Showing posts with label Quants. Show all posts
Showing posts with label Quants. Show all posts

Thursday, June 11, 2009

Don't agree; there was real panic after Lehman was allowed to fail. Noise prompting depositors to take their money out

TO BE NOTED: From:

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Tuesday, June 09, 2009

Plight of the risk managers

I'd like to recommend this podcast interview with Riccardo Rebonato. Rebonato, the author of the prescient book Plight of the Fortune Tellers, written before the financial crisis, is a former physicist turned quant.

Rebonato does not mince words, pointing out the weaknesses of mathematical models, and noting that most quants, although mathematically sophisticated, often lacked deep knowledge about markets and banking (I assume he does not include himself in this group). In my experience many quants never questioned the basic efficient market assumptions underlying their models, although some certainly did -- in particular, those with trading experience.

Rebonato is polite, even urbane, but disagrees with Econtalk interviewer Russ Roberts on many important issues. The most important question, which Rebonato addresses immediately, is whether enlightened, self-interested managers of financial institutions can be relied on to properly manage risk. Regulators accepted, on faith, the self-regulating abilities and properties of a system managed by such people. Thus, one of the main ingredients in the crisis was the ideological (as opposed to political or financial) capture of regulators by efficient market proponents.

Other interesting topics covered are the divergent risk tolerances and interests of bond holders vs equity holders vs regulators of banks [1], and whether moral hazard (anticipation of a bailout) played a role in the crisis -- Russ, the anti-government libertarian, says yes. Rebonato says no, the story only makes sense if told at the institutional level, whereas individual incentives were different. I think Rebonato's logic is impeccable. It's more persuasive to me that incentive schemes which allowed huge compensation based on short term (ultimately illusory) gains were much more of a factor. (See Clawbacks, fake alpha and tail risk.)


Dr. Riccardo Rebonato

Riccardo is Global Head of Market Risk and Global Head of Quantitative Research and Quantitative Analysis for Royal Bank of Scotland based in London. Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe desk and Head of Derivatives Research at Barclays Capital, where he worked for nine years.

Riccardo is a Visiting Lecturer at Oxford University in Mathematical Finance and Adjunct Professor at the Tanaka Business School, Imperial College, London.

Before joining the financial world, Riccardo was a Research Fellow in Physics at Oxford University (Corpus Christi College) and, before that, Visiting Scientist at Brookhaven National Laboratory.

Riccardo is the author of the books Plight of the Fortune Tellers ('07), The Perfect Hedger and the Fox (Wiley ’04), Modern Pricing of Interest-Rate Derivatives (Princeton University Press ’02), Interest-Rate Option Models (Wiley ’96,’98), Volatility and Correlation in Option Pricing (Wiley ’99). He has published several papers on finance (option modelling, computational techniques, risk management) in academic journals. He is a regular speaker at conferences worldwide.



[1] Footnote: see my earlier post on the vacuous Modigliani-Miller theorem. I recently learned from Vernon Smith's memoir (see pages 230-231 and 276) that he has similar opinions. Google books link; also search under "MM".






