Mandelbrot concludes by calling for systematic, replicable financial research and cautions that the commercial fractal strategies he surveys do not yet establish scientifically demonstrated investment success.

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We place control of the world's largest economy in the hands of a few elderly men, the central bankers. We do not understand what they do or how, but we have blind faith that they can somehow induce the economic spirits to bring us financial sunshine and rain and save us from financial frost and pestilence if there is one message i would wish to survive this book it is this finance must abandon its bad habits, and adopt a scientific method. I do not claim to have the answers. I know a few things, gleaned by long research and free thought. Interest in my hypothesis has waxed and waned over the years. After an initial burst of trendiness in the 1960s, my then half-formed financial theories fell out of fashion in the 1970s and 1980s. Only in the 1990s, by which time fractal geometry had become respectable and my theories had evolved, did a small but growing number of economists, mathematicians, and financiers join my labors.

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It is, in my view, premature to be hoping for serious gains from fractal finance. There is still too much we do not know. What follows is a brief summary of a few of the practical questions that need resolution. They give a flavor of what might become possible with fractal analysis and, I hope, they will inspire others to undertake serious study in the field. Problem 1. Analyzing Investments Wall Street likes to keep score. The Dow. P.E. Book to Market. E.B.I.T.D.A. No matter their meaning, the numbers keep multiplying. They help spot a trend, compare investments, measure performance, set bonuses, calculate returns. When it comes to measuring risk, however, the industry's toolkit is surprisingly bare. The two most common tools are alpha, or volatility, and beta, or the degree to which a stock's price changes correlate to those of the market overall.