Formulas for Disaster, Part 1

May 31, 2009

Up till now, I have stayed away from comments about our current economic and financial situation, dire though some aspects of it certainly are..  So much ink has been spilled, and so much hot air emitted, that it’s been hard to think of something to say that would be both thought-provoking and have some connection with reality.

However, I’ve just read an article in the June 8 edition of Newsweek that has led me to change my mind.  The article, “Revenge of the Nerd”, discusses how some of Wall Street’s “quants” contributed to the financial meltdown.

Imagine an aeronautics engineer designing a state-of-the-art jumbo jet. In order for it to fly, the engineer has to rely on the same aerodynamics equation devised by physicists 150 years ago, which is based on Newton’s second law of motion: force equals mass times acceleration. Problem is, the engineer can’t reconcile his elegant design with the equation. The plane has too much mass and not enough force. But rather than tweak the design to fit the equation, imagine if the engineer does the opposite, and tweaks the equation to fit the design.

It goes on to talk about some of the work being done by Dr. Paul Wilmott, who studied applied mathematics at Oxford; in 2003, he founded a “Certificate in Quantitative Finance” program, in the City of London, to teach quants the often messy practicalities of applying statistics and math to the real financial world.  He is well qualified for the task; Nassim Taleb, mathematician and author of The Black Swan, says:

He’s the only one who truly understands what’s going on … the only quant who uses his own head and has any sense of ethics.

I had the good fortune, back in 1994,  to attend a seminar on “The Mathematics of Financial Derivatives” at St. Hugh’s College, Oxford, presented by Dr. Wilmott and two colleagues, Dr. Jeff Dewynne and Dr. Sam Howison.  I know that they are three very bright guys, and their book, Option Pricing: Mathematical Models and Computation, has been on my office bookshelf ever since.  I think they really have identified one of the fundamental weaknesses in the industry that contributed to the current mess.

I started out in quantitative finance back in the 1970s, after I got my MBA at the University of Chicago. (I worked as a research assistant for Fischer Black, of the Black & Scholes option model, when I was in grad school.) The initial application of many  quantitative financial techniques were in markets like US equities, or listed stock options, where the assumptions that one participant couldn’t affect the overall market much, and that there were reliable sources of information on prices and liquidity, were probably at least somewhat reasonable.

But if you look at one of the key “villains” in this current mess, the credit-default swap [CDS] market, it’s an entirely different story. There is an article that appeared in Wired magazine 17.03, “The Formula that Killed Wall Street”,that discusses how much of the CDS market was based on a formula, developed by David Li, for estimating the correlation of default risks.  (A copy of Li’s paper, “On Default Correlation: A Copula Function Approach”, as a PDF, is available on the Web.)  When it was first unveiled, the formula and the approach it embodied were greeted with enormous enthusiasm; some people spoke of the possibility of Li receiving a Nobel Prize in economics.  The idea was eagerly adopted by participants in the rapidly expanding CDS market.

I have read Li’s paper on the Gaussian copula function, and had a look at an implementation, used for predicting the expected default rate in CDS valuation.  What it is essentially doing is using a statistical sampling function to estimate the expected lifetime to failure (= default) for a population of debt instruments. Now, there is nothing wrong with the math per se; similar approaches are used in manufacturing for quality assurance. However, there is big difference: estimating the failure rate of, say, light bulbs does not in itself have any effect on that rate. But in the case of the CDS, the failure rate is being used as an input to the model that is used to price the swap. If the default rate estimate is too low (too optimistic), the asset values will be too high — and that, in turn, will lead to lower estimates of the default rate. In essence, there is a built-in feedback mechanism that can act as an error amplifier, a problem that is exacerbated by the lack of transparency and liquidity in the CDS market.  Having large participants whose activities can impact the overall market only makes the problem worse.

Wilmott marvels at the carelessness of it all. “They built these things on false assumptions without testing them, and stuffed them full of trillions of dollars. How could anyone have thought that was a good idea?”

That’s a very good question.  There’s plenty of blame to go around. The managements, who should have known better, were bedazzled by the dollar signs seeming to float out of their economic perpetual-motion machine. The quants knew the math, and their hubris led them to think that nothing else was needed. And the investors, while proving anew the truth of P.T. Barnum’s Law of Applied Economics, forgot that there ain’t no free lunch.

A significant piece of the problem is related to how Wall Street’s compensation works.  Many of these swap deals are long term (20-30 years), and far from transparent.  Yet the folks who trade them are still largely compensated on the basis of short-term P&L, determined by market values computed from the models.  What could possibly go wrong with that?

Wilmott realizes he’s fighting a losing battle, and that changing finance will take a lot more than a few thousand better-prepared quants. As long as banks get paid in the first year for selling a CDO that doesn’t mature for 30 years, little will change.

I am glad that the current US administration is proposing tighter regulation of derivative securities.  However, the devil is always in the details.  I hope that someone on the Obama economic team is talking to people like Dr. Wilmott.


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