Mandelbrot was one of the founding thinkers of what has alternately been called Chaos and complexity science. The Misbehavior of Markets is his application of those principle to financial markets, and, in my opinion one of the best finance books ever written.
At the core of much financial theory is a reliance on Newtonian physics. This sounds sort of weird, but the history of early financial and economic theory is closely tied in with physics. However, as Mandelbrot shows, this creates a host of problems. Individuals don’t behave like random particles.
The fact that one particle in physics does something doesn’t increase or decrease the likelihood that another particle will. This is not so with humans. When your neighbor starts getting rich investing in tech stocks, it may influence you to do the same. When your other neighbor panics and sells his crashing stocks, you may be more likely to do the same in that case as well. Because of the interconnectedness of markets, they are better understood as complex systems which Mandelbrot studied rather than the simple systems many economists studies. Mandelbrot lies at the heart of a lot of the work I do at Mutiny Funds and my ongoing research into ergodicity.
In Misbehavior of Markets, Mandelbrot dismantles the efficient market hypothesis and much of traditional economic theory while laying the groundwork for a
My Highlights And Notes
Note: All the “Notes:” are my own additions and can be ignored if they don’t make sense. All bolding is mine, not the author’s.
“I have been a lone rider so often and for so long, that I’m not even bothered by it anymore,” he says. Or, as a mathematically minded friend put it, he moves orthogonally—at right angles—to every fashion.
Einstein famously said: “The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.”
reading this volume will not make you rich. But it will make you wiser—and may thereby save you from getting poorer.
Alas, the theory is elegant but flawed, as anyone who lived through the booms and busts of the 1990s can now see. The old financial orthodoxy was founded on two critical assumptions in Bachelier’s key model: Price changes are statistically independent, and they are normally distributed.
Notes: 1) flaws of efficient market hypothesis
the bell curve fits reality very poorly. From 1916 to 2003, the daily index movements of the Dow Jones Industrial Average do not spread out on graph paper like a simple bell curve. The far edges flare too high: too many big changes. Theory suggests that over that time, there should be fifty-eight days when the Dow moved more than 3.4 percent; in fact, there were 1,001. Theory predicts six days of index swings beyond 4.5 percent; in fact, there were 366. And index swings of more than 7 percent should come once every 300,000 years; in fact, the twentieth century saw forty-eight such days. Truly, a calamitous era that insists on flaunting all predictions. Or, perhaps, our assumptions are wrong.
Notes: 1) these are the fat tails
Market turbulence tends to cluster.
Notes: 1) markets have periods of high volatility with long lulls.
Markets have a personality.
Market time is relative.
Notes: 1) See Tempo book
Market professionals know far more than they even realize. Professional traders often speak of a “fast” market or a “slow” one, depending on how they judge the volatility at that moment. They would quickly recognize, and affirm, the concept of trading time.
Notes: 1) wisdom of grandmothers a la Taleb
We cannot know everything. Physicists abandoned that pipedream during the twentieth century after quantum theory and, in a different way, after chaos theory. Instead, they learned to think of the world in the second way, as a black box. We can see what goes into the box and what comes out of it, but not what happens inside; we can only draw inferences about the odds of input A producing output Z. Seeing nature through the lens of probability theory is what mathematicians call the stochastic view. The word comes from the Greek stochastes, a diviner, which in turn comes from stokhos, a pointed stake used as a target by archers. We cannot follow the path of every molecule in a gas; but we can work out its average energy and probable behavior, and thereby design a very useful pipeline to transport natural gas across a continent to fuel a city of millions.
Finance is a black box covered by a veil. Not only are the inner workings hidden, but the inputs are also obscured, by bad economic data, conflicting news reports, or outright deception.
The English phrase “at random” adapts a medieval French phrase, à randon. It denoted a horse moving headlong, with a wild motion that the rider could neither predict nor control. Another example: In Basque, “chance” is translated as zoria, a derivative of zhar, or bird. The flight of a bird, like the whims of a horse, cannot be predicted or controlled.
