Machine Design

Leland Teschler's Editorial: Mathematics of Financial Chaos

Computer graphic mavens are probably quite familiar with Benoit Mandelbrot.

The French mathematician is best known as the father of fractal geometry. In computer graphics, fractals are the method of choice for rendering realistic looking mountains, coastlines, and other natural phenomena.

But another part of Mandelbrot’s work has recently made headlines, at least indirectly. He devoted much of his early career to studying how financial markets behave. He eventually concluded that commodities and stock prices are best described by chaos theory — with frequent unpredictable rises and stupendous crashes — rather than by the orderly statistics of bell curves.

Even those who don’t know the stock market from a meat market would probably agree that chaos is an apt way to describe the instability of the economy over the past few weeks. One interesting facet of chaos theory is that a single snowflake in the right place can cause a catastrophic avalanche. In the case of world financial markets, the snowflake turned out to be bad mortgage loans, mainly in California and Florida. The avalanche is worldwide and may just be beginning.

But you don’t need higher mathematics to understand the financial products that caused this mess. Bob Lewis, a pundit and IT consultant, recently suggested that an Excel model would have exposed the circular logic behind the interlocking mortgage instruments that have proved so problematic. Fundamentally, the relationship between these entities was no different, Lewis says, from a spreadsheet that has the formula =B1+1 in cell A1 and =A1+1 in cell B1. Excel would have happily explained there was something wrong with this thinking.

One might hope the highly paid quantitative analysts on Wall Street would have noticed that the risks of all these instruments correlated with each other. So why no red flags until the entire system was on the verge of a meltdown?

Sadly, the debate surrounding legislative attempts at a bailout tends to confirm the worst suspicions about root causes. The point of this legislation, of course, was to help rebuild confidence in American capitalism. But what emerged was the impression that the mathematics of mortgages wasn’t so much the problem as the mathematics of avarice.

It was not exactly the financial industry’s finest hour when the subject turned to salaries for CEOs whose firms might benefit from the new Bill. Michael Lewitt, president of investment advisory firm Harch Capital Management LLC, summed up the situation as being downright discouraging. Lewitt put it this way: “Mssrs. Paulson and Bernanke tried to convince Congress that bank executives would prevent their institutions from participating in the bailout if it meant that their compensation would be capped. One would think, as the financial system teeters on the brink of collapse, that the Secretary of the Treasury and the Chairman of the Federal Reserve could make a more persuasive argument than one that poses the likelihood that corporate executives would knowingly violate their fiduciary duty and refuse to participate in a plan to rescue the financial system because it might limit their compensation.”

The mentality these public officials portray as typifying bank CEOs led to the crisis in the first place. All the higher math in the world won’t help avoid future disasters if financial institutions are run by people who lose sight of their public trust.

— Leland Teschler, Editor

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