Day of Opportunity

These are all the stocks that triggered our numbers today from last night's newsletter:

Let's start with the two longs that went over our spots:

POT 103.


MOS 48.


JOYG 28 short.

BUCY 24 short.



BRCM 21 short.


ATI 36 short.



SPG 49 short.


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Bucket of Cold Water on the XLF

We have great respect for Meredith Whitney. She saw the cracks in the house of cards before the crisis, then before the latest bank earnings came out she said she wouldn't be short the financials (because of the Government intervention) and now after the rally she says she wouldn't own them. As good as it gets for an analyst.

If you haven't already seen this then sit down for the next 10 minutes and soak it all in:

Intraday Updates

Thus far today the bulls have done a very good job of holding support. These are intraday updates of the daily charts -- look how well support held this morning. If the sell-off is to gain any traction then the bears have to push through the following support levels:

XLB 26 area held. If that goes later in the day, watch for a dive to 25.


The 20 SMA held on the QQQQ; the Nasdaq was the weakest index last week, and now is the first one to bounce.




KOL bounced near support (and 200 MA)in the 21.4 area.


Perfect example of one of our favorite commodity plays, BTU, bouncing on previous minor support of 31.

XME bounced on 35 support.



Watch those levels -- if they go and selling accelerates then it's likely this is not just a 1 day pull-back.

Market Talk

With the exception of the Nasdaq weakness (as we discussed on Friday) the bulls are still in control; however, this could change soon.

XLF long to the 200 SMA, after that we'll be looking for reversal shorts.


Commercial Real Estate looks like it has one more pop left but will offer an excellent shorting opportunity at the 200 SMA. Unless IYR shows very clear relative weakness, stay long until 40. Ideally we run for a day, and then gap-up to 40 -- that would be a very nice risk/reward spot short on 40 resistance.



If you're leaning bearish then hope for quick max pain; the longer we base under resistance the more chance that the break-out will be successful. This is the reason we're hoping for a very big run or gap-up to resistance as the urge to take profits will be very strong compared to a slow grind up and base at resistance (which would increase the success rate of any break-out). So if you're a bear, hope for a big 2 day rally!

We've been writing about this trend-line on the QQQQ for a while now in the newsletter. Note today that the QQQQ is in a peculiar spot: in a little box under the trend-line but bouncing for the second day in a row on the 200 SMA.

On the upside it still has room to 36 until next major resistance and on the down-side, selling might pick-up on any hard break of the 200 SMA or break of the 2 day low around 33.85. Our thoughts are that sentiment is still very bullish and any significant selling in tech (for example a move to 32) would be a good buying opportunity.

Resting spot

Bull litmus test

Tomorrow should be interesting as news has come out tonight that BAC will need 34 Billion in capital as per government stress tests.

We're surprised at the news (as is the market with futures down 1.2% as we write this post) as we assumed the stress test had the bars set very low, since after all, it was created by the government.

Tomorrow should test the bull's resolve; we'll be watching for down-side momentum, volume, and how broad the potential pull-back will be. We'll also be focusing on possible divergences between financials and commodities.

If we sell-off hard tomorrow (and more importantly Thursday when the details and not just the headline leaks come out), and on good volume, then most likely it will be a start of at least an intermediate pull-back. If the market pulls back only with mild losses, or no losses, or even gains (!) then chances are that the S&P will be going to 1000 with ease.

Update: it seems that the BAC news has now been interpreted differently (not a big surprise since we would have been shocked to see these quasi tests actually produce bad news) and futures rallied on better than expected economic news.

We'll see how they close them -- any mild pull-back this week would be bullish to base under resistance, especially in the QQQQ and IWM.

Our thoughts

If we extrapolate from Friday's action then we would be long USO OIH XME MOO as money rotates into the new leadership of commodities. Of course reacting strongly from a few days of market action is not always the wisest thing to do; however, if we get continuation this week of the alleged new trend, then there's a good chance that this is for real. What we're looking for is for money to flow out of REITS and financials and into commodities. The wild card of course is the release of the stress test on Thursday.

