copula, copulation, ah what' the difference?

Discussion in 'Wall St. News' started by fhl, Feb 24, 2009.

  1. fhl


    I guess there was a difference in the end.

    "Recipe for Disaster: The Formula That Killed Wall Street
    By Felix Salmon Email 13 hours ago

    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."

  2. This is stupid. Why blame or scapegoating a single individual for the Credit Model Boom and Bust?

    So many people helped create the Credit Model bubble, beginning with Robert Merton (the Merton model), Darrell Duffie, Janet Tavakoli, and so on and on and on. Not to mention the legions of greedy bullshitters working at the banks and the rating agencies.

    Are they implying that the financial system will be saved if they ban the copula functions to model correlations? Stoooooopid.

    The article is somewhat xenophobic, its point is that it's the chinks who got us in this mess. Riiiight.
  3. just21


  4. fhl


    funny how people see the same thing differently. i didn't see this article as blaming the developer of the theory at all. rather, i saw it as wall street glomming on to a theory and using it to create a "risk free product". that's wall street's stock in trade.
  5. But still, it's not Mr Li's theory or product. It's just a function in closed form inserted within a formula which was invented by other people.
    That's what I'm saying, if the formula was the problem as the article says, why not naming all the authors???

    Suppose that I use a new stochastic process that gives option prices in closed form using Black Scholes. Then if something goes wrong it's not necessarily the process which is faulty, maybe there's something wrong with Black Scholes, or something wrong estimating the parameters, or with pricing options with closed form formulas to begin with.

    "Guns don't kill people. People kill people"
  6. nkhoi

    nkhoi Moderator

    remind me of Discovery Channel's TV Series on crab fishing in Alaska. "Deadliest Catch".

    If a crab dies in the boat’s holding tank, it emits toxins that can poison the other crabs; one dead crab has the potential to wipe out the entire catch.
  7. fhl


    You don't seem to be able to get away from the view that the formula was the problem (in the author's view).

    The author took pains to disabuse that notion.
  8. Tavakoli has been a consistent critic of the models, but says the overwhelming problem was malfeasance. Those who think a new model will completely fix this are misguided. More than that, in all of her books and articles, she has spoken out against fraud and she makes a strong case that the models are flawed, but that wasn't the key problem. The data was cooked and structured finance professionals knowingly sold and leveraged faulty product. "Nothing to do with black swans or swans of any kind. The problem was Black Barts (like the California stage coach robber)."
  9. I thought she helped pump the credit model bubble through articles, books, teaching, media appearances, etc. I don't ever remember her criticizing the banking industry or fixed income hedge funds, she is an ex-banker herself so whatever the banks did she did it too.
    But then again it's been several years since I've been out of that racket I might have missed her criticisms.
  10. Yep. Definitely a white hat with the evidence to prove it. Her book DEAR MR. BUFFETT gives dates and articles of her criticism going back to a presentation she gave to the IMF in April 2005 as the bubble started expanding.

    She said the ABS CDOs were overrated (an excerpted clip is on her web site). She wrote about problems with credit derivatives, problem models and hidden leverage in her 1999 credit derivatives book. Her 2003 book on CDOs talked about fraud and her Sept 2008 book on structured products is more explicit. In her 2003 book she talked about overrated "AAA" products. Over the years the problem got worse, so she escalated in very specific ways. She was the first one to say the "AAA" ratings were a joke. There are scads of articles going back several years in THE JOURNAL OF STURCTURED FINANCE, GARP and more basically calling the correlation models a load. In Feb 2007, the SEC posted her letter on its site. She said Congress should revoke the NRSRO designation for the rating agencies with respect to structured products. She was the first person (in early 2007) to put it in writing that she thought the whole thing met the definition of a Ponzi scheme and showed how. You shoudl check her work on Merrill and AIG, too. There's a lot more and it's all documented in her book. It is very specific and it was all accurate.
    #10     Feb 24, 2009