And from EconLog:
Riccardo Rebonato of the Royal Bank of Scotland and author of Plight of the Fortune Tellers talks with EconTalk host Russ Roberts about the challenges of measuring risk and making decisions and creating regulation in the face of risk and uncertainty. Rebonato's book, written before the crisis, argues that risk managers often overestimate the reliability of the measures they use to assess risk. In this conversation, Rebonato applies these ideas to the crisis and to the challenges of designing effective regulation.
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0:36Intro. [Recording date: May 22, 2009.] Book, risk and uncertain, decisions in an uncertain world; written beforehand but prescient about the economic crisis. History of finance and housing in the United States, how banking changed. In 1990s, up to end of 2006; hiccup of 1998, after the fact purely contained to financial sector; within 6-9 months a blip. Regulators who look after soundness of banking system came to rely on quantitative models and the banking system being the forefront by making use of these quantitative models. Two steps back from technicalities, philosophy of faith in self-regulating properties of the system, managed by enlightened self-interested mangers and CEOs; skilled. Quants came from background in mathematical finance, not deep thinkers, not deep knowledge of the banking system. Supposed to guarantee that sufficient capital would be set aside to act as safeguard against unlikely events. We know now that that didn't happen. Book: we are not in a position of saying anything about extremely rare events. Might collect daily, monthly, quarterly data, spanning a few years--information about the last few years. Even with data going back to the 1950s or 1940s, leap of faith to say they are relevant to present market conditions. What about events every 100, 1000, or 4000 years? A 99.975 percentile one year horizon corresponds to one event that should not happen more frequently than once every 4000 years. Quants might have sophisticated theory, but how do we know the data are sufficiently homogeneous--belong to the same patch of history--to be giving information relevant today as opposed to 3 years ago. Similar point made on EconTalk, talking about the Great Depression: no consensus about how we got into it or how we got out of it because it's a one-time event. Easy to have a theory, hard to be confident that it applies today. Humility rather than hubris.
7:59Little more technical: one technique that came to be popular in the banking is Value at Risk. What is idea behind it and why did it become popular? Measure of risk with some nice features: expressed in units of money. If your value at risk one day, 95th percentile, is $20 million, it means you should exceed a loss of $20 million only 5 days out of 100, so basically one day in 20. Won't be a perfect measure, but gives idea of day-to-day volatility when nothing extraordinary happens. For a trader or for a bank as a whole. Look carefully at the time-frames we are talking about. Can I infer the type of losses I might typically incur over that period, one month or a few months? Yes. Supposed to be used to determine capital; but capital should be there to absorb losses that occur not just once every 20 days, but once every hundreds of years; any time to protect the solvency of the institution. Before the regulators slapped on a multiplier; didn't ask for more remote percentiles; just take a safety factor. Safety factors have illustrious pedigree. Physics, engineering: use same formula calculate the thickness of steel ropes (cables) in elevators; but at the end of the day, they multiply by 10. Calculations for landing gear of aircraft multiply by 1.1; always a safety factor. Sensible because it allowed the bank to calculate a statistical number that was meaningful; but then a multiplier. Goal of regulator: to prevent insolvency or disaster because if it spreads the entire financial system could be at risk, systemic problems, runs on the bank, recent problems. What nest egg, what buffer do you have to keep so that in the worst case scenario, your firm still survives?
13:40Complicated question: inherent tension between bondholders and stockholders in a bank, and between regulators and owners. How big would the buffer be without regulation? How much economic capital--the buffer--should a bank keep to entice its investors, both equity and bond, to be comfortable? Not precise; what are some of the conflicts? Lot of thinking after the crisis about the alignment of interests even of any enlightened owner and the interests of society. Economic capital: the nest egg, but how severe an event? Folklore came up with a number: the 99.975 percentile--events that should happen not more frequently than once every 4000 years. Really bad luck, recent crisis! How did that number come up? Example: I am a bank with a certain rating. How many AA-rated institutions went from double-A to default in one year? Probably a handful. Divide that over total number of companies, get approximately one in 4000. So to convince bondholder that I am a AA company I should set aside enough capital in order to convince them I will only go bust once every 4000 years. Align capital I am holding with observed frequency of default of a AA company within one year. Signaling device to tell regulators: I am double-A. Regulators shouldn't be asking for a great spread, because I am AA. In case of a bondholder, the only thing of interest is solvency--just want their money back. Why not go for triple-A? Because the shareholders care about the return on capital? So to convince bondholder that I am AAA, I'd have to hold so much capital that the shareholder would not get a great return for each dollar of that capital. Compromise. For most banks, the equilibrium is around AA level. Bondholder, short a put, only loses money if the bank defaults; but if things go extremely well, he doesn't share in the upside. Shareholder likes volatility, long a call. Recent crisis has made very clear that a shareholder can be perfectly rational but willing to accept a level of risk that a regulator may not like. June or July 2007, shareholder of one of the banks that eventually got in trouble looks at his portfolio: would have to need a repeat of the 1930s to take a big loss; to insure himself against that possibility he'd have to lock in losses that most likely he won't have to bear. Perfectly acceptable to take that risk. Regulators' view: in that calculus you haven't taken into account the systemic risk. Regulators' view is to step in to not allow taking on that level of risk. Those investors had extremely high rates of return during 2003-2006. If someone had said this is getting a bit out of hand, your competitors wouldn't have been doing the same. In 2006, plenty of signs, liquidity was too abundant, risk premia compressed too much, asset prices too high. Fracture line of an earthquake; people knew it had to give, not sustainable for a long period of time; but where and when the crack would occur. Stepping out too early is disastrous. Greenspan, irrational exuberance, uttered around 1994, 1996. Pulling out would mean having to explain to the shareholders what you are doing when everybody else is becoming rich.
23:35Competitive market issue, also a social issue. Small world, investment banks; events and parties where your colleague is doing very well, you look the fool in the short run if you pull out. Central question, heard that story before: that's the music that's playing, so if you are there to dance, you have to dance to the music. Everyone's investing in these mortgage-backed securities, etc., but it's the only game in town. Yet, there were people who did not play along. Range across institutions of how much exposure. Any speculative thoughts on why institutions differed? Bear Sterns vs. J.P. Morgan. Some institutions big in this area for a long period of time. Late-comers fared less well. Goldman Sachs, JP Morgan. Different levels of inventory reflected different stages of getting into this business. Could have been emerging markets, which were extremely resilient. Summer 2007, wobble in emerging markets; head trader described it as a week of panic buying of emerging market paper! For same amount of risk, less and less compensation being paid. Some have said this wouldn't have happened had the investment houses never gone public. Asymmetry of incentives facing traders, executives on one hand and investors on the other; not playing with their own money. From point of view of a private firm, it would have been a reasonable risk to take. Regulators different, system; level playing field. If I step off the bandwagon, disadvantage to a more reckless person or institution who remains on; people will have withdrawn their funds from me. Asset fund manager in the United Kingdom stepped out of the dot-com bubble a bit too early and got fired three weeks before the bubble burst. Difficult to swim against the tide; regulator should intervene to level the playing field, you will all be inhibited from taking this kind of risk.
30:15Two questions. One: amount of leverage in play here is one reason these gambles were so large. One thing to say you had a bad quarter or bad year; but why did you take such a roll of the dice that these losses in the U.S. housing market destroyed your legendary company? Simple answer: they were so leveraged--they had borrowed so much to finance that gamble that losing the gamble didn't just mean a bad quarter, but death. Point number two: People who swim against the tide, standard argument is investor psychology is such that no one really cares about risk. But in current environment, psychology might thus go the other way. Akerlof and Shiller book, Animal Spirits, talks about the importance of sentiment; reversals of sentiment affect markets and real economy. How do we get out of the current environment--v or double-v as shape of the downturn? Very uncertain, unstable state. A week ago, stock prices were going up, people saying we'd get out very quickly; a week later, a bit of negative information. Might become more cautious if protracted period of decline. If plan A works and we get out with a v-shaped recovery, expect risk aversion will disappear much more quickly than we think possible today. Good that we get out quickly, but same behavior will result again in the same risks and problems. Where will that liquidity come from?
34:51Basel II, regulatory arbitrage. Basel II was trying to make the capital a bank has to set aside more in line with the risk. Basel I, formulaic, simple rules for capital that did not reflect the risk taken by banks. Credit-worthiness of the bonds you hold--government of OECD countries considered very, very safe; banks of those countries considered very safe; little differentiation between lending to a double-A company and lending to a corner shop. Set aside $1000 to either the latter has higher return for apparently same risk. Basel II was attempt to remedy that. Overconfidence in statistical techniques' abilities to quantify risk. How did the ratings agencies come into this regulatory arbitrage issue? Set-up was role of the ratings agencies with securitization--process whereby banks accumulate assets, e.g., mortgages, package them, and by virtue of the diversification create a portfolio less risky than any of the individual items. Tranche the portfolio in different sections: first section bears risk of first losses, so gets more return if things go well; all the way up AAA. Ratings agencies were to check amount of diversification to be sure it was up to the right level. Human nature, and conflict of interest--rating agencies only got paid if the securitization went through. Agencies worked with the investment houses to meet the criteria for AA, AAA, and A ratings. Teacher sets test but goes over questions with the students the day before. Portfolios met the specific requirements, but not the best way to set up system. But someone who goes to hire a student from that kind of school knows to be skeptical. Everyone knew this about the ratings agencies. Value of franchise: only 18-24 months ago, enlightened self-interest of market players was viewed as best safeguard for financial system. If the ratings agency debase the currency of their name, they will lose credibility by giving away AAA for nothing. Self-regulating efficient market.
41:10Mark to market: what role did it play in the crisis? Whole problem or irrelevant? Controversial topic. Not fair to point to that. Like saying if I didn't have a thermometer this patient wouldn't have a fever. Dynamics of mark-to-market forcing certain actions. Nexus where it got things into trouble was that when securities got downgraded, certain institutions had to sell them. This caused forced unwinding, Special Interest Vehicles (SIVs), nobody talks about it today. Mark-to-market is good where there is a willing buyer and a willing seller. Equilibrium is good information about the fundamental value of what is bought and sold. If unbalanced selling or buying, mark to market ceases to have the same information content. Why are buyers no longer there? Could be that liquidity disappears. Pseudo-arbitrageurs, agents who bring things back to fundamentals don't have the firing power to deploy their money. Two sides, some information still there. Loss of trust may simply reflect vagaries of today's supply and demand. Mark-to-market requirement and regulatory capital buffer: If I'm holding an asset, will hold for 5 years. Mortgages will be paying out over time. Some will go into default, some will be prepaid, etc. I'm not going to resell. Meanwhile, if there is an increase in the default rate, the market value of this goes down. I may not be in compliance with my capital requirements today but over time I may be fine on a cash-flow basis. Somewhat compelling argument--forced to sell it because of the capital requirement, though I wouldn't ordinarily sell it. When creating a security, you have a choice to place it on the banking book or the trading book. Trading book attracts less capital but forces you to mark to market on a daily basis. Perhaps people have been placing into the trading book when the sky was blue, price high, prices almost for everything, a lot of things whose prices disappeared when liquidity was withdrawn. Traded loan on trading book; but if you plan to hold it to maturity, place it on your banking book, in which case you get a different capital and a different recognition of a value. Unless impairment, value of 100. Choices that were made through 2006-2007 was to place in trading book--less capital, abundant liquidity, blue sky days.
47:53Too big to fail. Enlightened self-interest, or maybe just self-interest. Some have argued that too much risk was taken because at the end of the day, "too big to fail" or U.S. Central Bank behavior would bail out these bad decisions. In the United States we have banks that are regulated by the Federal Deposit Insurance Corporation (FDIC). Also shadow banking system, investment banks not guaranteed, but it turned out that they kind of were--erratic decision: Lehman Brothers died, Bear Sterns sold at discount, Merrill Lynch sold to Bank of America, AIG made whole all the way through. How much was there a socialization of losses and a private set of gains? Fannie Mae and Freddie Mac turned out to be a catastrophic institutional structure that turned out to be implicitly guaranteed; many investment banks were not guaranteed at all. Was that rational? Instead of thinking of an institution in the abstract, think of the decision-makers. Perhaps institution might survive, but the individuals who made those bad choices don't. Deterrence from rolling the dice. Could argue it goes the other way: a lot of traders made a great deal of money along the way, and though some CEOs were both humiliated or financially destroyed, others turned out fine. CEO of AIG announced his resignation today, saying he was leaving the most horrible job in the world. Before the event, cannot know if you are going to be one of the survivors or not. If you are rescued by the government you have lost control.
51:58Systemic risk. There is a negative externality, so when you take a risk you are careful, but you are not as careful as you would be if you had to bear the other social costs of the other firms that will be called into question. Back to March of 2008, turning point when U.S. Federal Reserve became active in the financial system to a degree that had been unimaginable previously. Weekend in March, Bear Sterns informed Fed and Treasury that it was not going to be able to meet its obligations. Failure of democracy that Fed and Treasury never explained the urgency other than saying it was urgent and that it had to be done. Meltzer podcast, few cases where firms were allowed to fail, failure of incentives. Claim was that if they had failed so much would have cascaded down. A few months later they let Lehman Brothers fail, which people have debated. We now have information about their assets--they've gone through bankruptcy. Claim was that if Bear Sterns had been allowed to go through that, whole system would have frozen up. But whole system froze up anyway. Was that Bear Sterns an unsustainable event? What if it had been allowed to go through bankruptcy? Intense debates. Should we let the market work out its own problems or should we intervene? Records of different central bankers, they were more averse to interventions. Some central banks said rescue of Bear Sterns was a mistake. When Lehman came around, people who favored the open market had the upper hand. When they saw what happened, the central banks said that's it, no more. We would have had a preview of Lehman in March. John Taylor has a claim that the spike in the spreads occurred after the Lehman failure, not concurrent; and it was really the TARP bailout that spiked interest rates. Don't agree; there was real panic after Lehman was allowed to fail. Noise prompting depositors to take their money out. Pure speculation, counterfactual. Regulators in the dark--face their own set of incentives. In the United States, Ben Bernanke, an expert on the Great Depression was eager to not have another one under his watch.
57:09European perspective: tendency to blame much of the crisis on various U.S. policy decisions behind the housing crisis. In 1990s, and can even trace it back to the 1930s under Roosevelt, United States eagerly subsidized price of housing, inflating housing prices. Blames tax policy, Fannie and Freddie, but was it large enough? Those sympathetic to that argument often ignore similar housing price appreciations in Europe: Spain, Ireland, South Africa, Australia around the world. John Taylor argument: excess of liquidity searching for yield as central banks pushed out money. When something of the recent magnitude occurs, there is no single cause. Perfect storm, confluence. China prompts them to invest in Treasuries, depressing the yields and Fannie and Freddie, pumping them into housing in particular. Why housing? Environment with pretty low return on lots of assets in 2006, for many investors the most solid thing to invest in was houses. Home refinancing in the United States; houses looked at not as place to live but a place to invest. Magnitude and complexity and leverage of the instruments attached to mortgage securities. Government aiding and abetting increase in housing, but not the only cause. Money chasing places to go. But why Ireland and Spain and not England and France? Have to look at data; suggest looking at availability of mortgages.

Thursday, June 4, 2009

The optimist in Wilmott thinks that people realize these models don't work. But he's not really an optimist.

TO BE NOTED: From Newsweek Via Marginal Revolution:

Paul Wilmott is out to save Wall Street's soul—one dork at a time.

Matthew Philips
NEWSWEEK
From the magazine issue dated Jun 8, 2009

Jude Edginton / Redux for Newsweek

Imagine an aeronautics engineer designing a state-of-the-art jumbo jet. In order for it to fly, the engineer has to rely on the same aerodynamics equation devised by physicists 150 years ago, which is based on Newton's second law of motion: force equals mass times acceleration. Problem is, the engineer can't reconcile his elegant design with the equation. The plane has too much mass and not enough force. But rather than tweak the design to fit the equation, imagine if the engineer does the opposite, and tweaks the equation to fit the design. The plane still looks awesome, and on paper, it flies. The engineer gets paid, the plane gets built, and soon thousands just like it are packed full of people and sent out onto runways. They fly for a while, but eventually, because of that fatal tweak, they all end up crashing.

In a way, this is what's happened in quantitative finance. The planes are the complex derivatives—like collateralized debt obligations—that now lie smoldering on the balance sheets of banks. The engineers are the "quants": those math and science Ph.D.s who flocked to Wall Street over the past decade and used mathematical models to build these new investment products. These are the people Warren Buffett was talking about when he said, "Beware of geeks bearing formulas" in his letter to shareholders this year. The quants aren't entirely to blame for the financial meltdown; there's plenty of guilt to be shared by regulators, top executives and the investors who bought the instruments the quants created. Yet while aeronautical engineers who willfully designed a faulty plane might be on trial for criminal negligence, Wall Street's math gurus are, for the most part, still employed. Strangely, the banks need quants more than ever right now. If anyone's going to figure out how to price these toxic assets, it's them. Quantitative finance isn't going away, but it is in desperate need of reform. And one man—a math geek himself—thinks he knows where to start.

Paul Wilmott is a 49-year-old Oxford-trained mathematician and arguably the most influential quant today, the brightest star in their insular, nerdy universe. The Financial Times calls him a "cult derivatives lecturer." Nassim Taleb, the mathematician and author of the bestseller The Black Swan, calls him the smartest quant in the world. "He's the only one who truly understands what's going on ... the only quant who uses his own head and has any sense of ethics," says Taleb. Wilmott stands atop a veritable quant empire. His wonk-made-simple textbooks sell for hundreds of dollars. A subscription to his bimonthly magazine, Wilmott, costs $695 a year. His Web site, Wilmott.com, is the nerve center of the quant community, with 65,000 registered users and a chat forum that buzzes over such topics as geodesic stochastic manifolds and swaption vol arbitrage.

