Benoît B. Mandelbrot > Quotes

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
― Benoît Mandelbrot

“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”
― Benoît B. Mandelbrot

“For a thinking person, the most serious mental illness is not being sure of who you are.”
― Benoît B. Mandelbrot, The Fractalist: Memoir of a Scientific Maverick

“The brain highlights what it imagines as patterns; it disregards contradictory information. Human nature yearns to see order and hierarchy in the world. It will invent it where it cannot find it.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“I found myself in the position of that child in a story who noticed a bit of string and - out of curiosity - pulled on it to discover that it was just the tip of a very long and increasingly thick string...and kept bringing out wonders beyond reckoning”
― Benoît B. Mandelbrot, The Fractalist: Memoir of a Scientific Maverick

“A man is known by his heroes.”
― Benoît B. Mandelbrot, The Fractalist: Memoir of a Scientific Maverick

“Why is geometry often described as ""cold" and ""dry?" One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
― Benoît B. Mandelbrot, The Fractal Geometry of Nature

“For instance, suppose you offer somebody a choice: They can flip a coin to win $200 for heads and nothing for tails, or they can skip the toss and collect $100 immediately. Most people, researchers have found, will take the sure thing. Now alter the game: They can flip a coin to lose $200 for heads and nothing for tails, or they can skip the toss and pay $100 immediately. Most people will take the gamble. To the imagined rational man, the two games are mirror images; the choice to gamble or not should be the same in both. But to a real, irrational man, who feels differently about loss than gain, the two games are very different. The outcomes are different, and sublimely irrational.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“Too often, an event’s importance is not recognized until it is too late for proper recording.”
― Benoît B. Mandelbrot, The Fractalist: Memoir of a Scientific Maverick

“For most of my life, one of the persons most baffled by my own work was myself.”
― Benoît B. Mandelbrot

“My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.”
― Benoît B. Mandelbrot

“For a complex natural shape, dimension is relative. It varies with the observer. The same object can have more than one dimension, depending on how you measure it and what you want to do with it. And dimension need not be a whole number; it can be fractional. Now an ancient concept, dimension, becomes thoroughly modern.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“Be that as it may, for our present purposes, a bottom line emerges: Stock prices are not independent. Today's action can, at least slightly, affect tomorrow's action. The standard model is, again, wrong.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“The whole edifice of modern financial theory is, as described earlier, founded on a few simplifying assumptions. It presumes that homo economicus is rational and self-interested. Wrong, suggests the experience of the irrational, mob-psychology bubble and burst of the 1990's. A further assumption: that price variations follow the bell curve. Wrong, suggests the by-now widely accepted research of me and many others since the 1960's. And now the next assumption wobble: that price variations are what statisticians call i.i.d., independently and identically distributed-like the coin game with each toss unaffected by the last. Evidence for short-term dependence has already been mounting. And now comes the increasingly accepted but still confusing evidence of long-term dependence.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“(Since algebra derives from the Arabic jabara = to bind together, fractal and algebra are etymological opposites!)”
― Benoît B. Mandelbrot, The Fractal Geometry of Nature

“Rule 1. Markets are risky.

Rule 2. Trouble runs in streaks.

Rule 3. Markets have a personality.

Rule 4. Markets mislead.

