Bailout

Why didn?t people in finance pay attention to Benoit Mandelbrot?

By Justin Fox

Mathematician Benoit Mandelbrot was not one of those great thinkers who was ignored in his own time. He won lots of prestigious prizes. He wrote acclaimed books. He even gave two TED talks.

But it's curious how little of the acclaim and attention Mandelbrot received over the years, and after his death last week, came from the world of finance. Mandelbrot was, believe it or not, one of the founding fathers of modern quantitative finance. In the early 1960s, he and scholars at Harvard, MIT, Chicago and a couple other places began to explore the meanings of random walks in stock prices. (I spent several years immersing myself in this history for a book; hence my obsessive interest. Here's an excerpt from it related to Mandelbrot.)

In the early days, Mandelbrot was very much one of the random walk gang. He considered Eugene Fama, then a grad student at the University of Chicago, to be his student and protégé. A 1965 article by Mandelbrot in the Chicago B-school's Journal of Business proved that a rational financial market would be an unpredictable one, providing an essential building block for what soon came to be known as the efficient market hypothesis.

Before long, though, Mandelbrot and the finance crowd drifted apart. It was partly just that Mandelbrot was a curious guy, and got interested in other sources of the fractal patterns that he saw in stock prices. But he also felt that "an ominous cloud" was developing in his relationship with the other random walkers. As long as quantitative finance was mostly exploratory in nature, Mandelbrot and the economists and finance professors got along fine. But as soon as the latter groups started trying to develop tools for understanding and managing risk in financial markets, there were tensions. The tool builders wanted to shoehorn market-price behavior into a bell-curve statistical model. That is, they wanted to believe that while price movements couldn't be predicted, price volatility could. Mandelbrot thought volatility was far harder to capture than that. As Paul Cootner, a random walker from MIT's Sloan School, wrote in 1964:

Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears. If he is right, almost all of our statistical tools are obsolete . . . Surely, before consigning centuries of work to the ash pile, we should like to have some assurance that all our work is truly useless.

And so it went. For Mandelbrot, the crucial turning point came with the development?and widespread acceptance?of the Black-Scholes options pricing model in the early 1970s. Black-Scholes and the many financial risk models that have evolved from it (including Felix's friend the Gaussian copula) are all about volatility being measurable and predictable. "When Black-Scholes came out, I said, 'Well, it won?t last,'" he told me in 2005. "'I?ll come back when it?s gone.'"

After the 1987 stock market crash, brought on in part by portfolio insurance strategies built upon Black-Scholes, Mandelbrot began paying attention to finance again, and some financial practitioners actually began paying attention to him. So he made a partial comeback. But the reliance on risk-management systems based on the belief that price volatility can be easily measured and predicted has continued, and it has continued to lead the financial system to the brink of disaster every few years.

So why haven't finance academics and practitioners paid more attention to Mandelbrot's warnings? I think it's mainly that he didn't provide them a handy alternative to Black-Scholes. I can't pretend to fully understand the practical implications of his fractal view of markets (and yes, I've read his book for lay readers on the subject), but it does seem more useful as a critique than as a positive model of market behavior. You can't haul in big consulting fees or create giant new securitization markets with a critique. So the natural tendency of both scholars and bankers has been to hold on for dear life to the Black-Scholes approach to modeling market risk. They get paid well for doing so, after all.

Finally, to switch topics entirely: Thanks to Felix for inviting Barbara and me to procrastinate blog at his place for the next couple of weeks. It should be fun. And it won't normally be quite this wonky.

Full post as published by Macroprudential on October 18, 2010 (boomark / email).