Over the past decade, and increasingly since the crash, Wilmott has cultivated a loyal following of truth-seeking converts from the failed school of thought that the entire world can be turned into Greek symbols, plugged into equations, priced and predicted. He's especially critical of the notion that math can forecast human behavior, essentially the basis of finance. "This," says Wilmott, "is absolute rubbish." To rectify the situation, he's started his own training program, the Certificate in Quantitative Finance, or CQF. It's the gem of his empire, the key, he hopes, to saving the quants from themselves, not to mention all of us from their future destruction. In essence, the course is rehab for quants, a six-month, $18,000 program designed to break them of the abstract, theoretical approach to finance they learned in their Ph.D. or financial-engineering programs, and replace it with a more practical set of skills that are actually used on Wall Street. "What banks really need are quants who can translate theoretical math and tell them how it applies," says Wilmott. "Because what good is being fluent in geek if you can't apply it? You might as well stay in university."

Ever since Ed Thorp, the first true quant, left his job teaching math at UC Irvine to start a hedge fund in the 1970s, math and science types have been setting out from academia to try their hand at finance. The watershed came in the mid-1970s when MIT-trained economist Robert Merton along with Myron Scholes, a University of Chicago economist, and Fischer Black of Harvard developed the Black-Scholes equation for pricing options, which eventually garnered a Nobel Prize. Over the past 20 years, quantitative methods gradually spread into commercial and investment banks, fueling a huge demand for math savants. Since the mid-1990s, dozens of master's-degree programs in financial engineering have sprouted up at top universities. (The highest-rated ones are at Carnegie Mellon, Columbia, Stanford and Princeton.) Along with physics Ph.D. programs, these are the primary breeding grounds for the many thousands of quants who have found their way to Wall Street. It's these programs that Wilmott has taken direct aim at with his CQF. "I'm building a new army of quants," he says. His ranks currently stand at 1,273: the number of CQF alumni who have graduated since the program was founded in 2003. Wilmott realizes he's vastly outnumbered, but he's undaunted. "Ever see the movie Zulu?" he asks, referring to the 1964 Michael Caine film about a battalion of 140 British soldiers besieged by 4,000 African warriors in 1879. The Brits won, mostly because they were better-trained and -equipped, just as Wilmott wants his graduates to be.

The CQF is taught at night in London's financial district by Wilmott and a handful of his buddies, most of whom have worked in finance. These instructors are miles away from the stereotypical math or finance professors. Among them is Espen Haug, a Norwegian former JPMorgan options trader who looks like a cross between James Bond and Arnold Schwarzenegger, and often lectures in sunglasses and a tuxedo. One evening this spring, Wilmott is wrapping up the final class on interest rates and fixed income. He stands at a podium, looking out at about 30 students, most of whom have just gotten off work from their jobs at banks: Citigroup, Deutsche Bank, Credit Suisse. Another 100 or so watch the lecture streaming over the Internet. The official topic of the evening is how to decompose the random movements of the forward rate curve into its principal components—i.e., how to predict random fluctuations in interest rates in order to determine bond prices. "There's nothing difficult here," Wilmott says without irony. "If you can keep your head, you'll be fine."

He's just scribbled a handful of equations on a whiteboard, including one called the Heath-Jarrow-Morton model. Developed in the late 1980s, the formula looks horrifically complicated to the layman. But to a mathematician it's elegant, simple—and dangerous. Behind its simplicity lie hidden mistakes, unobservable variables like volatility and correlation that can provide a false sense of security. "With models, you want to see where things go wrong," says Wilmott. "You want to see the dirt. But HJM is actually just a big rug for [mistakes] to be swept under." For the next half hour, Wilmott deconstructs the thing, cautioning students on overreliance. "In the end, we should all like models that wear their faults on their sleeves," he tells the class.

Two hours later, Wilmott is treating his students to beers at a nearby pub. Among them are half a dozen fresh-faced Citigroup employees, all in their mid-20s, all recent physics or engineering Ph.D. graduates, and all being sponsored by Citigroup to take the CQF. (Banks have only recently started sponsoring students to take Wilmott's classes, a tacit acknowledgment that quants need more holistic training.) "There's an arms race going on in quantitative finance," says one of the students. "The CQF gives us another weapon in our arsenal."

On a typical April weekday, Wilmott spends the morning in his office, a small, gray room that's completely nondescript save for the giant blackboard filled with mathematical notation. There he goes over the final touches of an options formula he's getting ready to publish with a former student. He then takes the tube across town to London's posh Grosvenor Square to meet with three former investment bankers who want to hire him as a quant on call for their consultancy startup. They pitch Wilmott while sitting in the modern dining room of Gordon Ramsay's Maze Grill restaurant. Wilmott tells them he'll think about it, then sets off down Oxford Street, a stretch of shops that's swarming with tourists.

Picking his way through, on and off his cell phone, Wilmott talks about the contradictions in his life: he's a car enthusiast who hates to drive; he goes on Swiss ski trips but doesn't ski. Though he's nearly 50, he could pass for 30-something, especially when dressed in skinny jeans, black Chuck Taylors, Gucci eyeglasses and a retro zip-up cardigan. This is his outfit of choice so long as he's not giving a speech somewhere, in which case he might change his shoes and throw on a jacket.

Born in Birkenhead, a small town outside Liverpool, Wilmott studied applied math at Oxford. In his spare time, he dabbled in juggling and competitive ballroom dancing. After earning a Ph.D. in fluid mechanics from Oxford in 1985, he got his start as an applied mathematician, working on jet-engine turbines for Rolls-Royce and calculating detonation sites for an explosives company. In the late 1980s, he started applying math to finance. His first burst of fame came in 1993 when he co-wrote a textbook on derivatives. Soon he'd made a name for himself as a contrarian guru, writing more textbooks, and giving speeches around the world to rooms full of bankers. From 2001 to 2005 he ran a $170 million hedge fund that returned an average of 15 percent a year.

Back on Oxford Street, Wilmott walks by several tube stops, deep in conversation on the topic that gets him most agitated these days: structured credit, the area of finance most at fault in the crash, and where quants inflicted the most damage by applying mathematical models they swore could predict default rates. "A complete lapse of ethics and responsibility," he calls it.

A collateralized debt obligation (CDO) is the most common form of structured credit. Banks build CDOs by putting together a bunch of loans, slicing them into little pieces (tranches) and selling them off to investors. Think of it as disassembling a cow into different cuts of meat—from prime steaks to ground beef—that are priced according to their quality. The first CDO was issued in 1987 by Drexel Burnham Lambert, the same firm that went bust in 1990. After the fall of Drexel, CDOs went away for a while, until the quants came along. In 2000, the CDO market was jump-started by David X. Li, who, while working at JPMorgan, created the Gaussian copula function, a formula for determining the correlation between the default rates of different securities. In theory, the model tells you the odds that, if one CDO goes bad, others will too. The apparent genius of the Gaussian copula is its abstraction. Rather than relying on the immense amount of data used to figure the odds that a CDO might default, Li appeared to have discovered a law of correlation. That is, you didn't need the data; the correlation was just there. Armed with it, quants could price CDOs much faster, and traders could buy and sell them at record speeds. Gaussian was rocket fuel for the CDO market. The global volume of CDO deals went from $157 billion in 2004 to $520 billion in 2006. As more banks got in on the game, the once large profit margins started to shrink. In order for banks to make the same kind of returns, they had to pack more and more loans into a CDO, essentially making bigger bombs. Li was on his way to a Nobel Prize when the world blew up. Wilmott marvels at the carelessness of it all. "They built these things on false assumptions without testing them, and stuffed them full of trillions of dollars. How could anyone have thought that was a good idea?"

To Wilmott, Gaussian is an example of how dangerously abstract quant finance has become. "We need to get back to testing models rather than revering them," he says. "That's hard work, but this idea that there are these great principles governing finance and that correlations can just be plucked out of the air is totally false." Wilmott spends a lot of time with another former student trying to tackle the biggest problem facing quant finance right now: how to price all those CDOs sitting on the balance sheets of banks, the toxic assets we hear so much about. "We don't have the tools yet to truly price them," Wilmott says. "People thought we did, but they were nowhere near robust enough."

The optimist in Wilmott thinks that people realize these models don't work. But he's not really an optimist. "What I think is going to happen is that people will forget and we'll just keep going on the way we have been with nothing really changing," he says. Wilmott is encouraged by President Obama's proposals to tighten regulation of derivatives; he thinks it'll keep quants on a shorter leash. But he's also stunned by the lack of outrage over the financial mess. The violence that erupted at this year's G20 summit wasn't anywhere near what he thought it should've been. "Where the hell was everybody? If people aren't angry now, they'll never be."

Wilmott realizes he's fighting a losing battle, and that changing finance will take a lot more than a few thousand better-prepared quants. As long as banks get paid in the first year for selling a CDO that doesn't mature for 30 years, little will change. Still, he does sense a tidal shift. "I've been helped by recent events, but I don't really take solace in that. I'm not gonna say I told you so."

For now, Wilmott will go about the hard work of retraining his merry band of quant soldiers, hoping his attempts at remedial education can help minimize the odds of a future derivatives-fueled melt-down. Waiting for traffic in the shadow of St. Paul's Cathedral, having walked the three miles from Grosvenor Square, Wilmott realizes he's late for the CQF class. "My God, I'm lecturing in 10 minutes!" For investors who hope to be protected from these "financial weapons of mass destruction," it's not a moment too soon.

URL: http://www.newsweek.com/id/200015"

Monday, March 9, 2009

Call this the testosterone theory: physicists are attracted to Wall Street because they like the atmosphere

From Mother Jones:

"
Quants

Dennis Overbye has a piece in the New York Times today about "quants," the geeks and nerds who have converged on Wall Street in recent years and tried to use mathematical models to outsmart the market and generate vast sums of risk-free cash for their employers. I've read a bunch of stories in this genre, and most of them have something in common that's always slightly puzzled me. See if you can guess what it is based on these excerpts from Oberbye's piece:

Emanuel Derman....left particle physics for a job on Wall Street...."it had the quality of physics"....forerunner of the many physicists and other scientists who have flooded Wall Street....physics Web site arXiv.org....“My Life as a Quant: Reflections on Physics and Finance”

....Asked to compare her work to physics....There are a thousand physicists on Wall Street....Physicists began to follow the jobs from academia to Wall Street in the late 1970s....Lee Smolin, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo....J. Doyne Farmer, a physicist and professor at the Santa Fe Institute.

