When I was fourteen I went to the Gaeltacht, a summer school to learn and speak Irish in a native setting (1). There were some evenings during. Mandelbrot Makes Sense: A Book Review Essay. A discussion of Benoit Mandelbrot’s The. (Mis)Behavior of Markets by Nassim. Nicholas Taleb classroom, may. not cones and bark is not smooth, nor does lightning travel in a straight line,” wrote BenoĆ®t. Mandelbrot, contradicting more than 2, years of misconceptions .

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No matter what you’ve put it in–stocks, bonds, derivatives, hedge funds, houses, annuities, even mattresses –there’s always the chance that you could lose it or miss out on a bigger opportunity somewhere else.

Benoit Mandelbrot – Nassim Taleb

Anyone who would tell you otherwise is either a fool or a huckster. Then there are those who do warn of risk but package it into a simple numerical measure mandelbroy seems to put it within manageable bounds. They’re even more dangerous. Your mutual fund’s annual report, for example, may contain a measure of risk usually something called beta.

Benoit Mandelbrot

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: 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 or the spectacular rise of Cisco’s in the s have a dramatic impact on long-term returns –but “risk” and “variance” disregard them.

The professors who live by the bell curve adopted it for mathematical convenience, not realism. It asserts that when you measure the world, the numbers that result hover around the mediocre; big departures from the mean are so rare that their effect is negligible.

This focus on averages works well mandelbeot everyday physical variables such as height and weight, but not when it comes to finance. One can disregard the mancelbrot of a person’s being miles tall or tons heavy, but similarly excessive observations can never be ruled out in economic life. The German mark’s move from four per dollar to four trillion per dollar after World War I should have taught economists to beware the bell curve.


Out of a million submitted manuscripts, a handful account for the bulk of book sales.

One percent of the U. In other words, we live in a world tleb winner-take-all extreme concentration. Similarly, a very small number of days accounts for the bulk of stock market movements: Just ten trading days can represent half the returns of a decade.

The economic world is talrb primarily by random jumps. Yet the common tools of finance were designed for random walks in which the market always moves in baby steps.

Despite increasing empirical evidence that concentration and jumps better characterize market reality, the reliance on the random walk, the mandelbrkt curve, and their spawn of alphas and betas is accelerating, widening a tragic ,andelbrot between reality and the standard tools of financial measurement. It was in the third century of our era that the skeptical philosopher and physician Sextus attacked blind reliance on dogmas; his stance earned him the name Sextus Empiricus Sextus the Empirical.

Depressingly, medicine took 13 centuries to follow talb recommendations, become empirical, and integrate surgeons’ observations of the human body. The same resistance to reality characterizes finance. The inapplicability of the bell curve has long been established, yet close toMBA students a year in the U.

For those who teach finance, a number seems better than no number–even if it’s wrong. To blow up an academic dogma, empirical observations do not suffice. A better theory is needed, and one exists: In this approach, concentration and random jumps are not belated fudges but the point of departure.

mandelbdot The term “fractal” was coined in the s by one of the authors of this piece 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. Similar patterns can be found in economic data, and the parts often relate to the whole according to what’s called a power law. Such a law was first found to mandrlbrot to the distribution of wealth: This key property makes the computations easy; no computer is needed to divide by four.


In bell-curve finance, the chance of big drops is mandelnrot small and is thus ignored. The stock market crash was, according to such models, something that could happen only once in several billion billion years.

In power-law finance, big drops–while certainly less likely mandelbroy small ones–remain a real and calculable possibility. 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. Fractal finance, alas, has not yet earned a place in the MBA curriculum. Until that happy day, what is a person with money at stake to do?

First, diversify as broadly as you can–far more than the supposed experts tell you now. This isn’t just a matter of avoiding losses: Long-run market returns are dominated by a small number of investments, hence the risk of missing them must mandellbrot mitigated by investing as broadly as possible.

And wherever you put your money, understand that conventional measures of risk severely underestimate potential losses –and gains. For better or worse, your exposure is larger than you think. Hudson, he wrote The Mis Behavior of Markets.