen).
When the foot seeks the place of the head, the line is crossed. Know your place. Keep your place. Be a shoe.
Interesting, but really, blaming the seed on Jack looting the giant's castle? I used to write risk analysis software for the traders and market makers at the options exchange in Chicago (CBOE) and am intimately familiar with Black-Scholes algorithm (I've implemented it more than once). In the article, the sub-text to one photo, "Options allow a trader to have a delicious risk-free portfolio", is totally bogus! Options allow a trader to MINIMIZE the risk in their portfolios, and BS (no pun intended) helps traders to do that in a mathematically/statistically rigorous way. Misuse of any tool (using a hammer to kill someone, for example) is not the tool's fault, but the wielder of the tool!
-Rubberman
This was covered by the guardian a whole two months back. Link Partly debunked here
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.
I highly recommend the opera at http://www.youtube.com/watch?v=JhEH00rlmz8, from the Ig Nobel prizes a few years ago. It captured the most recent banking crisis rather well, and without the need to blame human greed on misused mathematical formula.
Once Risk became a commodity capable of being bought and sold, it was only a matter of time before market responded by producing more Risk.
the purpose of a tool has a meaning
give everyone a toilet brush, toilets will get cleaned. give everyone a hammer, nails will get pounded. give everyone a gun, people will get shot
the availability and easy access of a tool with an intended purpose and meaning makes certain outcomes easier. it's not complicated
the tool itself, and the presence of the tool, has significance. we all reach the limits of our temper at various points in our lives. we will confuse our teenage son sneaking into the house in the dark with an intruder. we will be drunk and clumsy. and in those situations, whether or not a gun is in easy reach radically changes the outcome of the situation
the purpose and presence of the tool matters
the proper quote is
"guns don't kill people, people with guns do"
if you want guns to be legal, fine. but don't depend upon flimsy easily dismantled logic to justify your beliefs
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
The same can be said for pretty much advance in science in the last 50 years. If you're truly interested in what can and cannot be predicted - given correct models, there's a science studying that, complexity theory.
But from finance over climate to even whether the planets will keep turning - all are too complex to be predicted, even though science has advanced to the point where individual events can be predicted short times in advance with near-certainty. However there's obvious things that can't be predicted. If the moon decides to crash into the earth, we will know in advance - but only a few weeks at the most. Yes, really.
In some ways this was inevitable. Science has moved from predicting individual events, like say a car collision, or physical changes happening inside an extremely well-described cloud, a single rational decision taken by someone considering a bank loan - to predicting the global effects of an undefined number of such interactions combined. The answer coming out of all this is rather disappointing : it's not working - and it isn't working any better outside of finance either. The mathematician's answer, chaos theory, is thoroughly disappointing : there is no valid way to make useful long-term predictions of any system more complex than X (btw: you want a nobel prize ? find what X is exactly) which does not require omniscience (which for any real world prediction would effectively be all the information that exists anywhere in the universe)
So the real question changes - if you require proof we can essentially predict nothing. If you even require valid inputs to statistical functions we can essentially predict nothing. Barely any recent science follows from first principles, except perhaps in Mathematics. Physics makes a good-hearted attempt, but it has to violate the first-principles - it's attempting to discover new ones. Every other science never even attempts to work from first principles, it just doesn't work.
Finance - the models only work when you assume decisions don't interact in the short term (ie. nobody decides to either sell a house or forestall selling it because of anything that happens that doesn't directly affect that loan. If this is true, then the financial crisis was impossible (yet also inevitable)). And of course the basic economic assumption - that everyone takes the rational course of action immediately - no matter how complex the logic, and irrespective of any personal convictions.
Climate - energy balance only has to sum up if you assume the entropy of the system is negligible, or if you work on infinite time-scales. Needless to say, infinite time scales are a bit long for practical usage. Entropy within our atmosphere is anything but negligible. The second big assumption made in climate science is that small portions of the atmosphere behave identical to large portions of the atmosphere.