Rule 5. Market time is relative”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“In the 1960's, some old-timers on Wall Street-the men who remembered the trauma of the 1929 Crash and the Great Depression-gave me a warning: "When we fade from this business, something will be lost. That is the memory of 1929." Because of that personal recollection, they said, they acted with more caution, than they otherwise might. Collectively, their generation provided an in-built brake on the wildest form of speculation, an insurance policy against financial excess and consequent catastrophe. Their memories provided a practical form of long-term dependence in the financial markets. Is it any wonder that in 1987 when most of those men were gone and their wisdom forgotten, the market encountered its first crash in nearly sixty years? Or that, two decades later, we would see the biggest bull market, and the worst bear market, in generations? Yet standard financial theory holds that, in modeling markets, all that matters is today's news and the expectations of tomorrow's news.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“Some economists, when thinking about long memory, are concerned that it undercuts the Efficient Market Hypothesis that prices fully reflect all relevant information; that the random walk is the best metaphor to describe such markets; and that you cannot beat such an unpredictable market. Well, the Efficient Market Hypothesis is no more than that, a hypothesis. Many a grand theory has died under the onslaught of real data.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“There is a rich vein of jokes about economists and their assumptions. Take the old one about the engineer, the physicist, and the economist. They find themselves shipwrecked on a desert island with nothing to eat but a sealed can of beans. How to get at them? The engineer proposes breaking the can open with a rock. The physicist suggests heating the can in the sun, until it bursts. The economist's approach: "First, assume we have a can opener....”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“Society was not a "social pyramid" with the proportion of rich to poor sloping gently from one class to the next. Instead, it was more of a "social arrow"- very fat at the bottom where the mass of men live, and very thing at the top where sit the wealthy elite. Nor was this effect by chance; the data did not remotely fit a bell curve, as one would expect if wealth were distributed randomly. It is a social law, he wrote: something "in the nature of man.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“No one is alone in this world. No act is without consequences for others. It is a tenet of chaos theory that, in dynamical systems, the outcome of any process is sensitive to its starting point-or, in the famous cliche, the flap of a butterfly's wings in the Amazon can cause a tornado in Texas. I do not assert markets are chaotic, though my fractal geometry is one of the primary mathematical tools of "chaology." But clearly, the global economy is an unfathomably complicated machine. To all the complexity of the physical world of weather, crops, ores, and factories, you add the psychological complexity of men acting on their fleeting expectations of what may or may not happen-sheer phantasms. Companies and stock prices, trade flows and currency rates, crop yields and commodity futures-all are inter-related to one degree or another, in ways we have barely begun to understand. In such a world, it is common sense that events in the distant past continue to echo in the present.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“In an ever-more complex world, Mandelbrot argues, scientists need both tools: image as well as number, the geometric view as well as the analytic. The two should work together. Visual geometry is like an experienced doctor's savvy in reading a patient's complexion, charts, and X-rays. Precise analysis is like the medical test results-the raw numbers of blood pressure and chemistry. "A good doctor looks at both, the pictures and the numbers. Science needs to work that way too," he says.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“If you can distill the essence of GE's stock behavior over the past twenty years, then you can apply it to financial engineering. You can estimate the risk of holding the stock over the next twenty years. You can estimate how many shares of the stock to buy for your portfolio. You can calculate the proper value of options you want to trade on the stock.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“But the financial industry is supremely pragmatic. While it may genuflect to the old icons, it invests its research dollars in the search for newer, better gods.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“The most-studied evidence, by the greatest number of economists, concerns what is called short-term dependence. This refers to the way price levels or price changes at one moment can influence those shortly afterwards-an hour, a day, or a few years, depending on what you consider "short." A "momentum" effect is at work, some economists theorize: Once a stock price starts climbing, the odds are slightly in favor of it continuing to climb for a while longer. For instance, in 1991 Campbell Harvey of Duke- he of the CFO study mentioned earlier-studied stock exchanges in sixteen of the world's largest economies. He found that if an index fell in one month, it had slightly greater odds of falling again in the next moth, or, if it had risen, greater odds of continuing to rise. Indeed, the data show, the sharper the move in the first, the more likely is is that the price trend will continue into the next month, although at a slower rate. Several other studies have found similar short-term trending in stock prices. When major news about a company hits the wires, the stock will react promptly-but it may keep on moving for the next few days as the news spreads, analysts study it, and more investors start to act upon it.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“But his observations of two forms of wildness remain: abrupt change, and almost-trends. These are the two basic facts of a financial market, the facts that any model must accommodate.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“In science, all important ideas need names and stories to fix them in the memory. It occurred to me that the market's first wild trait, abrupt change or discontinuity, is prefigured in the Bible tale of Noah. As Genesis relates, in Noah's six hundredth year God ordered the Great Flood to purify a wicked world. Then "were all the fountains of the great deep broken up, and the windows of heaven were opened." Noah survived, of course: He prepared against the coming flood by building a ship strong enough to withstand it. The flood came and went-catastrophic, but transient. Market crashes are like that. The 29.2 percent collapse of October 19, 1987, arrived without warning or convincing reason; and at the time, it seemed like the end of the financial world. Smaller squalls strike more often, with more localized effect. In fact, a hierarchy of turbulence, a pattern that scales up and down with time, governs this bad financial weather. At times, even a great bank or brokerage house can seem like a little boat in a big storm.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“In economics, there can never be a "theory of everything." But I believe each attempt comes closer to a proper understanding of how markets behave.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“The market's second wild trait-almost-cycles-is prefigured in the story of Joseph. Pharaoh dreamed that seven fat cattle were feeding in the meadows, when seven lean kine rose out of the Nile and ate them. Likewise, seven scraggly ears of corn consumed seven plump ears. Joseph, a Hebrew slave, called the dreams prophetic: Seven years of famine would follow seven years of prosperity. He advised Pharaoh to stockpile grain for bad times to come. And when all passed as prophesied, "Joseph opened all the storehouses, and sold unto the Egyptians...And all countries came into Egypt to Joseph to buy corn; because that the famine was so sore in all lands." Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur. That pattern, familiar from Hurst's work on the Nile, also appears in markets. A big 3 percent change in IBM's stock one day might precede a 2 percent jump another day, then a 1.5 percent change, then a 3.5 percent move-as if the first big jumps were continuing to echo down the succeeding days' trading. Of course, this is not a regular or predictable pattern. But the appearance of one is strong. Behind it is the influence of long-range dependence in an otherwise random process-or, put another way, a long-term memory through which the past continues to influence the random fluctuations of the present.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets

“If you are going to use probability to model a financial market, then you had better use the right kind of probability. Real markets are wild. Their price fluctuations can be hair-raising-far greater and more damaging than the mild variations of orthodox finance. That means that individual stocks and currencies are riskier than normally assumed. It means that stock portfolios are being put together incorrectly; far from managing risk, they may be magnifying it. It means that some trading strategies are misguided, and options mis-priced. Anywhere the bell-curve assumption enters the financial calculations, an error can come out.”
― Benoît B. Mandelbrot, The (Mis)Behavior of Markets