....“I think physicists should go back to the physics department and leave Wall Street alone”....Eric R. Weinstein, a mathematical physicist....Nigel Goldenfeld, a physics professor at the University of Illinois....too many physicists on Wall Street.

Did you figure it out? What's the deal with physicists? They always seem to be at the center of these stories, but the fundamental tool of the quants is math. So why not mathematicians instead of physicists?

Overbye suggests a couple of possibilities. #1 is the glut theory: "Physicists began to follow the jobs from academia to Wall Street in the late 1970s, when the post-Sputnik boom in science spending had tapered off and the college teaching ranks had been filled with graduates from the 1960s. The result, as Dr. Derman said, was a pipeline with no jobs at the end."

#2 is the affinity theory: "The Black-Scholes equation resembles the kinds of differential equations physicists use to represent heat diffusion and other random processes in nature. Except, instead of molecules or atoms bouncing around randomly, it is the price of the underlying stock."

Those both sound plausible, if incomplete, so here's another thing to think about. Even among the number crunching set, physics has a reputation as the most aggressive, male dominated branch of geekdom: only 14% of physics PhDs are women, the lowest of any of the sciences. (Math is pretty male dominated too, but pales compared to physics: 29% of math PhDs are women.) If the first thing that "aggressive and male dominated" reminds you of is the big swinging dick world of high finance, give yourself a gold star. Call this the testosterone theory: physicists are attracted to Wall Street because they like the atmosphere.

Any other theories? Leave 'em in comments."

Me:
Physics and Finance

"http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=122be933-0394-4405-802b-2d48a2803191&shouldResize=False"

I'd like to recommend the above lecture on Gauge Theory and Inflation by Eric Weinstein. It's pretty clear.

He seems to want to show that Gauge Theory applies in many areas, thereby showing that it's a basic feature of the universe I suppose. In any case, his presentation shows why some physicists are interested in economics and finance. It could be that this view is quite common, and explains both the use of physics and why physicists are thought to be competent at economics and finance. Just a thought.

Sunday, January 11, 2009

our fear circuitry kicks in and panic ensues, a flight-to-safety leading to a market crash. This is where we are today.

From Freakonomics:

"
This Is Your Brain on Prosperity: Andrew Lo on Fear, Greed, and Crisis Management
INSERT DESCRIPTIONAndrew Lo


Andrew W. Lo
is the Harris & Harris Group Professor at M.I.T. and director of its Laboratory for Financial Engineering. (Here are some of his papers.)

To my mind, he’s one of the most fluent guides to the state of modern finance in that he combines the rigors of a quant with a behavioralist’s appreciation for human intricacy( HUMAN AGENCY EXPLANATION ). He has agreed to write a guest post here (hopefully not his last — please encourage him!), an insightful look at how “extended periods of prosperity act as an anesthetic in the human brain,” lulling everyone involved into “a drug-induced stupor that causes us to take risks that we know we should avoid( WISHFUL THINKING ).”


Fear, Greed, and Crisis Management: A Neuroscientific Perspective
By Andrew W. Lo
A Guest Post

The alleged fraud perpetrated by Bernard Madoff is a timely and powerful microcosm of the current economic crisis, and it underscores the origin of all financial bubbles and busts: fear and greed( TRUE ).

Using techniques such as magnetic resonance imaging, neuroscientists have documented the fact that monetary gain stimulates the same reward circuitry as cocaine — in both cases, dopamine is released into the nucleus accumbens. Similarly, the threat of financial loss activates the same fight-or-flight circuitry as physical attacks, releasing adrenaline and cortisol into the bloodstream, which results in elevated heart rate, blood pressure, and alertness.( OK )

These reactions are hardwired into human physiology, and while some of us are able to overcome our biology through education, experience, or genetic good luck, the vast majority of the human population is driven( INFLUENCED ) by these “animal spirits” that John Maynard Keynes identified over 70 years ago.

From this neuroscientific perspective, it is not surprising that there have been 17 banking-related national crises around the globe since 1974, the majority of which were preceded by periods of rising real-estate and stock prices, large capital inflows, and financial liberalization. Extended periods of prosperity act as an anesthetic in the human brain, lulling investors, business leaders, and policymakers into a state of complacency, a drug-induced stupor that causes us to take risks that we know we should avoid( I AGREE THAT WISHFUL THINKING IS VERY IMPORTANT. HOWEVER, THOSE RISKS TAKEN INCLUDE CRIME, AND THE COMPLACENCY INCLUDES GOVERNMENT GUARANTEES AND EFFECTIVENESS. ).

In the case of Madoff, seasoned investors were apparently sucked into the alleged fraud despite their better judgment because they found his returns too tempting to pass up. In the case of subprime mortgages, homeowners who knew they could not afford certain homes proceeded nonetheless, because the prospects of living large and benefiting from home-price appreciation were too tempting to pass up. And investors in mortgage-backed securities, who knew that the AAA ratings were too optimistic given the riskiness of the underlying collateral, purchased these securities anyway because they found the promised yields and past returns too tempting to pass up.( SOME OF THIS IS CRIMINAL OR NEGLIGENT BEHAVIOR. )

If we add to these temptations a period of financial gain that anesthetizes the general population — including C.E.O.’s, chief risk officers, investors, and regulators — it is easy to see how tulip bulbs, internet stocks, gold, real estate, and fraudulent hedge funds could develop into bubbles. Such gains are unsustainable, and once the losses start mounting, our fear circuitry kicks in and panic ensues( I AGREE ), a flight-to-safety leading to a market crash. This is where we are today.( I AGREE COMPLETELY )

Like hurricanes, financial crises are a force of nature that cannot be legislated away, but we can greatly reduce the damage they do with proper preparation.( I DISAGREE. GOVERNMENT GUARANTEES AND BAGEHOT'S PRINCIPLES CAN RID US OF THIS PESTILENCE. )

Because the most potent form of fear is fear of the unknown, the most effective way to combat the current crisis is with transparency and education. In the short run, one way to achieve transparency is for our president-elect to convene a “crisis summit” once in office, in which all the major stakeholders involved in this crisis, and their most knowledgeable subordinates, are invited to an undisclosed location for an intensive week-long conference( NO ).

During this meeting, detailed information about exposures to “toxic assets,” concentrations of risky counterparty relationships, and other systemic weaknesses will be provided on a confidential basis to regulators and policymakers, and various courses of action can be proposed and debated in real time( NO. COLLUSION CENTRAL. ). Afterward, a redacted( YES. OF MEANING. ) summary of this meeting should be provided to the public by the president, along with a specific plan for addressing the major issues identified during the conference. This process would go a long way toward calming the public’s fears and restoring the trust and confidence that are essential to normal economic activity.( NO. GOVERNMENT GUARANTEES WILL. JAWBONING IS OF LIMITED, ALTHOUGH SOME, USE. )

In the long run, more transparency into the “shadow banking” system; more education for investors, policymakers, and business leaders; and more behaviorally oriented regulation( FINALLY. YES. ) will allow us to weather any type of financial crisis( I AGREE ). Regulation enables us to restrain our behavior during periods when we know we will misbehave; it is most useful during periods of collective fear or greed and should be designed accordingly( YES ). Corporate governance should also be revisited from this perspective; if we truly value naysayers during periods of corporate excess, then we should institute management changes to protect and reward their independence.( HOW ABOUT THEIR EFFECTIVENESS.)

If “crisis is a terrible thing to waste,” as some have argued, then we have a short window of opportunity — before economic recovery begins to weaken our resolve — to reform our regulatory infrastructure for the better. The fact that time heals all wounds may be good for our mental health, but it may not help maintain our economic wealth."

I disagree. Poor regulation and legislation result in a crisis. However hard and counterintuitive it is, we must address these issues in calmer times. This is no harder for a human to do than value investing.

He met the mathematicians at the heart of the City - and found out why some say they are to blame for the financial crisis.

Via Alea, another excellent BBC post:

"
The maths of the credit crunch

Tim Harford (image copyright: Fran Monks)
BBC Radio 4 and iPlayer
Subscribe to the podcast
As the downturn takes hold, BBC Radio 4's More or Less programme looks at the maths behind the credit crunch.

Since 2007, presenter and economist Tim Harford( HE'S VERY GOOD IN THE FT ) has been exploring and explaining the numbers which have contributed to - and have characterised - the global economic downturn.

He met the mathematicians at the heart of the City - and found out why some say they are to blame for the financial crisis.

He uncovered the flaws of the bankers' bonus system, and discovered a mathematical error which might have led the banks into trouble.

He interviewed quantitative finance expert Paul Willmott and The Financial Times journalist Gillian Tett.

And he met the guardians of what could be the financial world's most important number.

You can listen to all of Tim's reports here.

PAUL WILMOTT, QUANTITATIVE FINANCE EXPERT

Paul Wilmott is a lecturer in financial mathematics and runs the profession's most popular website. ( HE'S TERRIFIC )

Paul Wilmott

He is a fan of quantitative finance( AS AM I ) - but he thinks that its misuse( YES ) has played a part in creating the current banking crisis.

In November 2007, More or Less asked whether the financial mathematicians known as "quants" - short for quantitative analysts - were to blame for what was then being termed "the credit squeeze".

WHO ARE THE QUANTS?
Paul Wilmott discussed his concerns with Professor William Perraudin of the Tanaka Business School at Imperial College London.

Tim Harford chaired the discussion.

The risks of risk management

In December 2008, Tim invited Paul Wilmott back to talk about the problems in more detail.

Banks and hedge funds rely on highly-paid mathematicians and economists - "quants" - to evaluate risk.

So why did they not they see the credit crunch coming?

Paul Wilmott says some mathematicians have a tendency to get fixated on the numbers, failing to think about the big picture.

RISKY RISK MANAGEMENT

He posed a scenario.

Imagine you are at a magic show. The magician takes an ordinary pack of 52 playing cards, and gives it to a man in the audience to shuffle. He then asks a volunteer to think of a card. "The ace of spades," she replies.

The magician turns to the man with the pack of cards and removes a single card from the deck. What is the probability that the card is the ace of spaces?

To hear the answer listen to the interview, or read Paul Wilmott's article on the risks of risk management.

A fundamental mathematical error

Paul Wilmott says an additional cause of the credit crunch is that people simply got their sums wrong.

