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":



Related Links:

Recipe for Disaster

Will American Capitalism Survive?

K Street Booms as Main Street Suffers

5 comments:

Riaz Haq said...

Here's a very interesting "Recession for Dummies" narrative:

Pajja is the proprietor of a Siri-Paya and Nehari Shop in Lahore. Sales are low and, in order to increase them, he comes up with a plan to allow his customers to eat now and pay later. He keeps track of the meals consumed on a ledger.


Word gets around and as a result increasing numbers of customers flock to Pajja’s shop. Pajja’s suppliers are delighted and are very willing to sell more and more raw materials for the meals he prepares. Pajja shows them his ledger of receivables and they extend him credit.

A young and dynamic customer service consultant at the local bank recognizes these customer debts as valuable future assets and gives Pajja a credit line and then increases Pajja’s borrowing limit.

Taking advantage of his customers’ freedom from immediate payment constraints, Pajja jacks up the prices of his Nehari and Siri-Paye. Customers dont mind as they are not required to pay on the spot. Sales volume increases massively; Banks and suppliers lend more; Pajja opens more outlets. He sees no reason for undue concern since he has the debts of the customers as collateral.

At the bank’s corporate headquarters, expert bankers recognize Pajja’s customer loans as assets and transform these customer assets into BONDS. These negotiable instruments are given exotic names such as SIRIBOND, PAYABOND, MAGHAZBOND AND BONGBOND. These securities are then listed on the Stock Exchange and traded on markets worldwide. No one really understands what the names mean and how the securities are guaranteed but, nevertheless, as their prices continuously climb, the securities become top-selling items....


If you replace Pajja's receivables with sub-prime mortgages, I think this description captures the essence of the current crisis. Of course, it leaves out the part about how sophisticated mathematical functions such as mathematician David Li's Gaussian Copula Function were used to persuade investors to buy Pajja's debt as CDOs. To learn more about it, please read here.

Riaz Haq said...

Here's an excerpt from a story in the Guardian about growing wealth gap between whites and blacks in America:

"A huge wealth gap has opened up between black and white people in the US over the past quarter of a century – a difference sufficient to put two children through university – because of racial discrimination and economic policies that favour the affluent.

A typical white family is now five times richer than its African-American counterpart of the same class, according to a report released today by Brandeis University in Massachusetts.

White families typically have assets worth $100,000 (£69,000), up from $22,000 in the mid-1980s. African-American families' assets stand at just $5,000, up from around $2,000.

A quarter of black families have no assets at all. The study monitored more than 2,000 families since 1984.

"We walk that through essentially a generation and what we see is that the racial wealth gap has galloped, it's escalated to $95,000," said Tom Shapiro, one of the authors of the report by the university's Institute on Assets and Social Policy.

"That's primarily because the whites in the sample were able to accumulate financial assets from their $22,000 all the way to $100,000 and the African-Americans' wealth essentially flatlined."

The survey does not include housing equity, because it is not readily accessible and is rarely realised as cash. But if property were included it would further widen the wealth divide.

Shapiro says the gap remains wide even between blacks and whites of similar classes and with similar jobs and incomes.

"How do we explain the wealth gap among equally-achieving African-American and white families? The same ratio holds up even among low income groups. Finding ways to accumulate financial resources for all low and moderate income families in the United States has been a huge challenge and that challenge keeps getting steeper and steeper.

"But there are greater opportunities and less challenges for low and moderate income families if they're white in comparison to if they're African-American or Hispanic," he said.

America has long lived with vast inequality, although 40 years ago the disparity was lower than in Britain.

Today, the richest 1% of the US population owns close to 40% of its wealth. The top 25% of US households own 87%.

The rest is divided up among middle and low income Americans. In that competition white people come out far ahead.

Only one in 10 African-Americans owns any shares. A third do not have a pension plan, and among those who do the value is on average a fifth of plans held by whites.

The report shows that a typical white middle income family, earning
about $30,000 a year, has accumulated $74,000 in assets, five times that of a black family in the same class which has only about $14,000
in wealth.

The gap is even wider when it comes to families with an income above $50,000 a year."

Riaz Haq said...

Here's an excerpt from Michael Lewis's The Big Short on how Dr. Michael Burry made a fortune by buying credit default swaps (CDS) to bet against the sub-prime mortgages:

“You just have to watch for the level at which even nearly unlimited or unprecedented credit can no longer drive the [housing] market higher,” he wrote. “I am extremely bearish, and feel the consequences could very easily be a 50% drop in residential real estate in the U.S.…A large portion of current [housing] demand at current prices would disappear if only people became convinced that prices weren’t rising. The collateral damage is likely to be orders of magnitude worse than anyone now considers.”

