Saturday, March 7, 2009
Gaussian Copula: The Formula That Wrecked the World Economy
Not unlike Albert Einstein whose equation E=MC2 made possible the creation of physical weapons of mass destruction, Chinese mathematician David X. Li could go down in history as the man who enabled the development of financial weapons of mass destruction on Wall Street. Li's Gaussian copula models for the pricing of collateralized debt obligations (CDOs)are being blamed for the catastrophic losses leading to the global financial collapse.
In addition to underlying bonds, bond investors also invest in pools of hundreds or even thousands of mortgages. The sums involved are mind boggling: Americans now owe more than $11 trillion on their homes, according to Wired Magazine. But mortgage pools are not as simple as 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. Al of this makes it much more difficult to calculate risk on mortgage pools and CDOs than on conventional bonds or old-fashioned home loans.
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.
David Li simplified the risk models further by using market data of credit default swaps on underlying debt, including pools of disparate mortgages, as convenient proxy for the probability of default on various tranches the CDOs. Almost all of CDS market data, however, was accumulated during a period of rising real estate values and fairly robust job markets, when defaults were rare.
What are credit default swaps? Credit-default swaps are an indicator of the cost of bond "insurance" that varies with the risk of bond default. Credit default swaps are privately traded derivative contracts traditionally bought by bond holders from CDS issuers like AIG, Ambac, FGIC, and MBIA and other entities. Like other derivatives, CDSs are not regulated by government agencies. Any investor can sell CDSs. The CDS sellers are expected (not guaranteed or back-stopped by governments) to reimburse bondholders or buyers in case the bond issuing companies or governments default.
As an investor, you have a choice: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. In either case, you get a regular income stream—interest payments or insurance premiums —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 limited the way the supply of bonds is, so the CDS market managed to grow very raidly. Though credit default swaps were relatively new when Li proposed his idea, they soon became a bigger and more liquid market than the underlying bonds on which they were based.
The growth of the CDO market was exponential. Using Li's formula, Wall Street's quants saw a new range 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 quality of mortgages of various kinds that also proliferated. All they needed was that correlation number based on CDS data, and out would come a rating telling them how safe or risky the tranche was.
The CDS and CDO markets grew along similar trajectories, drawing strength from 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.
It all worked well until the housing market and job markets began to weaken, causing a wave of defaults, beginning with the less creditworthy borrowers. The CDS markets started to behave erratically out of fear. And the CDS data accumulated during the good times no longer served as a useful proxy for the actual risk of various trances of mortgage pools. Even the AAA rated tranches were hit by defaults, because some them contained subprime mortgages.
There were several people, including experts such as Darrell Duffie, Paul Wilmott and Janet Tavakoli, who warned about the dangers of blindly using Li's copula function as a basis for assessing risk of default for CDOs. But the greedy Wall Street executives and money managers, who were making enormous profits from such derivatives, ignored such warnings. And the politicians didn't care because they were receiving their share of the profits as Wall Street contributed large amounts of money to their campaign coffers.
The CDOs, based on Li's Copula function and created and traded on Wall street, now account for most of the toxic assets that have turned shares of major banks like Citicorp into penny stocks. The insolvent troubled banks are now receiving hundreds of billions of dollars from taxpayer funded bailouts orchestrated by the US treasury. The ongoing credit crunch and the wave of home foreclosures show no signs of abating. The negative effects of the US woes are being felt around the world. With globalization of the financial markets and trade, the rest of of the world is not immune from America's economic crisis.
Here's a video titled "The Formula That Wrecked the Economy":
Recipe for Disaster
Will American Capitalism Survive?
K Street Booms as Main Street Suffers