The articles above do a great deal to explain what has happened to America's (and the world's) economies and financial systems. But one key element is missing or taken for granted in their explanations: an element that makes it all make sense in a way that defied my prior understanding, and probably yours as well. That element was published weeks ago with little fanfare in this month's Wired Magazine, in the article The Secret Formula That Destroyed Wall Street, by Felix Salmon. Part of the reason that it received little attention was the inherent complexity of the subject (and it's tough enough that I still don't fully understand it); but its incredibly important upshot is one that has been missed or left out by most of the writers on the subject of the economic meltdown: that the value of the CDOs was being determined almost entirely by the value of the CDS bets against them. If you really understand the relationship between CDOs and CDSs, and the efforts being made to combat the current crisis by the Administration, this revelation is nearly earth-shattering in its implications.

Allow me to explain in the simplest terms I can, smoothing out a lot of details. A bunch of assholes on Wall St. decided they wanted to make a bunch of money they couldn't make before with responsible lending. So they took a bunch of risky mortgages and other bad loans, and stuffed them into big black boxes of debt together with good loans. They essentially sold all of these black boxes, to make a long tranche-filled story short, as good, safe loans with AAA ratings. These black boxes were called Collateralized Debt Obligations (CDOs).

Problem was, it was really tough to figure out what these things were really worth because they were made up of so many different loans. A bunch of these wall street assholes were worried about having so many potentially problematic CDOs; a bunch of other assholes saw a way to make lots more money, provided the housing market didn't go bust. That's where the Credit Default Swaps (CDSs) came in. CDSs are insurance on CDOs: if you own a bunch of CDOs, you can pay me a premium to insure you; if your CDO (or a particular part or "tranche" of it) defaults, I have to pay the entire value of the CDO (or tranche thereof).

The really fucked up part of the CDS deals was that the insurance provider didn't have to have the capital to pay out even a fraction of the premiums; worse still, you could take out "insurance" on loans neither of you had on "naked" CDS deals--basically, casino betting of a purer variety than standard Wall St. fare. There were potentially an infinite number of insurance CDSs that could be written just on one single CDO, by just about anybody willing to do so. Do the permutations, and that's how you get, by some estimates, almost $70 trillion in CDS deals alone on "just" $4.7 trillion of CDOs. That's more than the entire world's GDP.

Then the housing market went south, a bunch of the CDOs (or the worst "tranches") went kablooie, and all the shitheads holding CDS premiums (AIG, first and foremost) were fucked because they couldn't pay out. And, of course, the firms like Goldman Sachs who paid CDS firms like AIG want their damn insurance payouts, even if it's at taxpayer expense. And the banks who hold a bunch of CDOs can't move them, so they can't raise capital, so they don't lend. And when banks don't lend, a bunch of regular people lose their shirts. Compared the amount of money and carnage involved here, a couple hundred million dollars in bonuses to the same assholes who got us here may be infuriating, but it's chump change.

So what's the big mystery, you say? What's the big problem? Just cancel the CDS contracts, let CDS firms like AIG fail, let the taxpayer cover the downside of the worst subprimes in the "BBB" tranches of the CDOs, and let the CDO trading go on as before! Sounds simple, and that's exactly what our own Jerome a Paris is calling for. Well, you can't. And the Wired article explains why you can't, and why we're more fucked than you can possibly imagine. You see, the CDOs have No Determinable Value Without CDSs Attached. The CDSs determined the value of the CDOs. And no one is touching CDSs with a thousand foot pole right now, and with very good reason.

The key link that tied CDOs to CDSs forever was made by a mathematician named David X. Li, who pioneered a formula called the Gaussian Copula Function to solve the intractable problem of the correlative relationship between the loans in the CDO black box. This particular formula and its problems are also discussed The Black Swan, a book written prior to the collapse by a hedge fund manager. The Wired article explains:

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 (emphasis added)—-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.

In other words, you can't consider each loan individually within the box, as all the loans affect one another in some way. Plus, there's not enough past data to work from. How can you possibly judge one individual's risk of default on a Bank of America no-doc loan on a first home, when nobody at BofA knew the trustworthiness or even the income of the buyer? And how the hell were you supposed to figure out the value of an entire box full of these things when they impact each other? It's a statistician's nightmare. Without solving it, you can't know what a CDO, or even a tranche of a CDO, is really worth. That's where Li's Gaussian Copula Function came in:

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 your eyes didn't just bulge out of your head and plop on the keyboard, they should have. This genius decided that the underlying value of the loans really was irrelevant: what was really relevant was what the market decided they were worth, on the basis of the value of the CDS insurance hedges against them. The infinitely traded, completely unregulated, massively speculative pool of CDS bets against the CDOs that now contained the entire economy's lifeblood. You can't make this shit up:

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.

Rather than laugh at the simple-minded insanity of this "valuation" scheme, the brilliant Masters of the Universe on Wall St. could barely contain themselves with glee at the "solution" to their CDO valuation problem:

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.

Having created a system in which profits self-replicated like infinite reflections in funhouse mirrors in such a way that Dutch tulip merchants would laugh with schadenfreude, the rest makes you wonder if straitjackets might not be more appropriate than prison uniforms for this sorry bunch of Jokers:

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 entirety of the article is an absolute must read, but I would be remiss if I left out the following critical detail: nobody even factored in the possibility that the CDOs would go bust, because the the Gaussian copula formula based itself on the CDS, a derivative so brand spanking new that it had never seen a bear market. All these geniuses' models didn't even calculate for the possibility of negative growth: the formula for calculating it simply didn't exist.

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."

So now what?

I'll tell you what. As I have explained before, the big Geither vs. Krugman grudge match is overwrought, imbued with more long-term ideological than immediately practical significance. Both have one concern: get people, somehow, to start buying the CDOs banks have on their books. Geithner wants to give sweetheart deals to hedge funds to buy the black boxes for cheap, under the premise that the CDOs have real, decent value. Krugman and other progressive economists are less optimistic, feeling that only the federal government will take the plunge to purchase enough CDOs to make a dent in the banks' balance sheets and provide a real market for CDOs.

But there's a big problem with both plans: nobody has any idea what these things are worth. No one EVER DID. And without Li's hopelessly naive Gaussian copula formula, an entirely new method of calculating the value of these "toxic assets" will have to be found. But like trying to predict the long-term weather of any given local area, correlative influences and a lack of relevant predictive data make that task essentially impossible--almost as impossible as, say, attempting to predict the stock market or the probability that the Knicks will cover the spread against the Lakers on any given night.

And that's why the credit markets are frozen, and aren't coming unfrozen any time soon. That's why they're trying to rescue AIG and the CDS market. Because nobody has any other idea how to calculate the value of what amounts to the entire American economy: the vast majority of every mortagage loan, auto loan, business loan, credit card loan, and all manner of other financial debt transaction made by American consumers.

It's a mess I can't even begin to propose a solution for how to unwind--but we better, as a nation, figure it out fast. Then perhaps we can figure out how to employ our best mathematicians and statisticians in fields that actually producesomething of value, rather than destroy the world economy in one fell swoop.

That, truly, would be Change We Can Believe In.