GETTING THE SUMS WRONG
He told More or Less these errors might have contributed to the mispricing of financial derivatives, and thus to the travails of the banks, the credit crunch, and the economic downturn.

The maths of the bonus system

Many traders were paid bonuses if they made money.

And yet, collectively, their trades bankrupted some banks and nearly bankrupted many more.

THE TRADER'S DILEMMA
Why did traders, paid for performance, all make the same mistake at the same time?

Paul Wilmott set out the trader's dilemma.

AT HOME WITH THE QUANTS
In October 2007, Tim Harford got a glimpse into the world of the quants.


William Hooper
The most successful of these talented mathematicians will come up with mathematical formulae that make them and their bank or hedge fund employers millions of pounds per year.

They are highly secretive about their work, not wanting others to know the details of their systems.

MEET THE QUANTS
But one of them, William Hooper, invited Tim Harford into his beautiful London home.

Read more about quantitative analysts

A trader's apology

William Hooper has since left the world of finance to start his own business.

He has been reflecting on the global economic problems and the question of who is to blame - read A trader's apology.

GILLIAN TETT, THE FINANCIAL TIMES
Gillian Tett is an assistant editor of the Financial Times and oversees the global coverage of the financial markets.( SHE'S VERY GOOD )


Gillian Tett
Five years ago, she was shocked to discover what she says could best be described as an iceberg in the middle of the City.

The role of the media

She was studying media coverage of the City and began to realise journalists were doing lots of stories on stocks and shares, mergers and acquisitions, but nothing on what had become a much bigger part of finance - the credit and derivative markets.

She says business journalists were simply not covering the City in a representative way.

THE FINANCIAL ICEBERG

You had a small part of the financial system bobbing above the water but a vast shadowy mass of activity pretty much hidden beneath the waves.

And hidden not just from ordinary people, but hidden from politicians, from many regulators, and unfortunately from much of the media too.

UNDERSTANDING LIBOR

The London Interbank Offered Rate - LIBOR - has been dubbed the financial world's most important number.

A view of the City

Published each day in the UK, it is the rate at which the banks lend to each other and it influences over $150 trillion (£100 trillion) of funds worldwide.

The Libor number is compiled by putting together the estimates of the cost of borrowing from at least eight banks, and then discarding the highest and lowest of the sample to leave an average rate which then becomes the daily 'Libor Fix'.

LIBOR

But the figure's validity is being questioned, with critics dubbing it "the rate at which banks won't lend".

Tim Harford was granted exclusive access to the operations centre where the daily rate is compiled.

More or Less is broadcast on BBC Radio 4. To find out more, visit the programme website, or subscribe to the More or Less podcast."

Saturday, January 3, 2009

"When Wall Street stopped looking for dragons, nothing was going to save it. Not even VaR."

From Joe Nocera on the NY Times:

Zohar Lazar

Zohar Lazar

Christoph Niemann

Brian Cronin

Adrian Tomine

Gary Taxali

Christoph Niemann

Ronald Kurniawan

‘The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on( 1 ) quantification and numbers, determined by the patterns of the past, and those who base their decisions on( 2 ) more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved( TRUE ).’

— FROM THE INTRODUCTION TO ‘‘AGAINST THE GODS: THE REMARKABLE STORY OF RISK,’’ BY PETER L. BERNSTEIN

THERE AREN’T MANY widely told anecdotes about the current financial crisis, at least not yet, but there’s one that made the rounds in 2007, back when the big investment banks were first starting to write down billions of dollars in mortgage-backed derivatives and other so-called toxic securities. This was well before Bear Stearns collapsed, before Fannie Mae and Freddie Mac were taken over by the federal government, before Lehman fell and Merrill Lynch was sold and A.I.G. saved, before the $700 billion bailout bill was rushed into law. Before, that is, it became obvious that the risks taken by the largest banks and investment firms in the United States — and, indeed, in much of the Western world — were so excessive and foolhardy that they threatened to bring down the financial system itself. On the contrary: this was back when the major investment firms were still assuring investors that all was well, these little speed bumps notwithstanding — assurances based, in part, on their fantastically complex mathematical models( THIS IS WHERE THE REAL COMPLEXITY IS ) for measuring the risk in their various portfolios.

There are many such models, but by far the most widely used is called VaR — Value at Risk. Built around statistical ideas and probability theories that have been around for centuries, VaR was developed and popularized in the early 1990s by a handful of scientists and mathematicians — “quants,” they’re called in the business — who went to work for JPMorgan. VaR’s great appeal, and its great selling point to people who do not happen to be quants, is that it expresses risk as a single number, a dollar figure, no less.

VaR isn’t one model but rather a group of related models that share a mathematical framework. In its most common form, it measures the boundaries of risk in a portfolio over short durations, assuming a “normal” market. For instance, if you have $50 million of weekly VaR, that means that over the course of the next week, there is a 99 percent chance that your portfolio won’t lose more than $50 million. That portfolio could consist of equities, bonds, derivatives or all of the above; one reason VaR became so popular is that it is the only commonly used risk measure that can be applied to just about any asset class. And it takes into account a head-spinning variety of variables, including diversification, leverage and volatility, that make up the kind of market risk that traders and firms face every day.

Another reason VaR is so appealing is that it can measure both individual risks — the amount of risk contained in a single trader’s portfolio, for instance — and firmwide risk, which it does by combining the VaRs of a given firm’s trading desks and coming up with a net number. Top executives usually know their firm’s daily VaR within minutes of the market’s close.

Risk managers use VaR to quantify their firm’s risk positions to their board. In the late 1990s, as the use of derivatives was exploding, the Securities and Exchange Commission ruled that firms had to include a quantitative disclosure of market risks in their financial statements for the convenience of investors, and VaR became the main tool for doing so. Around the same time, an important international rule-making body, the Basel Committee on Banking Supervision, went even further to validate VaR by saying that firms and banks could rely on their own internal VaR calculations to set their capital requirements. So long as their VaR was reasonably low, the amount of money they had to set aside to cover risks that might go bad could also be low.

Given the calamity that has since occurred, there has been a great deal of talk, even in quant circles, that this widespread institutional reliance on VaR was a terrible mistake. At the very least, the risks that VaR measured did not include the biggest risk of all: the possibility of a financial meltdown. “Risk modeling didn’t help as much as it should have,” says Aaron Brown, a former risk manager at Morgan Stanley who now works at AQR, a big quant-oriented hedge fund. A risk consultant named Marc Groz says, “VaR is a very limited tool.” David Einhorn, who founded Greenlight Capital, a prominent hedge fund, wrote not long ago that VaR was “relatively useless as a risk-management tool and potentially catastrophic when its use creates a false sense of security among senior managers and watchdogs. This is like an air bag that works all the time, except when you have a car accident.” Nassim Nicholas Taleb, the best-selling author of “The Black Swan,” has crusaded against VaR for more than a decade. He calls it, flatly, “a fraud.”

How then do we account for that story that made the rounds in the summer of 2007? It concerns Goldman Sachs, the one Wall Street firm that was not, at that time, taking a hit for billions of dollars of suddenly devalued mortgage-backed securities. Reporters wanted to understand how Goldman had somehow sidestepped the disaster that had befallen everyone else. What they discovered was that in December 2006, Goldman’s various indicators, including VaR and other risk models, began suggesting that something was wrong. Not hugely wrong, mind you, but wrong enough to warrant a closer look.

“We look at the P.& L. of our businesses every day,” said Goldman Sachs’ chief financial officer, David Viniar, when I went to see him recently to hear the story for myself. (P.& L. stands for profit and loss.) “We have lots of models here that are important, but none are more important than the P.& L., and we check every day to make sure our P.& L. is consistent with where our risk models say it should be. In December our mortgage business lost money for 10 days in a row. It wasn’t a lot of money, but by the 10th day we thought that we should sit down and talk about it.”

So Goldman called a meeting of about 15 people, including several risk managers and the senior people on the various trading desks. They examined a thick report that included every trading position the firm held. For the next three hours, they pored over everything. They examined their VaR numbers and their other risk models. They talked about how the mortgage-backed securities market “felt.” “Our guys said that it felt like it was going to get worse before it got better,” Viniar recalled. “So we made a decision: let’s get closer to home.”

In trading parlance, “getting closer to home” means reining in the risk, which in this case meant either getting rid of the mortgage-backed securities or hedging the positions so that if they declined in value, the hedges would counteract the loss with an equivalent gain. Goldman did both. And that’s why, back in the summer of 2007, Goldman Sachs avoided the pain that was being suffered by Bear Stearns, Merrill Lynch, Lehman Brothers and the rest of Wall Street.

The story was told and retold in the business pages. But what did it mean, exactly? The question was always left hanging. Was it an example of the futility of risk modeling or its utility? Did it show that risk models, properly understood, were not a fraud after all but a potentially important signal that trouble was brewing? Or did it suggest instead that a handful of human beings at Goldman Sachs acted wisely by putting their models aside and making “decisions on more subjective degrees of belief about an uncertain future,” as Peter L. Bernstein put it in “Against the Gods?”

To put it in blunter terms, could VaR and the other risk models Wall Street relies on have helped prevent the financial crisis if only Wall Street paid better attention to them? Or did Wall Street’s reliance on them help lead us into the abyss?

One Saturday a few months ago, Taleb, a trim, impeccably dressed, middle-aged man — inexplicably, he won’t give his age — walked into a lobby in the Columbia Business School and headed for a classroom to give a guest lecture. Until that moment, the lobby was filled with students chatting and eating a quick lunch before the afternoon session began, but as soon as they saw Taleb, they streamed toward him, surrounding him and moving with him as he slowly inched his way up the stairs toward an already-crowded classroom. Those who couldn’t get in had to make do with the next classroom over, which had been set up as an overflow room. It was jammed, too.

It’s not every day that an options trader becomes famous by writing a book, but that’s what Taleb did, first with “Fooled by Randomness,” which was published in 2001 and became an immediate cult classic on Wall Street, and more recently with “The Black Swan: The Impact of the Highly Improbable,” which came out in 2007 and landed on a number of best-seller lists. He also went from being primarily an options trader to what he always really wanted to be: a public intellectual. When I made the mistake of asking him one day whether he was an adjunct professor, he quickly corrected me. “I’m the Distinguished Professor of Risk Engineering at N.Y.U.,” he responded. “It’s the highest title they give in that department.” Humility is not among his virtues. On his Web site he has a link that reads, “Quotes from ‘The Black Swan’ that the imbeciles did not want to hear.”