If you see the trend continuing and want a pair trade then go short IYR XLF, and go long USO OIH XME MOO. Our feeling is that the aforementioned commodity ETFs will not only outperform the financials and REITs but also the small-caps (IWM), the Nasdaq (QQQQ) and the S&P 500 (SPY).

Hopefully we'll find out this week whether Friday was an anomaly or the start of a new trend. Stay tuned.

HCPG

Sector D: Steel and Iron

The best two charts we could find from this sector are AKS and RIO.

We had AKS at 12.5 in our newsletter Wednesday night -- it still looks good.



RIO over the 200 SMA and looks great until at least 20.

Sector C: Crude Oil and Oil Services

We're move ambivalent about the Oil sector because of the lack of volume accompanying the recent break-out. If volume comes in, we'll change our stance, but until then we'd rather trade this sector with a bit more caution.

The two ETF's we like to use when focusing on crude and oil companies are USO and OIH. The other popular one, XLE, is also a good trading vehicle but the daily on OIH is much cleaner than in XLE.

We had USO long on the trend-line break of 29 in our newsletter on Friday. We still like it but want confirmation as the volume on the break was questionable.




OIH same story -- price looks good and it wouldn't surprise us if OIH rallied 10 points within 10 days but it needs to confirm as volume on Friday was weak.



SU looks good to go for run to 30.


Lots of clean air for COG as it sits above its 200 SMA.

EOG could be in for a good move through 67.

Sector B: Metals and Minerals

The ETF we like to trade in this sector is XME which looks set to go to the 200SMA and resistance around 38. Looks great.


Here are our favorite trading stocks within the sector:

MEE might need a few days to consolidate the Wednesday earning's move but it looks good to go for at least another 6 points. If you're a swing trader look to buy dips on this stock.

Huge volume break-out move on JRCC on Friday -- a bit of digestion under the 200 SMA would be excellent for this runner.



We had CNX in our newsletter with 33 alert for Friday. Stock looks good to 38.


We had BTU long alert for Friday at 27.5. The stock blew through our spot and now is basing under 30. Looks good to go for another 4 points.


This sector looks even better than the Ag-Chem in that a) it has less congestion (compare to MON) and b) has more up-side potential in that resistance is further away.

Sector A: Ag-Chems

Over the weekend we're going to be posting up charts of some sectors that could show some decent trading opportunities come next week. Let's start with the Ag-Chem sector:


There's no ETF we love for this sector (not liquid enough) but MOO seems to be the best of the bunch.

Clear break-out on increased volume (not difficult though as stock normally trades thin so a bit of day-trader attention would get the volume spike) but has 200 SMA to deal with relatively soon.


Angle of ascent is a big part of the way we trade. Note the increased angles of ascent in AGU (versus the more flat nature of S&P 500 in April versus March). This means that there could be fast up-move coming in the stock. Possible top? Maybe, but before then there should be an excellent long opportunity, at least to the October gap area.


CF is the leader of the group; excellent price action but possibly needs a bit of rest ahead of the 200SMA (at least that is what would happen in a rational market :-)


MON messier than the rest but important enough to be mentioned -- could easily run to 88, especially if it rests for one day.

POT looking good under 92.



Stay Tuned for this evening's post, Sector B: Metals

Commodity Rip

We'll have to see how they close them but commodites are on fire with more break-outs in the sector that we've seen in a while -- and note divergence with financials (XLF) and commercial real estate (IYR) asleep, and treasuries bleeding. Obviously, this is an inflation trade and it will be interesting to see how long it lasts. Ride the trend in the commodities -- here are some charts.

Metals:



Oil Service:


Crude:


And the poor Treasuries:


Gold lagging -- let's see if they catch up.


Update: today was one of the clearest change of leadership days we have seen in a long time. One day a trend does not make -- however, if we get continuation on Monday then it's a good bet we're going to get a very good run in the commodities with money flowing from the REITS and financials into metals, ags, coal, and oil.