Planets - planet's orbits only behave the way you're taught in school if they followed Newton. But that's not the worst assumption. The other assumption necessary to make Kepler work is that planetary orbits are independent, and no objects with mass can possibly cross into orbits (and obviously that orbits don't cross)
All these assumptions can be proven to be wrong - and rather trivially.
In one case this can be shown. Planetary orbits are extremely, extremely regular in the short term. This was useful for sea-faring when it was discovered as it provided a very accurate source of timing. And we still have the books from those days describing how those measurements worked. We still have books describing how to find a ship's position on earth by measuring the orbits of Jupiter's moons ... only they yield incorrect results. You might chalk that up to bad measurements, but that can't be : if the methods were truly useless, they would never have been written down. Plus we can correct the measurements so they work again. No, the reason is much simpler : Jupiter's moons have shifted so much over the course of 300 years that those me
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.
BS had zero to do with any of the problems which led to the various market meltdowns. What did? Ignorance of liquidity (more precisely, lack of liquidity), counterparty risk, seriously flawed assumptions about various correlations (think gdp, unemployment, geography, subprime mortgages), significant excess leverage financed at exceptionally low interest rates, creation of intstruments which allowed some holders to game the system (credit default swaps) and lastly, ignorance and greed. There are, of course, myriad other contributors but BS is not one of them.
Disclaimer: besides having a masters degree in computational finance I worked in the industry for nearly two decades.
FRAUD ALERT: It was not a mathematical model that caused the problem. It was fraud. Financial organizations convinced investors that they had a "mathematical model" so that they could steal. The theft was ENTIRELY deliberate, as is described in detail in the 1997 book F.I.A.S.C.O.: Blood in the Water on Wall Street, by Frank Partnoy. Somehow the issues were kept quiet for 11 more years until the theft could be completed in the 2008 financial crash. Traders called their work "ripping the client's face off" .
There are other editions of the book, such as this one published in 1999, Fiasco: The Inside Story of a Wall Street Trader, and a 2009 I-told-you-so edition of the original name.
Nothing has been done to reform the extremely corrupt financial system in the United States. No one in the SEC, U.S. Securities and Exchange Commission, the government organization that is supposed to police financial fraud, was prosecuted, even though the agency knew of the abuses. See the February 17, 2009 show Frontline: Inside the Meltdown.
Even though the U.S. dollar is experiencing rampant inflation in 2012, U.S. banks give less than 1% interest on savings. Those who would like to invest can't because the system is so corrupt it cannot be trusted. Corporations hold unprecedented amounts of cash. See, for example, the October 7, 2010 Washington Post article, U.S. companies buy back stock in droves as they hold record levels of cash.
F.I.A.S.C.O. stands for "Fixed Income Annual Sporting Clays Outing" (See page 100 of the 2009 edition.), held at a shooting range called "Sandanona, a club in upstate New York" (Page 97 of the 2009 edition). Traders would go there to shoot guns. The idea was to encourage their taste for violence so that they would be even more financially violent toward the customer.
Perhaps the April 27, 2012 BBC article, Black-Scholes: The maths formula linked to the financial crash referenced in this Slashdot story was influenced by public relations agencies trying to get people to believe that the crash was caused by errors in mathematical thinking, and not by fraud, so that the financial industry can continue stealing.
It would be helpful if Slashdot editors signed a statement about each story saying that they know of no conflict of interest, and no one was paid to run the story.
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!
In the Berkshire Hathaway 2002 Annual Report (PDF file), Warren Buffett said this on page 13:
"Derivatives
Charlie and I are of one mind in how we feel about derivatives and the trading activities that go with them: We view them as time bombs, both for the parties that deal in them and the economic system."
From page 14:
"I can assure you that the marking errors in the derivatives business have not been symmetrical. Almost invariably, they have favored either the trader who was eyeing a multi-million dollar bonus or the CEO who wanted to report impressive "earnings" (or both). The bonuses were paid, and the CEO profited from his options. Only much later did shareholders learn that the reported earnings were a sham."
On page 15:
"In our view, however, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal." [my emphasis]
Warren Buffett, the world's most famous investor, published that in 2003. It was widely reported. No one can say the fraud was unknown, or that the present severe economic problems are due to a faulty mathematical formula.
