I recently read Benoit Mandelbrot’s The (Mis)Behavior of Markets for The S^2 Podcast — a book club podcast that I co-host along with my friend Sari Siyam. I thought I’d put together a list of some of my favorite quotes I came across while reading it!
“Financial economics, as a discipline, is where chemistry was in the sixteenth century: a messy compendium of proven know-how, misty folk wisdom, unexamined assumptions, and grandiose speculation.”
“The flow of scientific information is sharply curtailed by self-interest. A bank in which the research department thinks it has discovered something new and useful will not share it with anyone else.”
“The precise mechanism that links news to price, cause to effect, is mysterious and seems inconsistent. Threat of war: Dollar falls. Threat of war: Dollar rises.”
“Patterns are the fool’s gold of financial markets. The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable. But a financial market is especially prone to such statistical mirages. My mathematical models can generate charts that—purely by the operation of random processes—appear to trend and cycle.”
“Greater knowledge of a danger permits greater safety. For centuries, shipbuilders have put care into the design of their hulls and sails. They know that, in most cases, the sea is moderate. But they also know that typhoons arise and hurricanes happen. They design not just for the 95 percent of sailing days when the weather is clement, but also for the other 5 percent, when storms blow and their skill is tested. The financiers and investors of the world are, at the moment, like mariners who heed no weather warnings.”
“IBM shares, the euro-dollar exchange rate, and wheat prices do not rise or fall by the mathematical rules of chance. Indeed, they do not—but they can be described as if they do.”
“Sure, after the fact, with enough time and effort, we can piece together a tolerable cause-and-effect story of why a price moved the way it did. But who cares? It is too late by then. Fortunes have been gained and lost. Before the fact, in the real world of fast markets, veiled motives, and uncertain outcomes, probability is the only tool at our disposal.”
“A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.” — Henri Poincaré
“All models by necessity distort reality in one way or another. A sculptor, when modeling in stone or clay, does not try to clone Nature; he highlights some things, ignores others, idealizes or abstracts some more, to achieve an effect. Different sculptors will seek different effects. Likewise, a scientist must necessarily pick and choose among various aspects of reality to incorporate into a model. An economist makes assumptions about how markets work, how businesses operate, how people make financial decisions. Any one of these assumptions, considered alone, is absurd.”
“The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight—as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required today in economics.” — John Maynard Keynes
“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.”
“It is an extraordinary feature of science that the most diverse, seemingly unrelated, phenomena can be described with the same mathematical tools.”
“When a man goes to clear a jungle he has relatively few types of tools: To cut, perhaps a machete; to knock down, a bulldozer; to burn, fire. Science is like that. When we explore the vast realm of natural and human behavior, we find our most useful tools of measurement and calculation are based on surprisingly few basic ideas. When a man has a hammer, all he sees around him are nails to hit. So it should be no great surprise that, with our small number of effective mathematical tools, we can find analogies between a wind tunnel and a Reuters screen.”
“The sensation of roughness had almost entirely been ignored by scientists.”
“As I put it in 1982, in my book-length manifesto, The Fractal Geometry of Nature: “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.””
“The fastest way to simplify things is to spot the symmetries, or invariances—the fundamental properties that do not change from one object under study to another.”
Aside: This quote above strongly relates to my post Faceting Reality.
“You could build fractals out of visualized, abstract concepts. Consider social science: The devastating rhythm of war and peace, the unequal distribution of wealth in society, the dominance of big companies in an industry—all can be analyzed as irregular fractal constructs that have more regularity to them than was first assumed. The variety of fractals is immense. But all have a few common traits. First, they scale up or down by a specific amount—that is, the parts echo the whole in accordance with a precise, measurable formula.”
“I have since found translators helpful when selling new ideas in a hostile marketplace.”
“Let us mull the promises that science makes to society to win its support. The grand promise is to endeavor solving the great mysteries—to the list of which I have added one. But there is also a more practical promise. It consists in helping society to improve, to prevent it from acting on the basis of theories that sound nice but are not true to the facts, and to help it act on the basis of facts—even if those facts have yet to find a theory that fully explains them.”
“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.”
“If you zoom in on an individual cluster of big changes, you find it is made up of smaller clusters. Zoom again, and you find even finer clusters. It is a fractal structure. Nor is it just the price changes of interest; at times, the price levels also exhibit some kind of irregular regularity. The charts sometimes rise or fall in long waves, or with small waves superimposed on bigger waves. But none of these phenomena—clusters of volatility, or irregular trends—resemble any of the cycles, waves, or other patterns that characterize those aspects of nature controlled through well-established science. There are no familiar sine or cosine waves, with regular periods, of the kind that undulate evenly across the green screen of an old oscilloscope. These peculiar patterns cannot be predicted; and so humans who bet on them often lose. Yet there clearly is a system to them. It is as if the charts have a memory of their past. If the price changes start to cluster, or the prices themselves start to rise, they have a slight tendency to keep doing so for a while—and then, without warning, they stop. They may even flip to the opposite trend.”
“To say much with little: Such is the goal of good science. But most established financial models say little with much. They input endless data, require many parameters, take long calculation. When they fail, by losing money, they are seldom thrown away as a bad start. Rather, they are “fixed.” They are amended, qualified, particularized, expanded, and complicated. Bit by bit, from a bad seed a big but sickly tree is built, with glue, nails, screws, and scaffolding. That people still lose money on these models should come as no great surprise.
The multifractal model, by contrast, begins with the unchanging, fundamental facts of market behavior—the “invariances,” a mathematician would call them. It is economical and flexible and mimics the real thing. In designing models, I think back to the great exemplars of history. Consider Newton’s famous law of gravity: The force of attraction between two bodies depends on their distance. He needed just a few pen strokes to express that thought, mathematically. But from it, he showed why the planets move as they do, where comets fly—even how high the tides flow. Later generations elaborated, until we had rockets, satellites, and men in space. His was a very small seed of thought, from which a great forest of science and engineering has grown. My hope is that, some day, the small seed of multifractal analysis can grow into a fruitful new way of managing the world’s money and economy.”
“Much of what passes for orthodoxy in economics and finance proves, on closer examination, to be shaky business. Since my youth, I have been shamelessly disrespectful of received wisdom. I question those who tell me such a thing is possible or such another is impossible. How would they know? Have they tried it themselves? My understanding of economics comes not from abstract theory, but from observation.”
“Unlike a broker, most investors do not care about “average” returns. For them, the rare, out-of-the-average catastrophes loom larger. Common sense and folk wisdom are often wrong, of course, but must never be ignored.”
“Pragmatism is needed in financial theory. It is the Hippocratic Oath to “do no harm.” In finance, I believe the conventional models and their more recent “fixes” violate that oath. They are not merely wrong; they are dangerously wrong. They are like a shipbuilder who assumes that gales are rare and hurricanes myth; so he builds his vessel for speed, capacity, and comfort—giving little thought to stability and strength. To launch such a ship across the ocean in typhoon season is to do serious harm. Like the weather, markets are turbulent. We must learn to recognize that, and better cope.”
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