Today's triggers

Here are all the triggers from last night's newsletter (BTU 27.5 long, CNX 33 long, FLR 37 short, USO trend-line long over 29). Arrows are places we will offer explanations on the why and where of entry (will be included on this weekend's newsletter).








These are day-trade entries but often our subscribers swing-trade many of our trigger spots. We ourselves are primarily day-traders and look for 1-4% moves with stops around 0.3%-0.5%.

Comp 200 SMA tag and reverse

We've been harping for a few days in our newsletter about the 200 SMA and the Nasdaq. The following chart shows a vertical run into the 200 SMA. Not a bad place for you swing-traders to take some profits.

CDC Warning-- Please refrain from the following:

Financial Fun

Expect a lot of volatility in the Financials this week with the news of GS offering and GS earnings. The "stellar" earnings on WFC has set the bar very high for the rest of the banks and "sell the news" reaction on other bank earnings would not be surprising.

XLF closed right at resistance. As much as we think this bank rally is overdone, we have to admit that this actually is a very bullish chart IF it can base under resistance for a few days and then have a high-volume breakout. We always tell each other that we think/feel is irrelevant; we feel bearish but we've been trading this rally long because that is clearly what the charts have shown in the last month. Opinions are fun and we talk to each other about how we "feel" all the time, however when it comes to actually putting our money on the line, we always defer to the charts.

If we had followed what we felt (our emotions) instead of what we saw (charts) we would have, without a doubt, given back all our ytd gains by buying FAZ SRS over the last few weeks. Decouple your emotions from your trading. Allow yourself to feel/voice/cry over whatever you want, but when it comes to actually pulling the trigger, always follow your system and not what you want/feel. If the two fall into synch, wonderful, if not, too bad, but do not even give yourself the option of following your emotions over what you see ahead of you (chart trends).


The bears will have their day in the sun again and we'll join them on the dark side; once the charts confirm the break of the rally.

We see what we want to see

From Wired Magazine:

Recipe for Disaster: The Formula That Killed Wall Street

By Felix Salmon 02.23.09

A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li's work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut—determining correlation, or how seemingly disparate events are related—and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.

For five years, Li's formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

David X. Li, it's safe to say, won't be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li's Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

How could one formula pack such a devastating punch? The answer lies in the bond market, the multitrillion-dollar system that allows pension funds, insurance companies, and hedge funds to lend trillions of dollars to companies, countries, and home buyers.

A bond, of course, is just an IOU, a promise to pay back money with interest by certain dates. If a company—say, IBM—borrows money by issuing a bond, investors will look very closely over its accounts to make sure it has the wherewithal to repay them. The higher the perceived risk—and there's always some risk—the higher the interest rate the bond must carry.

Bond investors are very comfortable with the concept of probability. If there's a 1 percent chance of default but they get an extra two percentage points in interest, they're ahead of the game overall—like a casino, which is happy to lose big sums every so often in return for profits most of the time.

Bond investors also invest in pools of hundreds or even thousands of mortgages. The potential sums involved are staggering: Americans now owe more than $11 trillion on their homes. But mortgage pools are messier than most bonds. There's no guaranteed interest rate, since the amount of money homeowners collectively pay back every month is a function of how many have refinanced and how many have defaulted. There's certainly no fixed maturity date: Money shows up in irregular chunks as people pay down their mortgages at unpredictable times—for instance, when they decide to sell their house. And most problematic, there's no easy way to assign a single probability to the chance of default.

Wall Street solved many of these problems through a process called tranching, which divides a pool and allows for the creation of safe bonds with a risk-free triple-A credit rating. Investors in the first tranche, or slice, are first in line to be paid off. Those next in line might get only a double-A credit rating on their tranche of bonds but will be able to charge a higher interest rate for bearing the slightly higher chance of default. And so on.