One is the most familiar and manageable form of chance, which I call “mild.” It is the randomness of a coin toss, the static of a badly tuned radio. Its classic mathematical expression is the bell curve, or “normal” probability distribution—so-called because it was long viewed as the norm in nature. Temperature, pressure, or other features of nature under study are assumed to vary only so much, and not an iota more, from the average value. At the opposite extreme is what I call “wild” randomness. This is far more irregular, more unpredictable. It is the variation of the Cornish coastline—savage promontories, craggy rocks, and unexpectedly calm bays. The fluctuation from one value to the next is limitless and frightening. In between the two extremes is a third state, which I call “slow” randomness
Gaussian math is easy and fits most forms of reality, or so it seems. But with the sharp hindsight provided by fractal geometry, the Gaussian case begins to look not so “normal,” after all. It was so-called only because science tackled it first; as ever in science, there is a healthy opportunism to begin with the problems easiest to handle. But the difference between the extremes of Gauss and of Cauchy could not be greater. They amount to two different ways of seeing the world: one in which big changes are the result of many small ones, or another in which major events loom disproportionately large. “Mild” and “wild” chance, described earlier, are my generalizations from Gauss and Cauchy. You can see analogs of this dichotomy all around. In history, modernists argue that the course of human events is shaped by many trends, economic and social, enacted in the lives of millions of forgotten individuals; the historian’s task is to trace these trends. By contrast, traditionalists, now coming back into fashion, contend that history was shaped and dominated by a few great men, Caesar or Napoleon, Newton or Einstein, for example.
Notes: 1) Gaussian problems were all solved in the 20th century. the easy ones are gone which is causing the shift back to Cauchy?
He once said: “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.”
Another tool inspired by Bachelier is Modern Portfolio Theory, a method for selecting investments devised in the 1950s by Harry M. Markowitz, a University of Chicago Ph.D. A third: the Black-Scholes formula for valuing options contracts and assessing risk;
Notes: 1) all of the efficient market hypothesis can be traced back to Gaussian curve vision of the world
And now a practical point, which helps explain why this formula became so popular in the world of finance. It takes all of Markowitz’s tedious portfolio calculations and reduces them to just a few. Work up a forecast for the market overall, and then estimate the β for each stock you want to consider. From 495 calculations for a thirty-stock portfolio with Markowitz and portfolio theory, you simplify to thirty-one with Sharpe and the Capital Asset Pricing Model, as it came to be called.
Notes: 1) people will always default to simple and easy even if wrong. this leaves margin in nuance and complex though this margin requires a lot of work.
Discontinuity, far from being an anomaly best ignored, is an essential ingredient of markets that helps set finance apart from the natural sciences.
Notes: 1) I like the explanation that we have applied Newtonian physics and natural phenomena to nonlinear human systems as the baasis for all these issues.
Brownian motion, again, is a term borrowed from physics for the motion of a molecule in a uniformly warm medium.
Big price changes were far more common than the standard model allowed. Large changes, of more than five standard deviations from the average, happened two thousand times more often than expected. Under Gaussian rules, you should have encountered such drama only once every seven thousand years; in fact, the data showed, it happened once every three or four years.
Notes: 1) the dagger!!!
have happened, not once. No bell curve. Four centuries of history and turmoil are recorded
Notes: 1) This is Taleb’s barbell of T bills and risky shit. The margin of where Everyone else is wrong is all in the middle and the far edges of the Cauchy distribution.
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 month, or, if it had risen, greater odds of continuing to rise.
Notes: 1) this has a lot of cross-domain applications. there are momentum effects in many fields.
A fractal, again, is a pattern or shape whose parts echo the whole. If you look closely at the frond of a fern, for instance, you see it is made up of smaller fronds that, in turn, consist of even-smaller leaf clusters. Of course, you can run such thinking forwards as well as backwards; you can analyze the fern down into its smaller parts, as well as synthesize the fern up from the smaller parts. Start with the smallest leaf shoots as the fern unfolds from its bud; then watch as each shoot grows and generates more shoots, which in turn grow and generate yet more shoots until the fern is fully formed.
Notes: 1) this is what waitzken does in The Art of Learning with making smaller circles.
What have we here? A new tool to measure, not how long, heavy, hot, or loud something is, but how convoluted and irregular it is. It provides science with its first yardstick for roughness.
Notes: 1) is roughness a better measure of volatility
Composer Gyorgy Ligeti, among others, has experimented with fractal music. He says: Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
Notes: 1) the foolscap method is fractal way to structure a book
The fractal dimension is defined as the ratio of the logarithm of 4 to the logarithm of 3. A pocket calculator converts that: 1.2618. … This makes intuitive sense. The curve is crinkly, so it fills more space than would a one-dimensional straight line; yet it does not completely fill the two-dimensional plane.
Given a starting condition, what is the probability that some event will happen? The absolute odds of being a billionaire are very low; but according to Pareto’s formula, the conditional probability of making a billion dollars once you have made half a billion is the same as that of making a million once you have made half a million. Money begets money, power makes power. Unfair, but true—both socially and mathematically.