Fraud is a big problem, but not the worst problem. I've grown concerned that we're all engaged in mass delusion. We think the world works a particular way, but we may be wrong. We can produce what seems to be supporting evidence. I am referring to a much more fundamental idea of finance: the formulas for rates. They're neat and simple, and wrong. Implicit in compound interest is exponential growth. The universe doesn't support exponential growth.
Historically, depending on who you talk to, the stock market has averaged an annual rate of return of 7% or 10% or even more. But that record is only about 100 years long. Can the stock market keep up 7% growth for another 100 years? If it can, how about 1000 years?
Intellectual Property is a monopolistic, selfish, and defective concept. It is "tyranny over the mind of man"
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!
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?!
I've heard this repeated several times but it's a load of misinformed crap. It's one of those "makes sense to someone who knows nothing but is totally false" myths.
When a central bank creates money through a loan and it is later paid back, it is only the principal of the loan that is created and destroyed. The interest portion is considered the bank's profit and is paid out to the bank's shareholders (whoever that may be, it differs depending on which country you're talking about, but usually member banks and/or the government). That money is not destroyed and re-enters circulation. How would it even make sense for the interest to be destroyed as well?? That would totally break the concept of double-entry accounting (which central banks do still follow).
I don't know where this myth started but it's 100% false. I realise the financial crisis has made everyone interested and out for easy answers, but "the only thing it can possibly end in is debt and the enslavement of entire nations... Exactly as designed"? Please. I hate bankers as much as the next person but i wish we could focus on the real problem (outright, unpunished fraud) rather than this kind of fairytale crap.
1. The time remaining until the contract expires
2. The current price of the undelying asset
3. The strike price (the contract gives its buyer the right or "option" to buy the asset at the strike price)
4. The risk-free rate of return on cash (return that could be earned by putting your money into, say, treasuries rather than stock)
5. The volatility of the underlying asset.
At the time the contract is written, the first four of these values are known (assuming of course that the risk-free rate stays constant, which is pretty close to a sure bet). The LAST value is the problem. It says how much the stock will fluctuate, between the present time and the time of expiry. This is unknown, because, after all, it requires knowledge of the future. Usually, PAST volatility is used in its place, going with the assumption that the stock will behave in the future the same way it behaved in the recent past.
If the stock suddenly becomes very quiet, and stops fluctuating, the buyer payed too much for the contract, on average. If the stock gets very wild, the buyer got a bargain, on average. In either case, the contract buyer and seller guessed wrong. They should have used a different volatility to price the option.
Of course, stock fluctuations do NOT follow a normal curve, after all. And option traders do NOT follow Black-Scholes exactly either (see "volatility smile"). But the much bigger flaw, I think, is lack of clairvoyance. The formula requires knowledge of the future.
Does it enter into it that the sales people targeted people likely to have a lack of financial knowledge?
I know of no DINK (dual income no kids) households that entered into neg-am loans. I know of lots of single women, and people that were have minimal English skills (enough to get by, but not enough to understand a legal contract, whether because of lack of education, or English being a second language that they had not yet mastered.)
The real idiots are the investment managers that bought the Asset Back Securities. Those people should be barred from managing anyone else's finances under any situation, and probably have their own assets put in a receivership for their own protection, a la Britney Spears.
Reforming the bankruptcy laws so people can keep their primary residence requires repealing existing law, not creating more law.
Work bio at MMWD
U.S. dollar inflation, some examples:
Food, +4.8% -- Food Price Outlook, 2012
Quote: "The food-at-home Consumer Price Index (CPI), in turn, increased more than expectedâ"4.8 percent in 2011â"which means that food price inflation was not as strong as in 2008 when it increased 6.4 percent over 2007."
Medical treatment, +8.5% -- Medical cost trends for 2012
"This year's report from PwC's Health Research Institute finds that the medical cost trend is expected to increase from 8% in 2011 to 8.5% in 2012."
University tuition, +8.3% -- College costs climb, yet again.
"Tuition at the average public university jumped 8.3% to $8,244."
Gas, +208% -- Historical Price Charts