“How many of you took statistics at Columbia?” he asked as he began his lecture. Most of the hands in the room shot up. “You wasted your money,” he sniffed. Behind him was a slide of Mickey Mouse that he had put up on the screen, he said, because it represented “Mickey Mouse probabilities.” That pretty much sums up his view of business-school statistics and probability courses.

Taleb’s ideas can be difficult to follow, in part because he uses the language of academic statisticians; words like “Gaussian,” “kurtosis” and “variance” roll off his tongue. But it’s also because he speaks in a kind of brusque shorthand, acting as if any fool should be able to follow his train of thought, which he can’t be bothered to fully explain.

“This is a Stan O’Neal trade,” he said, referring to the former chief executive of Merrill Lynch. He clicked to a slide that showed a trade that made slow, steady profits — and then quickly spiraled downward for a giant, brutal loss.

“Why do people measure risks against events that took place in 1987?” he asked, referring to Black Monday, the October day when the U.S. market lost more than 20 percent of its value and has been used ever since as the worst-case scenario in many risk models. “Why is that a benchmark? I call it future-blindness.

“If you have a pilot flying a plane who doesn’t understand there can be storms, what is going to happen?” he asked. “He is not going to have a magnificent flight. Any small error is going to crash a plane. This is why the crisis that happened was predictable.”

Eventually, though, you do start to get the point. Taleb says that Wall Street risk models, no matter how mathematically sophisticated, are bogus; indeed, he is the leader of the camp that believes that risk models have done far more harm than good. And the essential reason for this is that the greatest risks are never the ones you can see and measure, but the ones you can’t see and therefore can never measure. The ones that seem so far outside the boundary of normal probability that you can’t imagine they could happen in your lifetime — even though, of course, they do happen, more often than you care to realize. Devastating hurricanes happen. Earthquakes happen. And once in a great while, huge financial catastrophes happen. Catastrophes that risk models somehow always manage to miss.

VaR is Taleb’s favorite case in point. The original VaR measured portfolio risk along what is called a “normal distribution curve,” a statistical measure that was first identified by Carl Friedrich Gauss in the early 1800s (hence the term “Gaussian”). It is a simple bell curve of the sort we are all familiar with.

The reason the normal curve looks the way it does — why it rises as it gets closer to the middle — is that the closer you get to that point, the smaller the change in the thing you’re measuring, and hence the more frequently it is likely to occur. A typical stock or portfolio of stocks, for example, is far likelier to gain or lose one point in a day (or a week) than it is to gain or lose 20 points. So the pattern of normal distribution will cluster around those smaller changes toward the middle of the curve, while the less-frequent distributions will fall along the ends of the curve.

VaR uses this normal distribution curve to plot the riskiness of a portfolio. But it makes certain assumptions. VaR is often measured daily and rarely extends beyond a few weeks, and because it is a very short-term measure, it assumes that tomorrow will be more or less like today. Even what’s called “historical VaR” — a variation of standard VaR that measures potential portfolio risk a year or two out, only uses the previous few years as its benchmark. As the risk consultant Marc Groz puts it, “The years 2005-2006,” which were the culmination of the housing bubble, “aren’t a very good universe for predicting what happened in 2007-2008.”

This was one of Alan Greenspan’s primary excuses when he made his mea culpa for the financial crisis before Congress a few months ago. After pointing out that a Nobel Prize had been awarded for work that led to some of the theories behind derivative pricing and risk management, he said: “The whole intellectual edifice, however, collapsed in the summer of last year because the data input into the risk-management models generally covered only the past two decades, a period of euphoria. Had instead the models been fitted more appropriately to historic periods of stress, capital requirements would have been much higher and the financial world would be in far better shape today, in my judgment.” Well, yes. That was also the point Taleb was making in his lecture when he referred to what he called future-blindness. People tend not to be able to anticipate a future they have never personally experienced.

Yet even faulty historical data isn’t Taleb’s primary concern. What he cares about, with standard VaR, is not the number that falls within the 99 percent probability. He cares about what happens in the other 1 percent, at the extreme edge of the curve. The fact that you are not likely to lose more than a certain amount 99 percent of the time tells you absolutely nothing about what could happen the other 1 percent of the time. You could lose $51 million instead of $50 million — no big deal. That happens two or three times a year, and no one blinks an eye. You could also lose billions and go out of business. VaR has no way of measuring which it will be.

What will cause you to lose billions instead of millions? Something rare, something you’ve never considered a possibility. Taleb calls these events “fat tails” or “black swans,” and he is convinced that they take place far more frequently than most human beings are willing to contemplate. Groz has his own way of illustrating the problem: he showed me a slide he made of a curve with the letters “T.B.D.” at the extreme ends of the curve. I thought the letters stood for “To Be Determined,” but that wasn’t what Groz meant. “T.B.D. stands for ‘There Be Dragons,’ ” he told me.

And that’s the point. Because we don’t know what a black swan might look like or when it might appear and therefore don’t plan for it, it will always get us in the end. “Any system susceptible to a black swan will eventually blow up,” Taleb says. The modern system of world finance, complex and interrelated and opaque, where what happened yesterday can and does affect what happens tomorrow, and where one wrong tug of the thread can cause it all to unravel, is just such a system.

“I have been calling for the abandonment of certain risk measures since 1996 because they cause people to cross the street blindfolded,” he said toward the end of his lecture. “The system went bust because nobody listened to me.”

After the lecture, the professor who invited Taleb to Columbia took a handful of people out for a late lunch at a nearby diner. Somewhat surprisingly, given Taleb’s well-known scorn for risk managers, the professor had also invited several risk managers who worked at two big investment banks. We had barely been seated before they tried to engage Taleb in a debate over the value of VaR. But Taleb is impossible to argue with on this subject; every time they raised an objection to his argument, he curtly dismissed them out of hand. “VaR can be useful,” said one of the risk managers. “It depends on how you use it. It can be useful in identifying trends.”

“This argument is addressed in ‘The Black Swan,’ ” Taleb retorted. “Not a single person has offered me an argument I haven’t heard.”

“I think VaR is great,” said another risk manager. “I think it is a fantastic tool. It’s like an altimeter in aircraft. It has some margin for error, but if you’re a pilot, you know how to deal with it. But very few pilots give up using it.”

Taleb replied: “Altimeters have errors that are Gaussian. You can compensate. In the real world, the magnitude of errors is much less known.”

Around and around they went, talking past each other for the next hour or so. It was engaging but unsatisfying; it didn’t help illuminate the role risk management played in the crisis.

The conversation had an energizing effect on Taleb, however. He walked out of the diner with a full head of steam, railing about the two “imbeciles” he just had to endure. I used the moment to ask if he knew the people at RiskMetrics, a successful risk-management consulting firm that spun out of the original JPMorgan quant effort in the mid-1990s. “They’re intellectual charlatans,” he replied dismissively. “You can quote me on that.”

As we approached his car, he began talking about his own performance in 2008. Although he is no longer a full-time trader, he remains a principal in a hedge fund he helped found, Black Swan Protection Protocol. His fund makes trades that either gain or lose small amounts of money in normal times but can make oversize gains when a black swan appears. Taleb likes to say that, as a trader, he has made money only three times in his life — in the crash of 1987, during the dot-com bust more than a decade later and now. But all three times he has made a killing. With the world crashing around it, his fund was up 65 to 115 percent for the year. Taleb chuckled. “They wouldn’t listen to me,” he said finally. “So I decided, to hell with them, I’ll take their money instead.”

“VaR WAS INEVITABLE,” Gregg Berman of RiskMetrics said when I went to see him a few days later. He didn’t sound like an intellectual charlatan. His explanation of the utility of VaR — and its limitations — made a certain undeniable sense. He did, however, sound like somebody who was completely taken aback by the amount of blame placed on risk modeling since the financial crisis began.

“Obviously, we are big proponents of risk models,” he said. “But a computer does not do risk modeling. People do it( FINALLY, THE MAIN POINT ). And people got overzealous and they stopped being careful. They took on too much leverage( VERY TRUE. BUT THAT WAS THE POINT OF CDSs AND CDOs IN THE FIRST PLACE. IN OTHER WORDS, LEVERAGE WASN'T A BYPRODUCT, IT WAS THE GOAL. ). And whether they had models that missed that, or they weren’t paying enough attention, I don’t know. But I do think that this was much more a failure of management than of risk management. I think blaming models for this would be very unfortunate because you are placing blame on a mathematical equation. You can’t blame math( I AGREE COMPLETELY. HOWEVER, MY VERSION OF TALEB IS THAT HE IS SAYING THE SAME THING. ),” he added with some exasperation.

Although Berman, who is 42, was a founding partner of RiskMetrics, it turned out that he was one of the few at the firm who hadn’t come from JPMorgan. Still, he knew the back story. How could he not? It was part of the lore of the place. Indeed, it was part of the lore of VaR.

The late 1980s and the early 1990s were a time when many firms were trying to devise more sophisticated risk models because the world was changing around them. Banks, whose primary risk had long been credit risk — the risk that a loan might not be paid back( THAT IS IN FACT THE WHAT THE PROBLEM WITH SUBPRIME AND OTHER MORTGAGES IS. THESE BAD LOANS CANNOT BE BLAMED ON MATH MODELS. IT IS STRAIGHTFORWARD CREDIT RISK. ) — were starting to meld with investment banks, which traded stocks and bonds. Derivatives and securitizations — those pools of mortgages or credit-card loans that were bundled by investment firms and sold to investors — were becoming an increasingly important component of Wall Street. But they were devilishly complicated to value( THEN THEY ARE INHERENTLY RISKY. WHY DO YOU THINK PEOPLE WANT US TREASURIES NOW? ONE REASON IS THAT THE ARE LIQUID=LESS RISKY ). For one thing, many of the more arcane instruments didn’t trade very often, so you had to try to value them by finding a comparable security that did trade( RISKY ). And they were sliced into different pieces — tranches they’re called — each of which had a different risk component( REALLY NO DIFFERENT THAN DIFFERENT GRADES OF BONDS. ). In addition every desk had its own way of measuring risk that was largely incompatible with every other desk.

