If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever to do it, the formula must exist just as if one could. - Tom Stoppard, Arcadia
One of our editors at MarketMinder, Jason Dorrier, read this quote and said: “Now make every one of those atoms into a human being and you’ve got a market. Predict that will you?” Indeed. The Stoppard quote describes the credo of the misguided masses of finance: The fetishistic seeking after math-based formulae to explain stock markets.
Simply, markets aren’t metaphors. They’re markets! Markets can be compared to, but aren’t weather systems, evolution, physics, math, or anything other than markets. As a philosopher might say, they are “as such,” a category unto themselves. We must take markets on their own terms, not on the terms of some obtuse metaphorical vehicle.
Of all the many things I’ve been privileged to learn from Ken Fisher, it’s been to study markets, not theories about them, not mathematical constructs, psychological theories, or otherwise. Focus on what stocks do—allow the results to drive your explanation; do not shoehorn your interpretation of reality to fit your preferred theory. If they don’t match, trust what actually happened and adjust your theory.
To a mathematician, markets are math; to a psychologist, markets are neuroscience. But math is not a thing, it’s a logical description of things. Psychology is not the mind, it is an—often poor—explanation of the mind. These are useful ways to think about markets, but ultimately they’re not markets.
It’s against this backdrop we encounter Benoit Mandelbrot’s Misbehavior of Markets. He’s the founder of fractal theory—a now well-established sect of mathematics. In a nutshell, it’s the idea that small and jagged instances can give rise to larger, predictable, smoother patterns. (Click here for more about it.)
Mandelbrot is the archetypal wizard for the Modern: the white-haired, disheveled mathematician as today’s Merlin. I was lucky enough to see him speak earlier this year, and though widely acclaimed as a maverick of the academy, in person he seems a diminutive, gracious man.
Of course, as one of the mathematical titans of the time, Mandelbrot sees markets as math-based. The Misbehavior of Markets explains how markets behave like his fractal theory. This produces both unique insights and a handful of misconceptions but is ultimately a worthy addition to financial theory. We should note that Mandelbrot openly and honestly says he doesn’t know how to make money with these ideas, he’s instead reporting what he’s observed. (Ah, the freedom of the academic life!)
Mandelbrot might seem the forerunner to now famous market gurus like Nassim Nicholas Taleb (of Black Swan fame). This is one of the first accounts of the now-vogue ideology that markets are actually riskier than most believe, and that the so-called “fat tail” or “Black Swan” events are much more frequent than current financial theory can account for. Indeed, the last few years have been a veritable tidal wave of backlash against the bell curve (or, more formally, Gaussian distribution) and random walk (or, Brownian motion) theories of stock markets—averages don’t matter, reality is very wild, with unlikely events the norm. The sum of all this is, essentially, a critique on risk as most financiers see it.
On that basis, Mandelbrot is indeed the father of Taleb-ian thinking. True, finance inappropriately defines risk as some smooth, average volatility, which is fine for statistical analysis but captures nothing of the true, visceral, emotional, and ultimately very spiky (like a fractal’s edge) range of features risk manifests in us, and therefore markets. Financial risk measures (“beta” and the like) are really another kind of broad, reductionist calculation (though not without its usefulness), but not an appropriate way of viewing the actual, ontological, thing that is risk.
But Mandelbrot often mixes the short with the long term, sometimes to good and sometimes to ill effect. He never seems to note that a long-term investor doesn’t actually care about things like the 1987 crash or the more recent “flash” crash in May—a long-term investor may or may not even realize it happened, but a trader—on that single day—could be ruined. It’s this inability to differentiate between short/long that disallows Mandelbrot to preach one of the most important lessons of investing: That yes, stocks can be highly volatile, but they actually go up over time despite the seeming perpetual world tribulation. To miss that lesson is to miss the point of investing entirely. It’s tragic that he doesn’t offer that lesson for the investing masses, and somewhat puzzling considering his mathematics is based on the idea that the small instances can roll up into larger patterns.
Yet, Mandelbrot also offers a novel observation: That we should not think about markets in terms of our experience of time. Rather, we should think of markets as having their own sense of time. This is remarkable, and correct. Most investors I meet think about stock returns on their time—“I have five years till I retire and want XX return”, or, I want to buy a boat in seven years and need XX% return by then”. And so on. But the market doesn’t care; it does it’s own thing on its own time. This is a vital lesson.
And here is where comparisons between he and folks like Taleb end. Taleb believes in pure stochasticity (random chance), and even views stocks’ long-term returns as “random drift.” Mandelbrot does not: He is a firm believer in patterns and that fundamentals ultimately rule stock returns—and the power of probability in forecasting future prices.
He’s right, but Mandelbrot goes too far. Finance theorists have long held that stocks are not auto-correlated, which means that past returns don’t influence future returns. Mandelbrot disagrees, proclaiming that “long dependence” has a profound effect on future prices. Effectively, that all past prices have an effect on the probability of a stock to move one way or the other. This actually might be true for very short-term observations of stock moves. But, if so, it’s only true in a non-practical, theoretical sense. The math of fractals could predict probabilities—slightly, and I mean really slightly—better than 50/50. But with transaction costs and the rise of hedge funds with high frequency trading to arbitrage most such possibilities away, this is all but an impossibility in the real world. Or, said differently, if the idea of market long dependence were true, Mandelbrot would be a trillionaire by now. He acknowledges this indirectly by admitting anticipation is unique to markets, and at the heart of how they work. Again, an uncommon insight, and a correct one, but somewhat lost among murkier premises.
And that is the way this book goes. By now, there are better, sharper analyses on these topics. But we must credit Mandelbrot as among the first to really present such ideas to the wider public. His fractal theory doesn’t explain markets, but turns out to be a sometimes effective mechanism to help contemplate them.
Another favorite Stoppard quote:
Skill without imagination is craftsmanship and gives us many useful objects such as wickerwork picnic baskets. Imagination without skill gives us modern art.
In today’s world, where mathematician is Merlin, Mandelbrot’s book focuses his prodigious—and imaginative—intellect on markets to provide some worthy insights. But be wary, math, at its core, is often the Modern Art of stock market interpretation. |