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The mysterious Dr. Li

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Written by Stew Goodwin
April 02, 2010


Strange stories have emerged from the recent, and ongoing, financial crisis. None of them are more disturbing than the tale of the mysterious Dr. Li. You haven't heard of him? Don't worry, I hadn't either until I was most of the way through a pile of books and articles about our financial situation. Here is what I found.

In the late 1990s a team at JPMorganChase was working on a new product. Its members were trying to determine how mortgages might be packaged so that they would be appealing to institutional investors. The idea they hit upon was to bundle mortgages together into bonds, a process that was called securitization. This process was intended to broaden exposure and thus lessen the vulnerability to difficulties with any single mortgage. But, there was a problem.

Institutional investors have differing requirements. Some want high quality and are willing to accept lower returns. Others want higher returns and will absorb lower quality to get them. With these differences in mind the team split the bundled securities into ten layers, like a torte. Each layer contained a bundle of similar quality mortgages. The layers carried a yield calibrated to reflect the risk entailed. But, there was another problem.

The three lowest quality layers (subprimes) were not easy to sell because the attendant risk was too great for all but the most adventurous investors, like aggressive hedge funds. The team searched for a way to make these subprime bundles palatable to a wide range of investors. And that is where Dr. Li came in.

During the early 1990s a Chinese national who was supported by his government arrived in Canada seeking advanced degrees in mathematics. After several years of study he was able to obtain both a masters and a Ph.D. With these degrees in his pocket Dr. Li went to work for the Canadian Imperial Bank of Commerce. He gained experience there and around the turn of the century migrated to JPMorganChase in New York City.

He arrived on the scene just as the mortgage securitization team was despairing of ever finding a way to make subprime bundles salable. At this critical juncture Dr. Li presented the team with the solution they had sought so feverishly.

His solution involved complex mathematics. The technique Dr. Li employed was called the Gaussian copula function. The result was a series of equations that put a percentage figure on the possibility that a large number of subprimes would default simultaneously. Maybe the team thought they understood the mathematics. Maybe the equations looked like a gift from the gods and they just accepted it. In any case Dr. Li's work was incorporated into the subprime bundles.

He had calculated that the simultaneous default risks for the three lowest quality layers were 0.34 percent; 0.49 percent; and 0.88 percent, respectively. With Dr. Li's magic numbers in hand the team came up with a device that could transform subprime mortgage bundles into investment grade securities. It was called a Credit Default Swap (CDS). The CDS was a derivative attached to each subprime bundle. This derivative permitted an investor who bought one of these securities to swap the risk of default with a designated counterparty, such as AIG. The price of the CDS, determined by the market's assessment of the imbedded risk, was the insurance fee paid by the investor.

The newly minted investment grade securities flew out the door. Hundreds of billions worth of them ended up in the coffers of institutions. The CDSs were even more popular. They started trading independently as bets on the likelihood of specific defaults (counterparties still had to pay off in the event of default). Before long $60 trillion worth of them (an amount larger than all the economies of the world combined) were outstanding.

Given the gigantic amount that had been permitted to circulate, even if Dr. Li's percentages had been correct there would have been significant pressure on counterparty equity. But unfortunately Dr. Li's calculations were wrong, disastrously so. The actual percentage of defaults for the bottom three layers turned out to be 48.73 percent; 56.10 percent; and 66.67 percent. The financial consequences were catastrophic, as we all discovered.

And what happened to Dr. Li? He disappeared. Nobody seems to know where he is. Conspiracy theorists can be forgiven for wondering this episode was part of an intricate plot to destroy our system. If so, it almost worked, and may yet do so.

The Barnstable Patriot - The mysterious Dr. Li
 
David X. Li is at CICC. The author called Dr. Li "disappeared" simply because he did not do his homework.

Julian Shaw mentioned the misunderstanding of "the formula" in how i became a quant if i remember correctly. i think there have already been quite a lot academic work on the topic.
 
His wikipedia page has more information than this article, and is balanced at least.

David X. Li - Wikipedia, the free encyclopedia

Li himself apparently understood the limitation of his model, in 2005 saying "Very few people understand the essence of the model."<sup id="cite_ref-wsj_3-0" class="reference">[4]</sup> Li also wrote that "The current copula framework gains its popularity owing to its simplicity....However, there is little theoretical justification of the current framework from financial economics....We essentially have a credit portfolio model without solid credit portfolio theory."<sup id="cite_ref-4" class="reference">[5]</sup>"
 
I've been reading about Copulas for my PhD research for the past few weeks and even with such short exposure, I find Gaussian copulas inappropriate for modeling correlation in financial time series. So it's kind of weird for me how people in WS fell in love with this model.
 
I've been reading about Copulas for my PhD research for the past few weeks and even with such short exposure, I find Gaussian copulas inappropriate for modeling correlation in financial time series. So it's kind of weird for me how people in WS fell in love with this model.

bsm was also inappropriate for its unrealistic assumptions in early 70's. why people in WS fell in love with this model?
 
bsm was also inappropriate for its unrealistic assumptions in early 70's. why people in WS fell in love with this model?

I think BSM is a bit different story.. In the 70's, alternative models such as Stochastic Volatility and GARCH were not developed and modern finance was still an infant.
In 90's, however, people has a good knowledge of financial math and stats (and in particular copulas). I see papers dating back to 90's noting different forms of copulas ( t-copulas in particular) and inefficiency of Gaussian copulas for financial time series.
 
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