“The same quadratic equation with which the ancients drew right angles to build their temples can be used today by a banker to calculate the yield to maturity of a new, two-year bond. The same techniques of calculus developed by Newton and Leibniz two centuries ago to study the orbits of Mars and Mercury can be used today by a civil engineer to calculate the maximum stress on a new bridge, or the volume of water to pass beneath it.”
— Benoit Mandelbrot
The above quote is from a book recommended recently in a Twitter thread from Mike Lawlor, and which I haven’t been able to put down for very long. And it’s not even about science or math per se, but rather the stock market: The Misbehavior of Markets: A Fractal View of Financial Turbulence.
For anyone interested in human behavior, decision-making, culture, science, history, or computers, it’s hard to escape the gravity of “finance” as a natural way to get a slice of understanding about all of them at once. And Mandelbrot, who pioneered the discipline of (and coined the term) “fractals,” has a way of overturning convention in this otherwise conventional field of study in a way that feels light, visually intuitive, and almost playful. This book is a natural complement (precursor?) to Nassim Taleb’s bestseller The Black Swan: The Impact of the Highly Improbable, and just as exuberantly defiant.
I started reading the book the other day, the same day I happened to be catching up on this 2017 podcast episode from Patrick O’Shaughnessy involving a wide-ranging discussion with investors Ted Seides and Brent Beshore, and 1 month after blazing through Steven Strogatz’s completely excellent Infinite Powers: How Calculus Reveals the Secrets of the Universe as I was gathering up dots to connect I started feeling a faint shimmer of insight:
None of this is about numbers.
Numbers are the shadow of information, not information itself. Our theories and models are the scaffolding with which we can build understanding — they are not understanding itself. Patterns are resemblances of potential meaning, not meaning itself. We talk about subjects like math and finance as if they are about numbers or values, which isn’t accurate. What something is about tends to be different than the tools you use to get at its “aboutness.”
What I’m getting from my brief foray into this arcane world of logarithms, integrals, and fractal dimensionality is not an appreciation for math (that was already there), but the unexpected discovery of philosophical principles for the art of living a life. Principles that can be used to domesticate emotions, flourish with inertia, and value what matters.
For example, A big theme I’ve noticed throughout the Invest Like The Best podcast is this idea that the rise of robo-advisors such as Betterment and Wealthfront (following the hands off revolution of set-it-and-forget-it mutual funds) isn’t likely to make active investment managers obsolete. Why? Because the biggest value a good active manager provides isn’t in their investment philosophy or the stocks they pick but in their ability to stoically withstand the emotional tumult of markets. They earn fees not for their ability to beat the market but the mental discipline to adhere to the plan and not pull out when things get rough. A philosophy, whether financial or otherwise, is a system of behavior used for making decisions consistent with your values. When you deviate from the system, then you are more likely to suffer.
Or consider this excerpt from The Misbehavior of Markets making a point about a market peculiarity but hitting on the insight underlying habit-building and the compounding gains of nutrition, exercise, and intimacy. He also ends by deploying the “infinite” — the idea at the heart of calculus:
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 awhile longer.
[…] Just the opposite appears to happen in the medium term, three to eight years. A stock that was rising over one multi-year stretch has slightly greater odds of falling in the next.
I have another view of dependence. To me, its most important effect is not over a short term, but over the very long term — in theory, an infinite effect. This has some unusual consequences. 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.
During the the flow of discussion between O’Shaughnessy, Seides, and Beshore there was general agreement that in the end, despite a deep fascination with and study of financial investments whether public (Seides) or private (Beshore), that the best investment continues to be in yourself — that your own knowledge, skills, and relationships are what give the best returns. It turns out, even for successful investors, compound interest has less intrinsic value than compounding interests.
Or, to cast it in more Strogatzian light: maybe the derivative of your life at any particular moment — your rate of change — is closely related to how much personal value you’re able to accumulate before it’s over.
“It is an extraordinary feature of science that the most diverse, seemingly unrelated, phenomena can be described with the same mathematical tools.”
— Benoit Mandelbrot