On May 19, 2005, Mike Burry did his first subprime-mortgage deals. He bought $60 million of credit-default swaps from Deutsche Bank—$10 million each on six different bonds. “The reference securities,” these were called. You didn’t buy insurance on the entire subprime-mortgage-bond market but on a particular bond, and Burry had devoted himself to finding exactly the right ones to bet against. He likely became the only investor to do the sort of old-fashioned bank credit analysis on the home loans that should have been done before they were made. He was the opposite of an old-fashioned banker, however. He was looking not for the best loans to make but the worst loans—so that he could bet against them. He analyzed the relative importance of the loan-to-value ratios of the home loans, of second liens on the homes, of the location of the homes, of the absence of loan documentation and proof of income of the borrower, and a dozen or so other factors to determine the likelihood that a home loan made in America circa 2005 would go bad. Then he went looking for the bonds backed by the worst of the loans.

It surprised him that Deutsche Bank didn’t seem to care which bonds he picked to bet against. From their point of view, so far as he could tell, all subprime-mortgage bonds were the same. The price of insurance was driven not by any independent analysis but by the ratings placed on the bond by Moody’s and Standard & Poor’s. If he wanted to buy insurance on the supposedly riskless triple-A-rated tranche, he might pay 20 basis points (0.20 percent); on the riskier, A-rated tranches, he might pay 50 basis points (0.50 percent); and on the even less safe, triple-B-rated tranches, 200 basis points—that is, 2 percent. (A basis point is one-hundredth of one percentage point.) The triple-B-rated tranches—the ones that would be worth zero if the underlying mortgage pool experienced a loss of just 7 percent—were what he was after. He felt this to be a very conservative bet, which he was able, through analysis, to turn into even more of a sure thing. Anyone who even glanced at the prospectuses could see that there were many critical differences between one triple-B bond and the next—the percentage of interest-only loans contained in their underlying pool of mortgages, for example. He set out to cherry-pick the absolute worst ones and was a bit worried that the investment banks would catch on to just how much he knew about specific mortgage bonds, and adjust their prices.

Once again they shocked and delighted him: Goldman Sachs e-mailed him a great long list of crappy mortgage bonds to choose from. “This was shocking to me, actually,” he says. “They were all priced according to the lowest rating from one of the big-three ratings agencies.” He could pick from the list without alerting them to the depth of his knowledge. It was as if you could buy flood insurance on the house in the valley for the same price as flood insurance on the house on the mountaintop.

The market made no sense, but that didn’t stop other Wall Street firms from jumping into it, in part because Mike Burry was pestering them.

Riaz Haq said...

Here's an excerpt from Michael Lewis's The Big Short on how Dr. Michael Burry made a fortune by buying credit default swaps (CDS) to bet against the sub-prime mortgages:

“You just have to watch for the level at which even nearly unlimited or unprecedented credit can no longer drive the [housing] market higher,” he wrote. “I am extremely bearish, and feel the consequences could very easily be a 50% drop in residential real estate in the U.S.…A large portion of current [housing] demand at current prices would disappear if only people became convinced that prices weren’t rising. The collateral damage is likely to be orders of magnitude worse than anyone now considers.”

On May 19, 2005, Mike Burry did his first subprime-mortgage deals. He bought $60 million of credit-default swaps from Deutsche Bank—$10 million each on six different bonds. “The reference securities,” these were called. You didn’t buy insurance on the entire subprime-mortgage-bond market but on a particular bond, and Burry had devoted himself to finding exactly the right ones to bet against. He likely became the only investor to do the sort of old-fashioned bank credit analysis on the home loans that should have been done before they were made. He was the opposite of an old-fashioned banker, however. He was looking not for the best loans to make but the worst loans—so that he could bet against them. He analyzed the relative importance of the loan-to-value ratios of the home loans, of second liens on the homes, of the location of the homes, of the absence of loan documentation and proof of income of the borrower, and a dozen or so other factors to determine the likelihood that a home loan made in America circa 2005 would go bad. Then he went looking for the bonds backed by the worst of the loans.

