The Quant who Killed your IRA: David X. Li and the Guassian Copula Function: The Risk Management Model that Imploded

When the economy started to collapse, one of the first things I wondered was how it could happen so fast, in so many sectors. I was baffled that so many bright math & finance minds did not seem to have the tools to communicate the depths of the problem in a way that decision-makers could understand.

At that point in time, pre- Bernie Madoff, I still had some faith in our system, but still, I wondered how so many math "geniuses" could be asleep at the wheel, all at the same time! I came across an article by Saul Hansell in the New York Times in September 2008 that explained things just enough to open my eyes to the reality of the situation: "How Wall Street Lied to Its Computers: So where were the quants?"

Well, that was five months ago.The economy continues to plummet, gasping for breath from time-to-time. The article below does a good job of explaining some of the more confusing sets of events:

Recipe for Disaster: The Formula That Killed Wall Street Felix Salmon, Wired Magazine, 02/23/09

"Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired."

Probability Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.	Survival times The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.	Equality A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.
Copula This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.	Distribution functions The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.	Gamma The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.

More from the Wired article:

"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."

Related:

"Responding to FAQ: What is Tranching?" Mark Chu-Carroll, Bad Math, Good Math blog, 9/19/2007

"In many cases, the investors have no clue how many levels of re-bundling are going on to create their top-tranch low-risk bond. And you've got all sorts of people who thought they were buying conservative investments who are now stuck with their money invested in bundles of low-tranch shit loans."

Conde Nast's Interactive Graphic: What's a CDO? 5/5/07

Via Flowing Data: Sculptural Data Visualization: Derivatives volume and GDP, 2007, created by Andreas Nicolas Fischer - and related information

The top layer of the map represents the derivatives volume, and the bottom layer represents the GDP.

Andreas Nicolas Fischer: "This sculpture is a statistical map, a hybrid between physical and conceptual space. The horizontal arrangement equates to the Mercator projection of a world map and the vertical axis metaphorically corresponds to the financial activity of the country."

Related Articles: Derivatives Volume

OTC Derivatives Volume Posing Problems
Gregory Bresiger, Traders Magazine 3/19/2008
"The explosion in over-the-counter derivatives trading could overwhelm the timely processing and settlement procedures of brokerages."

"Alleviating the Credit Derivatives Crisis" Report Offered by BearingPoint As NY Fed Prepares to Meet to Study Issues -bobsguide (The Guide to Software & Technology in Asset Management, Banking & Risk Management)

“In fact, the overstressed credit derivatives market infrastructure has created the potential for a financial disaster if an event triggers a significant strain, such as a major U.S. company filing for bankruptcy. Unless this technology is updated and improved, the industry will continue to operate with lead weights and put the health of the market overall at risk,” added Benedetto."

Financial Markets- Subprime mortgage crisis: are credit derivatives to blame? -laCaixa Research Department, Monthly Report, num 308- December 2007

"Warren Buffet, the world’s best-known investor, once called financial derivatives «time bombs». On the other hand, Alan Greenspan, former governor of the Federal Reserve, believes they are «indispensable tools for managing risk». Surely, however, both would be in agreement that financial derivatives constitute one of the key factors in the subprime mortgage crisis."

"But, what are financial derivatives? A derivative is a financial instrument whose value is based on the price of another asset, called an underlying asset. An example is an option to buy 1,000 General Electric shares within one year at a fixed price of 40 dollars. The option buyer has a benefit if within one year the price goes above 40 dollars since he will be able to buy an asset which perhaps is worth 60 dollars although it cost only 40. In this case, the possibility, but not the obligation, to buy is what we understand by a financial derivative and the General Electric shares constitute the underlying asset, that is, the pre-existing asset and what gives us the price of the derivative."



Credit Derivatives: An Overview (pdf)
David Mengle, Head of Research, International Swaps and Derivatives Association
Atlanta Fed's May 2007 Financial Markets Conference, "Credit Derivatives: Where's the Risk?"

