Wisdom on Catastrophic Risks -- Benoit Mandelbrot, "The Misbehavior of Markets"

A recurring theme at the American Accounting Association convention last week, on the challenged condition of the large audit firms and the risk of their collapse, is their version of the unforeseen tumult suffered since last year in the credit markets:

Namely -- just as trading markets seized up when valuation models broke down and expectations were blind-sided -- there is a fundamental disconnection between the moderate, inside-the-bell-curve nature of auditor assurance, carefully limited to “reasonable” and “fair” presentation, within “material” limits, and the severe and dramatic events that auditors do not foresee – typically large-scale corporate failure or fraud – that have the potential to trigger a firm’s catastrophic disintegration.

Nassim Nicholas Taleb’s 2007 best-seller, “The Black Swan”, which I reviewed here, provided the now-popular name for these unexpected but severely consequential events. Better, Taleb pays homage to Yale University mathematician Benoit Mandelbrot – whose 2005 book, “The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward', is highly recommended reading for anyone engaged in strategic decision-making under conditions of risky and incomplete information.

My review, below, was originally published in the International Herald Tribune on April 16, 2005:

Book Report: Why Markets Don't Perform

That Benoit Mandelbrot's latest book, "The (Mis)Behavior of Markets," should be squirreled away on the Accounting shelf of my local bookstore speaks volumes about the Yale University mathematician's reach - and his creativity.

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Mandelbrot, 80, is probably best known for his groundbreaking work on fractal geometry: the cloud formations, wind tunnel patterns and rocky coastlines by which he has over several decades illustrated the underlying structural orders within nature's unpredictabilities. As popularized since his 1982 book, "The Fractal Geometry of Nature," and in James Gleick's 1987 best seller "Chaos: Making a New Science," fractal geometry describes complex, irregular phenomena. Seen as patterns whose shapes repeat up and down many orders of magnitude, from the distribution of galaxies in the universe to the shapes of cauliflower florets, fractals are modeled by turbulence and volatility, not by the smooth laws of certainty going back to 17th-century calculus.

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In Mandelbrot's new book, written with Richard Hudson, a former editor and reporter for The Wall Street Journal, his skeptical message is aimed at the broad audience of investors and other participants in the world's securities markets. The same fractal approach that explains the limits on advance calculation of the path of a hurricane or the collapse of a species' population also teaches that markets are more risky, more vulnerable to violent disruptions and less well understood than conventional wisdom is prepared to understand or acknowledge.

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To back up his assertion that the entire body of market learning, based on the concept of an efficient market, is elegant but fundamentally flawed, Mandelbrot observes that conventional theory greatly understates the likelihood of ruinous events. As evidence, he cites the "Black Monday" collapse of the Dow Jones industrial average on Oct. 19, 1987; the meltdown of the Long-Term Capital Management hedge fund in 1998; and, most ruinously, the calamitous upheavals of Sept. 11, 2001.

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As Mandelbrot puts it, these events disprove the conventional bell curve of events spread over a smoothly continuous time distribution. They reveal the entire body of economic model-building - on which depend modern financial strategies ranging from index funds to the Black-Scholes formula for stock option pricing - to be as archaic as the tinkering of geocentric astronomers before Galileo came along.

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Mandelbrot sees the need for a new body of fractal analysis that would illustrate that stock-price bubbles and market crashes are inevitable - so long as investors continue to behave as if they can search out patterns in the markets' patternless behavior.

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In other words, there is great learning in the truism that as flawed and obsolete as the old methods are, they work well most of the time - except when they break down and don't work at all, which is exactly when great fortunes are made but mostly lost.

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Mandelbrot himself has spent a lifetime surmounting the odds of extreme and unlikely events: He was a wartime refugee and fugitive in France, an academic survivor as a dropout from that country's top school, diverted from university life to the labs of IBM.

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This perspective would explain why he engages in no small amount of ax-grinding over the hostility his views on the markets have elicited. His well-sharpened tools are on full and genial display. But by consigning all his mathematics to the book's endnotes, Mandelbrot asks most readers to take his positions about market behavior on a combination of faith, persuasion and good graphics.

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As a self-proclaimed seeker of patterns in a universe governed by rules both simple and elegant, even if their consequences are turbulent and chaotic, he draws connections from the everyday vocabulary of common observations: The stock traders' colloquial description of a "stormy" day in the trading pits is echoed in the swirling turbulence of swings in commodity pricing. And he finds useful the observation that stock price charts follow similar shapes, whether scaled by the day, month, year or decade - just as with other patterns in fractal geometry.

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Mandelbrot has not produced a how-to manual that can make readers rich. But he does assert that it can help them from getting poorer - unless readers suspect and act otherwise, in which case the symmetry of marketplace purchases and sales will lure some to take Mandelbrot as a guide to taking up risks that others would shun.

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The careful would find inspiration, if not from the deeply skeptical Mandelbrot himself, in the advice of Shakespeare's Julius Caesar: that the tide in the affairs of man, if taken at the flood, leads on to fortune.

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