"...correlation is charlatanism"
Photo: AP photo/Richard Drew

The reason that ratings agencies and investors felt so safe with the triple-A tranches was that they believed there was no way hundreds of homeowners would all default on their loans at the same time. One person might lose his job, another might fall ill. But those are individual calamities that don't affect the mortgage pool much as a whole: Everybody else is still making their payments on time.

But not all calamities are individual, and tranching still hadn't solved all the problems of mortgage-pool risk. Some things, like falling house prices, affect a large number of people at once. If home values in your neighborhood decline and you lose some of your equity, there's a good chance your neighbors will lose theirs as well. If, as a result, you default on your mortgage, there's a higher probability they will default, too. That's called correlation—the degree to which one variable moves in line with another—and measuring it is an important part of determining how risky mortgage bonds are.

Investors like risk, as long as they can price it. What they hate is uncertainty—not knowing how big the risk is. As a result, bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quantitative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoever—in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.

Yet during the '90s, as global markets expanded, there were trillions of new dollars waiting to be put to use lending to borrowers around the world—not just mortgage seekers but also corporations and car buyers and anybody running a balance on their credit card—if only investors could put a number on the correlations between them. The problem is excruciatingly hard, especially when you're talking about thousands of moving parts. Whoever solved it would earn the eternal gratitude of Wall Street and quite possibly the attention of the Nobel committee as well.

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it's harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation's macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?

Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired.

Probability Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.	Survival times The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.	Equality A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.
Copula This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.	Distribution functions The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.	Gamma The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.

Enter Li, a star mathematician who grew up in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; he later moved to Barclays Capital and by 2004 was charged with rebuilding its quantitative analytics team.

Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street's ever more complex investment structures.

In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

If you're an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream—interest payments or insurance payments—and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.

When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. It's hard to build a historical model to predict Alice's or Britney's behavior, but anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything.

The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's—or anybody wanting to model the risk of a tranche—no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.

As a result, just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them—an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn't matter. All you needed was Li's copula function.

The CDS and CDO markets grew together, feeding on each other. At the end of 2001, there was $920 billion in credit default swaps outstanding. By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.

At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations. "Correlation trading has spread through the psyche of the financial markets like a highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.

The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.

David X. Li
Illustration: David A. Johnson

In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.

In finance, you can never reduce risk outright; you can only try to set up a market in which people who don't want risk sell it to those who do. But in the CDO market, people used the Gaussian copula model to convince themselves they didn't have any risk at all, when in fact they just didn't have any risk 99 percent of the time. The other 1 percent of the time they blew up. Those explosions may have been rare, but they could destroy all previous gains, and then some.

Li's copula function was used to price hundreds of billions of dollars' worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up.

"Everyone was pinning their hopes on house prices continuing to rise," says Kai Gilkes of the credit research firm CreditSights, who spent 10 years working at ratings agencies. "When they stopped rising, pretty much everyone was caught on the wrong side, because the sensitivity to house prices was huge. And there was just no getting around it. Why didn't rating agencies build in some cushion for this sensitivity to a house-price-depreciation scenario? Because if they had, they would have never rated a single mortgage-backed CDO."

Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number. They also should have noticed that the results they were seeing were much less volatile than they should have been—which implied that the risk was being moved elsewhere. Where had the risk gone?

They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked. They could, however, understand something as simple as a single correlation number. That was the problem.

"The relationship between two assets can never be captured by a single scalar quantity," Wilmott says. For instance, consider the share prices of two sneaker manufacturers: When the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endorsements and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It's impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.

No one knew all of this better than David X. Li: "Very few people understand the essence of the model," he told The Wall Street Journal way back in fall 2005.

"Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.

Nassim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."

Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the US. Last year, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn't talk without permission from the PR department. In response to a subsequent request, CICC's press office sent an email saying that Li was no longer doing the kind of work he did in his previous job and, therefore, would not be speaking to the media.

In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.

As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."

— Felix Salmon (felix@felixsalmon.com) writes the Market Movers financial blog at Portfolio.com.