Wired magazine recently published an intriguing article by Felix Salmon in which he discusses the complex formula that is being blamed for spurring the collapse of the financial sector. I will try to explain the seven pages of text in a nutshell, a mortgage-backed nutshell.

We must begin with the bond market. There are numerous types of bonds such as government bonds, municipal bonds and corporate bonds. These are deemed by investors as relatively safe as historical data shows a low default risk, or a low risk of nonpayment upon maturation. A more complex part of the bond market is mortgage pools. Investing in mortgage pools is different than investing in the aforementioned bonds because there’s no guaranteed interest rate, no fixed maturity date and, by far the most important, there’s no way to assign probability to the chance of default. This is all due to the fact that the pools consist of hundreds of mortgages, all carrying different rates, maturity dates and default risks.

As a solution to the risk factors of investing in mortgage pools, quantitative analysts invented mortgage tranches. Tranches are composed of hundreds of mortgages (possibly more) and usually classified as A, B, C and so on. As an example, tranche A would be composed of assets with a first lien on them, and therefore considered a “senior” rated tranche. Senior tranches were rated AAA, AA or A, signaling an extremely safe investment. A tranche composed of second lien assets would still be considered safe, though since it carries a slightly higher risk of default, it would be rated BBB or BB or B, and so on.

The problem with tranches and their ratings is that they don’t take into consideration the fact that at some point, hundreds, thousands or millions of homeowners could default on their loans. What were the chances of that happening? Wall Street needed an answer – a default correlation.

Meet David X. Li, a star mathematician with a master’s degree in economics, actuarial science and business administration along with a PhD in statistics. His career spanned the Canadian Imperial Bank of Commerce, Barclays Capital and JPMorgan Chase. While employed with JPMorgan, Li published “On Default Correlation: A Copula Function Approach” in The Journal of Fixed Income in which he explained a way to model default correlation without using historical data as a basis. Instead, Li relied on the prices of credit default swaps.

His idea was that instead of waiting to assemble enough data about actual defaults, which rarely happen, he would use historical prices from the CDS market, insinuating that prices on credit default swaps and the probability of defaults were correlated, or moved in the same direction together. In other words, he was claiming that if CDS market prices went up, then so did the chance of default. But Li was effectively using oranges to measure apples. He invented a model based on price, when all along it should have been based on real-world default data.

Soon, the only thing investors or ratings companies such as Moody’s cared about was that correlation number, which Li’s complex math formula produced. One formula, one output – that’s all that trillions of dollars worth of investments were based upon. Soon, warnings were issued, and subsequently ignored.

"His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored."

I will continue with part II tomorrow, where discussion of the foreseeable damage, the CDO market and the affect on risk management will take place.

For a very informative illustration of how this whole credit crisis came to be, click here.

Emily Holbrook
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COMMENTS:

"The misbehaviour of markets have NEVER been normal in distribution. Risk is always in the tails Cauchy would have been better  ... our brightest are idiots. Economics ignores the truth and stands on conjecture. The basic hypotheses have never been tested as in all real sciences economic theory, money theory ... M Friedman,  and the sky hook are about equally probable.

Charlie Thomas, Saguaro-Juniper Corporation, 2/26/09 4:59 p.m.