It surprised him that Deutsche Bank didn’t seem to care which bonds he picked to bet against. From their point of view, so far as he could tell, all subprime-mortgage bonds were the same. The price of insurance was driven not by any independent analysis but by the ratings placed on the bond by Moody’s and Standard & Poor’s. If he wanted to buy insurance on the supposedly riskless triple-A-rated tranche, he might pay 20 basis points (0.20 percent); on the riskier, A-rated tranches, he might pay 50 basis points (0.50 percent); and on the even less safe, triple-B-rated tranches, 200 basis points—that is, 2 percent. (A basis point is one-hundredth of one percentage point.) The triple-B-rated tranches—the ones that would be worth zero if the underlying mortgage pool experienced a loss of just 7 percent—were what he was after. He felt this to be a very conservative bet, which he was able, through analysis, to turn into even more of a sure thing. Anyone who even glanced at the prospectuses could see that there were many critical differences between one triple-B bond and the next—the percentage of interest-only loans contained in their underlying pool of mortgages, for example. He set out to cherry-pick the absolute worst ones and was a bit worried that the investment banks would catch on to just how much he knew about specific mortgage bonds, and adjust their prices.

Once again they shocked and delighted him: Goldman Sachs e-mailed him a great long list of crappy mortgage bonds to choose from. “This was shocking to me, actually,” he says. “They were all priced according to the lowest rating from one of the big-three ratings agencies.” He could pick from the list without alerting them to the depth of his knowledge. It was as if you could buy flood insurance on the house in the valley for the same price as flood insurance on the house on the mountaintop.

The market made no sense, but that didn’t stop other Wall Street firms from jumping into it, in part because Mike Burry was pestering them.

Riaz Haq said...

Someone has to stop the Federal Reserve before it crushes what remains of America’s Main Street economy, argues former budget director David Stockman in a piece for Marketwatch.com:

n the last few weeks alone, it launched two more financial sector pumping operations which will harm the real economy, even as these actions juice Wall Street’s speculative humors.

First, joining the central banking cartels’ market rigging operation in support of the yen, the Fed helped bail-out carry traders from a savage short-covering squeeze. Then, green lighting the big banks for another go-round of the dividend and share-buyback scam, it handsomely rewarded options traders who had been front-running this announcement for weeks.

Indeed, this sort of action is so blatant that the Fed might as well just look for a financial vein in the vicinity of 200 West St., and proceed straight-away to mainline the trading desks located there.

In any event, the yen intervention certainly had nothing to do with the evident distress of the Japanese people. What happened is that one of the potent engines of the global carry-trade — the massive use of the yen as a zero cost funding currency — backfired violently in response to the unexpected disasters in Japan.

Accordingly, this should have been a moment of condign punishment — wiping out years of speculative gains in heavily leveraged commodity and emerging market currency and equity wagers, and putting two-way risk back into the markets for so-called risk assets.

Instead, once again, speculators were reassured that in the global financial casino operated by the world’s central bankers, the house is always there for them—this time with an exchange rate cap on what would otherwise have been a catastrophic surge in their yen funding costs.

Is it any wonder, then, that the global economy is being pummeled by one speculative tsunami after the next? Ever since the latest surge was trigged last summer by the Jackson Hole smoke signals about QE2, the violence of the price action in the risk asset flavor of late — cotton, met coal, sugar, oil, coffee, copper, rice, corn, heating oil and the rest — has been stunning, with moves of 10% a week or more.

In the face of these ripping commodity index gains, the Fed’s argument that surging food costs are due to emerging market demand growth is just plain lame. Was there a worldwide fasting ritual going on during the months just before the August QE2 signals when food prices were much lower? And haven’t the EM economies been growing at their present pace for about the last 15 years now, not just the last seven months?

Similarly, the supply side has had its floods and droughts — like always. But these don’t explain the price action, either. Take Dr. Cooper’s own price chart during the past 12 months: last March the price was $3.60 per pound — after which it plummeted to $2.80 by July, rose to $4.60 by February and revisited $4.10 per pound.

That violent round trip does not chart Mr. Market’s considered assessment of long-term trends in mining capacity or end-use industrial consumption. Instead, it reflects central bank triggered speculative tides which begin on the futures exchanges and ripple out through inventory stocking and de-stocking actions all around the world — even reaching the speculative copper hoards maintained by Chinese pig farmers and the vandals who strip-mine copper from the abandoned tract homes in Phoenix.

The short-covering panic in the yen forex markets following Japan’s intervention, and the subsequent panicked response by the central banks, wasn’t just a low frequency outlier — the equivalent of an 8.9 event on the financial Richter scale. Rather, it is the predictable result of the lunatic ZIRP monetary policy which has been pursued by the Bank of Japan for more than a decade now--and with the Fed, BOE and ECB not far behind.