JPMorgan’s chairman at the time VaR took off was a man named Dennis Weatherstone. Weatherstone, who died in 2008 at the age of 77, was a working-class Englishman who acquired the bearing of a patrician during his long career at the bank. He was soft-spoken, polite, self-effacing. At the point at which he took over JPMorgan, it had moved from being purely a commercial bank into one of these new hybrids. Within the bank, Weatherstone had long been known as an expert on risk, especially when he was running the foreign-exchange trading desk. But as chairman, he quickly realized that he understood far less about the firm’s overall risk than he needed to. Did the risk in JPMorgan’s stock portfolio cancel out the risk being taken by its bond portfolio — or did it heighten those risks? How could you compare different kinds of derivative risks? What happened to the portfolio when volatility increased or interest rates rose? How did currency fluctuations affect the fixed-income instruments? Weatherstone had no idea what the answers were. He needed a way to compare the risks of those various assets and to understand what his companywide risk was.( I'M NOT SURE THAT I UNDERSTAND THIS. IF NOTHING IS RISKY, HOW DOES IT ADD UP TO RISKY? )

The answer the bank’s quants had come up with was Value at Risk. To phrase it that way is to make it sound as if a handful of math whizzes locked themselves in a room one day, cranked out some formulas, and — presto! — they had a risk-management system. In fact, it took around seven years, according to Till Guldimann, an elegant, Swiss-born, former JPMorgan banker who ran the team that devised VaR and who is now vice chairman of SunGard Data Systems. “VaR is not just one invention,” he said. “You solved one problem and another cropped up. At first it seemed unmanageable. But as we refined it, the methodologies got better.”

Early on, the group decided that it wanted to come up with a number it could use to gauge the possibility that any kind of portfolio could lose a certain amount of money over the next 24 hours, within a 95 percent probability. (Many firms still use the 95 percent VaR, though others prefer 99 percent.) That became the core concept. When the portfolio changed, as traders bought and sold securities the next day, the VaR was then recalculated, allowing everyone to see whether the new trades had added to, or lessened, the firm’s risk( THIS MAKES SENSE ).

“There was a lot of suspicion internally,” recalls Guldimann, because traders and executives — nonquants — didn’t believe that such a thing could be quantified mathematically. But they were wrong. Over time, as VaR was proved more correct than not day after day, quarter after quarter, the top executives came not only to believe in it but also to rely on it( VERY BAD ).

For instance, during his early years as a risk manager, pre-VaR, Guldimann often confronted the problem of what to do when a trader had reached his trading limit but believed he should be given more capital to play out his hand. “How would I know if he should get the increase?” Guldimann says. “All I could do is ask around. Is he a good guy? Does he know what he’s doing? It was ridiculous. Once we converted all the limits to VaR limits, we could compare. You could look at the profits the guy made and compare it to his VaR. If the guy who asked for a higher limit was making more money with lower VaR” — that is, with less risk — “it was a good basis to give him the money.”( THIS DOES MAKE SENSE )

By the early 1990s, VaR had become such a fixture at JPMorgan that Weatherstone instituted what became known as the 415 report because it was handed out every day at 4:15, just after the market closed. It allowed him to see what every desk’s estimated profit and loss was, as compared to its risk, and how it all added up for the entire firm. True, it didn’t take into account Taleb’s fat tails, but nobody really expected it to do that( YES ). Weatherstone had been a trader himself; he understood both the limits and the value of VaR. It told him things he hadn’t known before. He could use it to help him make judgments( YES ) about whether the firm should take on additional risk or pull back. And that’s what he did.

What caused VaR to catapult above the risk systems being developed by JPMorgan competitors was what the firm did next: it gave VaR away. In 1993, Guldimann made risk the theme of the firm’s annual client conference. Many of the clients were so impressed with the JPMorgan approach that they asked if they could purchase the underlying system. JPMorgan decided it didn’t want to get into that business, but proceeded instead to form a small group, RiskMetrics, that would teach the concept to anyone who wanted to learn it, while also posting it on the Internet so that other risk experts could make suggestions to improve it. As Guldimann wrote years later, “Many wondered what the bank was trying to accomplish by giving away ‘proprietary’ methodologies and lots of data, but not selling any products or services.” He continued, “It popularized a methodology and made it a market standard, and it enhanced the image of JPMorgan.”

JPMorgan later spun RiskMetrics off into its own consulting company. By then, VaR had become so popular that it was considered the risk-model gold standard. Here was the odd thing, though: the month RiskMetrics went out on its own, September 1998, was also when Long-Term Capital Management “blew up.” L.T.C.M. was a fantastically successful hedge fund famous for its quantitative trading approach and its belief, supposedly borne out by its risk models, that it was taking minimal risk.( THIS IS A VERY IMPORTANT POINT )

L.T.C.M.’s collapse would seem to make a pretty good case for Taleb’s theories. What brought the firm down was a black swan it never saw coming: the twin financial crises in Asia and Russia. Indeed, so sure were the firm’s partners that the market would revert to “normal”( THIS IS SILLY. ) — which is what their model insisted would happen — that they continued to take on exposures that would destroy the firm as the crisis worsened, according to Roger Lowenstein’s account of the debacle, “When Genius Failed.” Oh, and another thing: among the risk models the firm relied on was VaR.

Aaron Brown, the former risk manager at Morgan Stanley, remembers thinking that the fall of L.T.C.M. could well lead to the demise of VaR. “It thoroughly punctured the myth that VaR was invincible( TRUE ),” he said. “Something that fails to live up to perfection is more despised than something that was never idealized in the first place.” After the 1987 market crash, for example, portfolio insurance, which had been sold by Wall Street as a risk-mitigation device, became largely discredited.

But that didn’t happen with VaR. There was so much schadenfreude associated with L.T.C.M. — it had Nobel Prize winners among its partners! — that it was easy for the rest of Wall Street to view its fall as an example of comeuppance. And for a hedge fund that promoted the ingeniousness of its risk measures, it took far greater risks than it ever acknowledged.

For these reasons, other firms took to rationalizing away the fall of L.T.C.M.; they viewed it as a human failure( IT WAS ) rather than a failure of risk modeling. The collapse only amplified the feeling on Wall Street that firms needed to be able to understand their risks for the entire firm. Only VaR could do that. And finally, there was a belief among some, especially after the crisis abated, that the events that brought down L.T.C.M. were one in a million. We would never see anything like that again in our lifetime( SILLY ).

So instead of diminishing in importance, VaR become a more important part of the financial scene. The Securities and Exchange Commission, for instance, worried about the amount of risk that derivatives posed to the system, mandated that financial firms would have to disclose that risk to investors( GOOD ), and VaR became the de facto measure( BAD ). If the VaR number increased from year to year in a company’s annual report, it meant the firm was taking more risk. Rather than doing anything to limit the growth of derivatives, the agency concluded( PEOPLE DID ) that disclosure, via VaR, was sufficient.

That, in turn, meant that even firms that had resisted VaR now succumbed. It meant that chief executives of big banks and investment firms had to have at least a passing familiarity with VaR. It meant that traders all had to understand the VaR consequences of making a big bet or of changing their portfolios. Some firms continued to use VaR as a tool while adding other tools as well, like “stress” or “scenario” tests, to see where the weak links in the portfolio were or what might happen if the market dropped drastically. But others viewed VaR as the primary measure they had to concern themselves with.

VaR, in other words, became institutionalized. RiskMetrics went from having a dozen risk-management clients to more than 600. Lots of competitors sprouted up. Long-Term Capital Management became an increasingly distant memory, overshadowed by the Internet boom and then the housing boom. Corporate chieftains like Stanley O’Neal at Merrill Lynch and Charles Prince at Citigroup pushed( YES ) their divisions to take more risk because they were being left behind in the race for trading profits. All over Wall Street, VaR numbers increased, but it still all seemed manageable — and besides, nothing bad was happening!

VaR also became a crutch. When an international banking group that advises national regulators decided the world needed more sophisticated ways to gauge the amount of capital that firms had to hold, Wall Street firms lobbied the group to allow them to use their internal VaR numbers. Ultimately, the group came up with an accord that allowed just that. It doesn’t seem too strong to say that as a direct result( ACTUALLY IT DOES, BECAUSE YOU'RE FOREGETTING THAT LOWER CAPITAL STANDARDS WAS THE WHOLE POINT OF THE EXERCISE. THESE ARE MERELY RATIONALIZATIONS. THEY PROVIDED A VENEER OF SAFETY TO INHERENTLY RISKY INVESTMENTS. ), banks didn’t have nearly enough capital when the black swan began to emerge in the spring of 2007.

ONE THING THAT surprised me, as I made the rounds of risk experts, was that if you listened closely, their views weren’t really that far from Taleb’s diagnosis of VaR. They agreed with him that VaR didn’t measure the risk of a black swan. And they were critical in other ways as well. Yes, the old way of measuring capital requirements needed updating, but it was crazy to base it on a firm’s internal VaR, partly because that VaR was not set by regulators and partly because it obviously didn’t gauge the kind of extreme events that destroy capital and create a liquidity crisis — precisely the moment when you need cash on hand.( I AGREE )

Indeed, Ethan Berman, the chief executive of RiskMetrics (and no relation to Gregg Berman), told me that one of VaR’s flaws, which only became obvious in this crisis, is that it didn’t measure liquidity risk( A CALLING RUN ) — and of course a liquidity crisis is exactly what we’re in the middle of right now. One reason nobody seems to know how to deal with this kind of crisis is because nobody envisioned it.( WAIT. THAT WAS WHAT LTCM WAS. A CALLING RUN WAS EXACTLY WHAT THEY SHOULD HAVE FEARED SINCE THEY WERE, AND READ THIS CAREFULLY, LOWERING CAPITAL STANDARDS. IS THERE ANYTHING COMPLICATED IN WHAT I'M SAYING? )

In a crisis, Brown, the risk manager at AQR, said, “you want to know who can kill you and whether or not they will and who you can kill if necessary. You need to have an emergency backup plan that assumes everyone is out to get you. In peacetime, you think about other people’s intentions. In wartime, only their capabilities matter. VaR is a peacetime statistic( SILLY. IT WAS A TOOL THAT WAS MISUSED. ).”

