this news is several days old, but still interesting if u haven’t heard about it. wired has a good story about how an equation written by a chinese guy david x. li brought down the entire investment banking industry. the equation in question is a gaussian copula function. gaussian describes the fact that the rate of housing defaults have a normal distribution, while the word copula means the equation combines to normal distributions into a single probability. it basically gives u the probability that two things will happen at once. apparently wall street investors took this equation and applied it to all sorts of credit default swaps w/o really understanding that the probability could change.
typically correlations between defaults are low. if one house in ur neighborhood goes into foreclosure, the chances another house will go bust at the same time are very low. this low number gave a warm fuzzy feeling to the quants who traded these things, and they bought and sold the securities w/o understanding the nature of the formula or the assets. they didn’t count on businesses like countrywide giving tons of subprime loans to ppl who lied on their income forms for instance. so once the bubble popped, all these formerly low probabilty occurrences became high probability occurrences. the probability went to 1 essentially and these securities became pretty much unsellable b/c there’s no way the income generated by these things would cover the cost of buying them unless the price dropped precipitously. if the banks sold these assets at the market price, they’d lose billions.
but what compounded the issue was the nature of credit default swaps. the assets these things were based on are mortgage backed securities, which are house loans. housing is a limited asset. anyone trading these has a limited revenue stream b/c there’s only a limited number of houses. but w/ cds’s, u’re really selling insurance. and u can sell insurance to an unlimited number of investors based on a single asset. so the insurance market on these assets ballooned to far far exceed the value of the underlying assets. wired says, “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 $62 trillion was based on $4.7 trillion of housing assets.
the funny thing is that way back in 2005, david li himself said this:
“The most dangerous part,” Mr. Li himself says of the model, “is when people believe everything coming out of it.” Investors who put too much trust in it or don’t understand all its subtleties may think they’ve eliminated their risks when they haven’t.
Much of that money is riding on Mr. Li’s idea, which he freely concedes has important flaws. For one, it merely relies on a snapshot of current credit curves, rather than taking into account the way they move. The result:Actual prices in the market often differ from what the model indicates they should be.
As with any model, forecasts investors make by using the model are only as good as the inputs. Someone asking the model to indicate how CDO prices will act in the future, for example, must first offer a guess about what will happen to the underlying credit curves – that is, to the market’s perception of the riskiness of individual bonds over several years. Trouble awaits those who blindly trust the model’s output instead of recognizing that they are making a bet based partly on what they told the model they think will happen. Mr. Li worries that “very few people understand the essence of the model.”
[The May incident] wasn’t really the fault of the model, which was designed mainly to help price the tranches, not to make predictions. True, the model had assumed the various credit curves would move in sync. But it also allowed for investors to adjust this assumption – an option that some, wittingly or not, ignored.
The credit-derivatives market has since bounced back. Some say this shows that the proliferation of hedge funds and of complex derivatives has made markets more resilient, by spreading risk.
“The events of spring 2005 might not be a true reflection of how these markets would function under stress,” says the annual report of the Bank for International Settlements, an organization that coordinates central banks’ efforts to ensure financial stability. To Stanford’s Mr. Duffie, “The question is, has the market adopted the model wholesale in a way that has overreached its appropriate use? I think it has.”
Mr. Li says that “it’s not the perfect model.” But, he adds: “There’s not a better one yet.”