"Costs. It is often argued that the flip side of wider and deeper risk transfer is that,
instead of exerting a stabilizing influence on markets, it is potentially destabilizing
because it transfers risk from participants that specialize in credit risk (that is, banks)
to participants with less experience in managing credit risk—for example, insurers
and hedge funds (“Risky business” 2005, for example). In addition, there is the danger
that anything used to disperse risk can also be used by investors seeking yield
enhancement to concentrate risk. Finally, these new institutions generally fall outside
the regulatory reach of agencies that oversee various aspects of the credit markets."

Regulation and Financial Innovation
Speech: Chairman Ben S. Bernanke, Atlanta Fed's May 2007 Financial Markets Conference
Conclusion
"Financial innovation has great benefits for our economy. The goal of regulation should be to preserve those benefits while achieving important public policy objectives, including financial stability, investor protection, and market integrity. Although financial innovation promotes those objectives in some ways, for example by allowing better sharing of risks, certain aspects of financial innovation--including the complexity of financial instruments and trading strategies, the illiquidity or potential illiquidity of certain instruments, and explicit or embedded leverage--may pose significant risks. These risks should not be taken lightly."


Credit Derivatives: Boon to Mankind or Accident Waiting to Happen?
Speech by Thomas Huertas, Director, Wholesale Firms Division, at the Rhombus Research Annual Conference, April 26, 2006 (UK)

"The difficulties lie in the details, and that is where accidents could happen."

"During 2004 and 2005 it was increasingly apparent that institutions were not obtaining the necessary consents prior to assigning their obligations to a third party. The danger arose that this would become market-practice – a situation that would have undermined the very usefulness of the credit derivatives market. Unauthorised assignments posed the risk that participants in the credit derivatives market could not be sure who their counterparties were and to what extent they could rely on the credit derivatives that they had written or bought. If a credit default event occurred, the buyer of protection would not necessarily have been able to find the entity responsible to provide protection and/or to enforce its claim on that provider. Correspondingly, regulators had concerns as to whether banks and investment firms could accurately measure counterparty risk and/or credit risk. This had knock-on effects on firms' ability to calculate large exposures and capital requirements."

OCC Reports Derivatives Volume Tops $96 Trillion
Hoosier Banker, 10/01/2005
"Derivatives held by U.S. commercial banks increased by $5.1 trillion in the second quarter of 2005, to $96.2 trillion, the Office of the Comptroller of the Currency reported Sept. 30 in its quarterly Bank Derivatives Report."

"Kathryn Dick, Deputy Comptroller for Risk Evaluation, said that while the notional amount of derivatives is a reasonable reflection of business activity, it does not represent the amount at risk for commercial banks. The risk in a derivatives contract is a function of a number of variables, such as whether counterparties exchange notional principal, the volatility of the currencies or interest rates used as the basis for determining contract payments, the maturity and liquidity of contracts, and the creditworthiness of the counterparties in the transactions, she said.The OCC also reported that credit derivatives increased by $981 billion, to $4.1 trillion.

"Low worldwide interest rates and credit spreads have let to strong client demand for credit instruments, and the growth in notional volumes reflects that," said Dick. "Our large dealer banks have targeted credit derivatives as an important segment of their product mix, and a critical aspect of our supervision is to work with other agencies to ensure that the dealer community has the appropriate operational infrastructure to support this growing market".

Risky Business: Credit Derivatives (pdf )8/18/05, The Economist

"Of course, things can go wrong. It is possible that the pricing of ever more complicated instruments might sometimes be too much even for the ultra-brainy lot who do it, with expensive results. Tranched instruments have no clear market price, so they have to be valued with complex models. Working out whether a default in a portfolio is likely to be an isolated event, or is a harbinger of more to come, is especially tricky, not least because data on credit defaults are relatively sparse. Some worry about the increased activity of hedge funds which, lured by the yield on illiquid, complicated instruments, make up as much as 70% of trading volume in credit derivatives, by some counts."

Glossary of Derivatives Terminology, ISDA