Pictures can deceive as well as instruct. 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.
his observation of two forms of wildness remain: abrupt change, and almost-trends.
long-term dependence so that an event here and now affects every other event elsewhere and in the distant future.
shows turbulence in a wild kind of variation far outside the normal expectations of the bell curve;
Notes: 1) sensitivity to initial conditions 2) fat tails
this book has proceeded, the evidence and theory have appeared bit by bit. But it all comes together in the metaphor of turbulence.
To drive a car, you do not need to know how it goes; similarly, to invest in markets, you do not need to know why they behave the way they do.
From 1986 to 2003, the dollar traced a long, bumpy descent against the Japanese yen. But nearly half that decline occurred on just ten out of those 4,695 trading days.
Notes: 1) fat tails
Continuity is a common human assumption. If we see a man running at one moment here and a half-hour later there, we assume he has run a line covering all the ground in between. It does not occur to us that he may have stopped to rest and then hitched a ride.
the capacity for jumps, or discontinuity, is the principal conceptual difference between economics and classical physics.
Notes: 1) once you involve humans you cant use classical physics metaphors. nonlinear as a species we are.
The contradictory view, popular among market pundits: Time is different for every investor. Each time-scale you consider, each holding period for a stock or bond, has its own kind of risks. Under this view, a quick day-trade poses entirely different scales of risk than does a six-month investment—and in most eyes, the day-trader is the more likely to go broke. Things need not be so complicated. The genius of fractal analysis is that the same risk factors, the same formulae apply to a day as to a year, an hour as to a month. Only the magnitude differs, not the proportions. In fractal analysis, a price series is like a long, folding car antenna. You can look at its full length, segment by segment; or you can simply collapse it so each length is stacked inside the next. This is the scaling property of financial price series, as described earlier. Statistically speaking, the risks of a day are much like those of a week, a month, or a year. But the price variations scale with
Notes: 1) fractals explain Waitzken’s smaller circles idea. You can start small and you can leearn without the noise but under the same regime then apply those principles and fingerspitzengefuhl to larger stuff.
People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not. We see patterns where there are none.
Forecasting Prices May Be Perilous, but You Can Estimate the Odds of Future Volatility.
Notes: 1) you can measure fragility
The classic Random Walk model makes three essential claims. First is the so-called martingale condition: that your best guess of tomorrow’s price is today’s price. Second is a declaration of independence: that tomorrow’s price is independent of past prices. Third is a statement of normality: that all the price changes taken together, from small to large, vary in accordance with the mild, bell-curve distribution. In my view, that is two claims too many. The first, though not proven by the data, is at least not (much) contradicted by it; and it certainly helps, in an intuitive way, to explain why we so often guess the market wrong. But the others are simply false. The data overwhelmingly show that the magnitude of price changes depends on those of the past, and that the bell curve is a nonsense. Speaking mathematically, markets can exhibit dependence without correlation. The key to this paradox lies in the distinction between the size and the direction of price changes. Suppose that the direction is uncorrelated with the past: The fact that prices fell yesterday does not make them more likely to fall today. It remains possible for the absolute changes to be dependent: A 10 percent fall yesterday may well increase the odds of another 10 percent move today—but provide no advance way of telling whether it will be up or down. If so, the correlation vanishes, in spite of the strong dependence. Large price changes tend to be followed by more large changes, positive or negative. Small changes tend to be followed by more small changes. Volatility clusters.
So how, you ask, does one survive in such an existentialist world, a world without absolutes? People do it rather well all the time. The prime mover in a financial market is not value or price, but price differences; not averaging, but arbitraging. People arbitrage between places or times. Between places: I had a friend who made his life as graduate student less tough by buying a convertible cheaply in his snowy home state, Minnesota, repairing it with his own hands, and then driving it to sunny California to sell dear. And arbitrage between times: A scalper buys a block of tickets today, and hopes to profit next month by reselling them dearly once the show is sold out. These arbitrage tactics assume no “intrinsic” value in the item being sold; they simply observe and forecast a difference in price, and try to profit from it. Of course, I am by no means the first to suggest the importance of arbitrage in financial theory; one of the latter-day “fixes” of orthodox finance, called Arbitrage Pricing Theory, tries to make the most of this. But a full understanding of multifractal markets begins with the realization that the mean is not golden.
Notes: 1) instead of waiting for people to become rational and the price to return to intrinsic value, just profit off of human irrationality via arbitrage.
Last Updated on May 14, 2022 by Taylor Pearson