The Hindu Business Line : `Move from bell curve to fractal view'

The odds of financial ruin in a free, global market economy have been grossly underestimated, says Benoit Mandelbrot, a French mathematician in his celebrated book, The (mis) Behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Best known as the `father of fractal geometry,' he cointed the term `fractal' in the 1970s to describe the many phenomena of Nature in which small parts resemble the whole: The veins in leaves look like branches; branches look like miniature trees; rocks look like miniature mountains.

And this branch of mathematics has been applied by Mandelbrot in a dozen fields, including the stock markets. In his view, the extensive reliance on the normal distribution (or the bell-shaped curve) to explain much of modern finance and investment theory is a serious flaw. And to disprove this theory, he articulated his alternate finance theory in this book published in 2004.

"The seemingly improbable happens all the time in financial markets. A year earlier (August 1997), the Dow had fallen by 7.7 per cent in one day (probability: one in 50 billion). In July 2002, the index recorded three steep falls within seven trading days (probability: one in four trillion). And on October 19, 1987, the worst day of trading in at least a century, the index fell 29.2 per cent. The probability of that happening, based on the standard reckoning of financial theorists, was less than one in 10 (to the power 50) — odds so small they have no meaning."

Extract from the book, The (mis)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward.

"Your mutual fund's annual report, for example, may contain a measure of risk (usually something called beta). It would indeed be useful to know just how risky your fund is, but this number won't tell you. Nor will any of the other quantities spewed out by the pseudoscience of finance: standard deviation, the Sharpe ratio, variance, correlation, alpha, value at risk, even the Black-Scholes option pricing model. The problem with all these measures is that they are built upon the statistical device known as the bell curve.

This means they disregard big market moves: They focus on the grass and miss out on the (gigantic) trees. Rare and unpredictably large deviations like the collapse of Enron's stock price in 2001 or the spectacular rise of Cisco's in the 1990s have a dramatic impact on long-term returns — but `risk' and `variance' disregard them."

"Another aspect of the real world tackled by fractal finance is that markets keep the memory of past moves, particularly of volatile days, and act according to such memory. Volatility breeds volatility; it comes in clusters and lumps. This is not an impossibly difficult or obscure framework for understanding markets. In fact, it accords better with intuition and observed reality than the bell-curve finance that still dominates the discourse of both academics and many market players."

— Extract from an article in Fortune titled, "How the Finance Gurus Get Risk All Wrong" — by Benoit Mandelbrot and Nassim Nicholas Taleb.

"When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed." "Markets, like oceans, have turbulence. Some days the change in markets is very small, and some days it moves in a huge leap. Only fractals can explain this kind of random change."

Krishnan Thiagarajan

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