Back in October I posted about Credit Default Swaps and their role in bringing down the American economy.

Well meet David X. Li whose Gaussian Copula enabled the development of credit default swaps and the collateralized debt obligations that the CDS is supposed to protect.

Here is the story as I understand it.

In 1997 investment banks were beginning to toy with the idea of pooling corporate bonds and selling off pieces. The idea behind these collaterilized debt obligations was to make investing less risky by diversifying the pool. that way if one company defaulted you didn’t lose everything. Good idea right? Well then people decided to get cute.

By further splitting these pools into smaller slices of increasing risk they allowed investors to assume more risk for greater gain by buying the slice of the pool with the most risk.

In order for this to work the banks had to be able to figure out the odds of all the companies in a particular slice of the pool defaulting at once. Something called correlation.

Investment banks, in order to figure out the rates of return at which to
offer each slice of the pool, first had to estimate the likelihood that
all the companies in it would go bust at once. Their fates might be
tightly intertwined. For instance, if the companies were all in closely
related industries, such as auto-parts suppliers, they might fall like
dominoes after a catastrophic event. In that case, the riskiest slice of
the pool wouldn’t offer a return much different from the conservative
slices, since anything that would sink two or three companies would
probably sink many of them. Such a pool would have a “high default
correlation.”

But if a pool had a low default correlation — a low chance of all its
companies stumbling at once — then the price gap between the riskiest
slice and the less-risky slices would be wide.

(1)

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.

(2)

That’s where David X. Li and his Gaussian Copula come in. Based off a model used in actuarial science Li’s model looked at how bonds were being handled by traders and how likely they think it is that a company will default in each of the next 10 years. It does this for all the companies in a pool and plots the results together and the model comes up with a default correlation. This allows banks and traders to come to agreement on what are the riskiest slices of a bond pool and how much they should yield.

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.

(2)

It also allowed the misuse of the credit default swap through the creation of the synthetic CDO and other instruments.

Some people buy credit-default swaps even though they don’t own any
bonds. They buy just because they think the swaps may rise in value.
Their value will rise if the issuer of the underlying bonds starts to
look shakier.

Say somebody wants default protection on $10 million of GM bonds. That
investor might pay $500,000 a year to someone else for a promise to
repay the bonds’ face value if GM defaults. If GM later starts to look
more likely to default than before, that first investor might be able to
resell that one-year protection for $600,000, pocketing a $100,000 profit.

Just as investment banks pool bonds into CDOs and sell off riskier and
less-risky slices, banks pool batches of credit-default swaps into
synthetic CDOs and sell slices of those. Because the synthetic CDOs
don’t contain any actual bonds, banks can create them without going to
the trouble of purchasing bonds. And the more synthetic CDOs they
create, the more money the banks can earn by selling and trading them.

Synthetic CDOs have made the world of corporate credit very sexy — a
place of high risk but of high potential return with little money tied up.

Someone who invests in a synthetic CDO’s riskiest slice — agreeing to
protect the pool against its first $10 million in default losses –
might receive an immediate payment of $5 million up front, plus $500,000
a year, for taking on this risk. He would get this $5 million without
investing a dime, just for his pledge to pay in case of a default, much
like what an insurance company does. Some investors, to prove they can
pay if there is a default, might have to put up some collateral, but
even then it would be only 15% or so of the amount they’re on the hook
for, or $1.5 million in this example.

This setup makes such an investment very tempting for many hedge-fund
managers. “If you’re a new hedge fund starting out, selling protection
on the [riskiest] tranche and getting a huge payment up front is
certainly something that’s going to attract your attention,” says Mr.
Hinman of Ares Management. It’s especially tempting given that a hedge
fund’s manager typically gets to keep 20% of the fund’s winnings each year.

(1)

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.

(2)

And that is where the problem comes in. Because banks don’t actually have to buy bonds it’s easier to make money. Unfortunately there are problems with this setup:

First – The data used to set come up with the credit curves and the yield rates is just a snap shot in time. It doesn’t reflect reality at any given moment.

Second – The GIGO problem. The predictions are only as good as the input data, and that is all guesswork. Li himself worried that many people didn’t understand that.

Third – Everyone is using the same model so when someone makes a wrong guess the damage spills over.

“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.

(2)

These issues initially came to light in 2005 when GM’s credit rating was downgraded

When a credit agency downgraded General Motors
Corp.’s debt in May, the auto maker’s securities sank. But it wasn’t
just holders of GM shares and bonds who felt the pain.

Like the proverbial flap of a butterfly’s wings rippling into a tornado,
GM’s woes caused hedge funds around the world to lose hundreds of
millions of dollars in other investments on behalf of wealthy
individuals, institutions like university endowments — and, via pension
funds, regular folk.

(1)

But because the market bounced back many took that as a sign of how hedge funds and credit derivatives had made things more resilient. At the time however the Bank of International Settlements warned about future issues:

“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.”

(1)

Despite this and other warnings banks continued to use Li’s model and then the mortgage crisis hit:

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.”

(2)

Because decision makers had come to rely almost unquestioningly on the output from Li’s model and may have lacked the math skills to question it’s results no one looked to see what the actual risk of the mortgage based securities were.

So now here we stand. The world’s most dynamic economic engine brought to it’s knees by one guy.

(1) Slice of Risk, Mark Whitehouse, Wall Street Journal, 9/12/2005
(2) Recipe for Disaster: The Formula That Killed Wall Street, Felix Salmon, Wired Magazine, 2/23/09

This entry was posted on Tuesday, March 3rd, 2009 at 7:12 am by Chad and is filed under Big Thoughts, How Not To Succeed In Business. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.