VaR DIDN’T GET EVERYTHING right even in what it purported to measure. All the triple-A-rated mortgage-backed securities churned out by Wall Street firms and that turned out to be little more than junk? VaR didn’t see the risk because it generally relied on a two-year data history( THAT ALONE SHOULD LEAD YOU TO DISTRUST IT FOR ANY MAJOR RISK ASSESSMENT. COME ON. ). Although it took into account the increased risk brought on by leverage( OBVIOUSLY IT DIDN'T, BECAUSE IT DIDN'T EVEN CONTEMPLATE A CALLING RUN. ), it failed to distinguish between leverage that came from long-term, fixed-rate debt — bonds and such that come due at a set date — and loans that can be called in at any time and can, as Brown put it “blow you up in two minutes.” That is, the kind of leverage that disappeared the minute something bad arose.( A CALLING RUN. )

“The old adage, ‘garbage in, garbage out’ certainly applies,” Groz said. “When you realize that VaR is using tame historical data to model a wildly different environment, the total losses of Bear Stearns’ hedge funds become easier to understand. It’s like the historic data only has rainstorms and then a tornado hits( ACTUALLY THEY USED WEATHER DATA TO MODEL SOME OF THE RISK. SILLY. ).”

Guldimann, the great VaR proselytizer, sounded almost mournful when he talked about what he saw as another of VaR’s shortcomings. To him, the big problem was that it turned out that VaR could be gamed( FRAUD ). That is what happened when banks began reporting their VaRs. To motivate managers, the banks began to compensate them not just for making big profits but also for making profits with low risks. That sounds good in principle, but managers began to manipulate( FRAUD ) the VaR by loading up on what Guldimann calls “asymmetric risk positions.” These are products or contracts that, in general, generate small gains and very rarely have losses. But when they do have losses, they are huge. These positions made a manager’s VaR look good because VaR ignored the slim likelihood of giant losses, which could only come about in the event of a true catastrophe. A good example was a credit-default swap, which is essentially insurance that a company won’t default( WAIT A MINUTE. THE WHOLE POINT OF A CDS IS TO CONTEMPLATE FORECLOSURE OR DEFAULT. ). The gains made from selling credit-default swaps are small and steady — and the chance of ever having to pay off that insurance was assumed to be minuscule( SILLY ). It was outside the 99 percent probability, so it didn’t show up in the VaR number. People didn’t see the size of those hidden positions lurking in that 1 percent that VaR didn’t measure.

EVEN MORE CRITICAL, it did not properly account for leverage( AGAIN. THAT'S THE WHOLE POINT OF A CDS AS OPPOSED TO JUST REGULAR INSURANCE. ) that was employed through the use of options. For example, said Groz, if an asset manager borrows money to buy shares of a company, the VaR would usually increase. But say he instead enters into a contract that gives someone the right to sell him those shares at a lower price at a later time — a put option. In that case, the VaR might remain unchanged. From the outside, he would look as if he were taking no risk, but in fact, he is( THAT'S NEGLIGENCE. ). If the share price of the company falls steeply, he will have lost a great deal of money. Groz called this practice “stuffing risk into the tails.”

And yet, instead of dismissing VaR as worthless, most of the experts I talked to defended it. The issue, it seemed to me, was less what VaR did and did not do, but how you thought about it. Taleb says that because VaR didn’t measure the 1 percent, it was worse than useless — it was downright harmful( IN THE WRONG HANDS. HE'S CALLING THESE PEOPLE IDIOTS. ). But most of the risk experts said there was a great deal to be said for being able to manage risk 99 percent of the time, however imperfectly, even though it meant you couldn’t account for the last 1 percent.

“If you say that all risk is unknowable,” Gregg Berman said, “you don’t have the basis of any sort of a bet or a trade. You cannot buy and sell anything unless you have some idea of the expectation of how it will move( TRUE ).” In other words, if you spend all your time thinking about black swans, you’ll be so risk averse you’ll never do a trade. Brown put it this way: “NT” — that is how he refers to Nassim Nicholas Taleb — “says that 1 percent will dominate your outcomes. I think the other 99 percent does matter. There are things you can do to control your risk( TRUE ). To not use VaR is to say that I won’t care about the 99 percent, in which case you won’t have a business. That is true even though you know the fate of the firm is going to be determined by some huge event. When you think about disasters, all you can rely on is the disasters of the past. And yet you know that it will be different in the future. How do you plan for that?”( BAGEHOT'S PRINCIPLES SIR )

One risk-model critic, Richard Bookstaber, a hedge-fund risk manager and author of “A Demon of Our Own Design,” ranted about VaR for a half-hour over dinner one night. Then he finally said, “If you put a gun to my head and asked me what my firm’s risk was, I would use VaR.” VaR may have been a flawed number, but it was the best number anyone had come up with.

Of course, the experts I was speaking to were, well, experts. They had a deep understanding of risk modeling and all its inherent limitations. They thought about it all the time. Brown even thought VaR was good when the numbers seemed “off,” or when it started to “miss” on a regular basis — it either meant that there was something wrong with the way VaR was being calculated, or it meant the market was no longer acting “normally.” Either way, he said, it told you something useful( THAT'S ALL THAT MODELS OR THEORIES CAN EVER DO ).

“When I teach it,” Christopher Donohue, the managing director of the research group at the Global Association of Risk Professionals, said, “I immediately go into the shortcomings. You can’t calculate a VaR number and think you know everything you need( TRUE ). On a day-to-day basis I don’t care so much that the VaR is 42. I care about where it was yesterday and where it is going tomorrow. What direction is the risk going?” Then he added, “That is probably another danger: because we put a dollar number to it, they attach a meaning to it( GOOD POINT ).”

By “they,” Donohue meant everyone who wasn’t a risk manager or a risk expert. There were the investors who saw the VaR numbers in the annual reports but didn’t pay them the least bit of attention. There were the regulators who slept soundly in the knowledge that, thanks to VaR, they had the whole risk thing under control. There were the boards who heard a VaR number once or twice a year and thought it sounded good. There were chief executives like O’Neal and Prince. There was everyone, really, who, over time, forgot that the VaR number was only meant to describe what happened 99 percent of the time. That $50 million wasn’t just the most you could lose 99 percent of the time. It was the least you could lose 1 percent of the time. In the bubble, with easy profits being made and risk having been transformed into mathematical conceit, the real meaning of risk had been forgotten. Instead of scrutinizing VaR for signs of impending trouble, they took comfort in a number and doubled down, putting more money at risk in the expectation of bigger gains. “It has to do with the human condition,” said one former risk manager. “People like to have one number they can believe in( THIS IS ANOTHER WAY OF SAYING THAT PEOPLE WERE PREDISPOSED TO EXTEND RISK, AND VAR GAVE THEM THE EXCUSE. HOWEVER, NOTHING FORCES YOU TO EXTEND RISK OR THROW OUT INVESTING AND BANKING COMMON SENSE. ).”

Brown told me: “You absolutely could see it coming( I AGREE ). You could see the risks rising( I AGREE ). However, in the two years before the crisis hit, instead of preparing for it, the opposite took place to an extreme degree. The real trouble we got into today is because of things that took place in the two years before, when the risk measures were saying that things were getting bad( I AGREE ).”

At most firms, risk managers are not viewed as “profit centers,” so they lack the clout of the moneymakers on the trading desks. That was especially true at the tail end of the bubble, when firms were grabbing for every last penny of profit.

At the height of the bubble, there was so much money to be made that any firm that pulled back because it was nervous about risk would forsake huge short-term gains and lose out to less cautious rivals. The fact that VaR didn’t measure the possibility of an extreme event was a blessing to the executives. It made black swans all the easier to ignore( NEGLIGENCE ). All the incentives — profits, compensation, glory, even job security — went in the direction of taking on more and more risk, even if you half suspected it would end badly( THIS IS WHERE GOVERNMENT GUARANTEES COME IN ). After all, it would end badly for everyone else too( THIS IS WHERE GOVERNMENT GUARANTEES COME IN ). As the former Citigroup chief executive Charles Prince famously put it, “As long as the music is playing, you’ve got to get up and dance.” Or, as John Maynard Keynes once wrote, a “sound banker” is one who, “when he is ruined, is ruined in a conventional and orthodox way.”

MAYBE IT WOULD HAVE been different if the people in charge had a better understanding of risk. Maybe it would have helped if Wall Street hadn’t turned VaR into something it was never meant to be. “If we stick with the Dennis Weatherstone example,” Ethan Berman says, “he recognized that he didn’t have the transparency into risk that he needed to make a judgment( THAT'S THE TICKET ). VaR gave him that, and he and his managers could make judgments. To me, that is how it should work. The role of VaR is as one input into that process. It is healthy for the head of the firm to have that kind of information. But people need to have incentives to give him that information( WHAT'S THEIR JOB? ).”

Which brings me back to David Viniar and Goldman Sachs. “VaR is a useful tool,” he said as our interview was nearing its end. “The more liquid the asset( YES ), the better the tool. The more history( YES ), the better the tool. The less of both, the worse it is. It helps you understand what you should expect to happen on a daily basis in an environment that is roughly the same. We had a trade last week in the mortgage universe where the VaR was $1 million. The same trade a week later had a VaR of $6 million. If you tell me my risk hasn’t changed — I say yes it has!” Two years ago, VaR worked for Goldman Sachs the way it once worked for Dennis Weatherstone — it gave the firm a signal that allowed it to make a judgment about risk. It wasn’t the only signal, but it helped. It wasn’t just the math that helped Goldman sidestep the early decline of mortgage-backed instruments. But it wasn’t just judgment either. It was both. The problem on Wall Street at the end of the housing bubble is that all judgment was cast aside. The math alone was never going to be enough.( TRUE )

Like most firms, Goldman does have other models to test for the fat tails. But even Goldman has been caught flat-footed by the crisis, struggling with liquidity, turning itself into a bank holding company and even, at one dire moment, struggling to combat rumors that it would be the next to fall.

“The question is: how extreme is extreme?” Viniar said. “Things that we would have thought were so extreme have happened. We used to say, What will happen if every equity market in the world goes down by 30 percent at the same time? We used to think of that as an extreme event — except that now it has happened. Nothing ever happens until it happens for the first time.”( LTCM. THE S & L CRISIS. )

Which didn’t mean you couldn’t use risk models to sniff out risks. You just had to know that there were risks they didn’t sniff out — and be ever vigilant for the dragons. When Wall Street stopped looking for dragons, nothing was going to save it. Not even VaR.

Joe Nocera is a business columnist for The Times and a staff writer for the magazine."

It's good post, with some good points, but it still didn't mention fraud or government guarantees, for instance. This pathetic view of math models is so silly that going over it again and again seems like overkill, but maybe it isn't. In the end, the math models didn't cause the problem. People did. Even the most basic explantion, that the models fooled people, I consider to be negilgence, since the inherent risk of leveraging is apparent to everyone, including people being paid millions for managing investments.