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The Participants Roger Ibbotson r Professor of finance at the Yale School of Management and chairman and CIO of Zebra Capital Management, which manages equity long-short hedge funds. r Founded Ibbotson Associates, a wholly owned subsidiary of Morningstar. r Co-writer of the annual Stocks, Bonds, Bills and Inflation (Morningstar, Inc.), the standard reference for information on investment market returns. r His many books include Global Investing: The Professional’s Guide to World Capital Markets, with Gary Brinson (McGraw Hill, 1992). George Cooper r Principal of Alignment Investors, a division of BlueCrest Management, Ltd. r Studied at Durham University. r Worked as a fund manager at Goldman Sachs and as a strategist for Deutsche Bank and JPMorgan. r Author of The Origin of Financial Crises (Vintage Books, 2008). Benoit Mandelbrot r Sterling Professor Emeritus of Mathematical Science at Yale. r Fellow Emeritus at IBM’s Thomas J. Watson Research Center. r Inventor of fractal geometry. r Received the Wolf Prize in Physics, the Japan Prize in Science and Technology, and awards from the U.S. National Academy of Sciences, the IEEE, and numerous universities. r His many books include The (Mis)behavior of Markets (Basic Books, 2004). that provoke sharp, even overwhelming, discontinuities. Then, I found that the same is true for the prices of wheat, stocks, and a multitude of other price series. The standard theory of price variation assumed continuity, but the data were very discontinuous. I became hooked on this problem and have worked on it ever since. By training, I am a mathematician, but a very peculiar one, for an easily identifiable reason. During World War II, I studied by myself, up in the mountains and not in proper school. Therefore, I read many things that nobody else read, and I didn’t learn many things other people learned, consciously or not. So I decided to look more and more carefully at price changes and see whether the fact that anything close to the simplest random walk fails to catch the variability of the process was something particular to the data I dealt with, or more widespread. Kaplan: What you’re saying, Dr. Mandelbrot, is that when you began to look at financial data, you observed that contrary to the standard models, which say that returns follow a bell-curve distribution and move in a continuous fashion, the data were dominated by lurches and discontinuities. Today, of course, there’s a lot of talk about “black swans,” and you’ve coined the term “gray swans” to indicate events that differ significantly from the norm and should be planned for. Mandelbrot: That’s correct. When asked to schools. Nobel Prizes have been awarded for mean-variance analysis, the capital asset pricing model, the Black-Scholes model of options pricing—all of which are based upon this notion that prices move in a continuous fashion. Should Dr. Mandelbrot’s work be taught in business school? Ibbotson: It’s fine to teach it in business school, comment about this, I always say that I’ve been studying gray swans, just because the problem is not just with one specific extreme event. You may say there are swans of every level of blackness, from almost white to completely black, and “completely black” has no limit. Kaplan: Dr. Mandelbrot’s thinking is very but let me say that I don’t think you have to throw out all the standard deviation work because there are jumps and discontinuities in return series. I don’t think there’s any doubt that we have jumps and discontinuities and special events. If you think of the implied volatility in the BlackScholes model, that implied volatility takes on widely different numbers at different times. It’s not a constant, and in fact, where we typically have standard deviations of, say, 20% implied in the stock market, or even 15% different from what is taught in business MorningstarAdvisor.com 43

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Morningstar Advisor - February/March 2009

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