My first exposure to Mandelbrot was through his joint work with Richard L. Hudson in The (Mis)Behavior of Markets, which was published in 2004 and stands as a testament to the contributions he made to finance beginning with this work in 1962. Mandelbrot follows the rules that led him through Part 2 of his life, and in doing so is presented with a unique opportunity to extend humanity’s understanding of financial markets. He takes full advantage of the opportunity, but then draws on the lessons learned in Part 1 to realize that the political inertia of this industry will blunt the impact of his magnificent contribution. Rather than dwell on this, he collects on the cache and karma of his contributions and continues on his life.
There are several impressive things that Mandelbrot does not do:
- He doesn’t sever his ties with IBM to become a financier.
- He doesn’t dig his heels in to fight the financial establishment – despite his convictions that he is right.
- He refines his work on his terms, rather than trying to take the theory to far.
- He continues to support the next generation of scientists in this area of finance by working with Eugene Fama and Merton Miller. Mandelbrot does not shepherd his work, he pushes it out and extends its reach.
- He misses career opportunities that would be soul crushing and unrecoverable for many, but instead he plots onward.
- Mandelbrot does not get stuck on the nature of his contribution to finance, despite its enormous value. He reads the situation accurately and moves on.
“MY INVOLVEMENT WITH THE BEHAVIOR of financial prices—absolutely unplanned—became a constant of my scientific life.”Mandelbrot’s The Fractalist, Chapter 22
Mandelbrot’s path to achieving his Keplerian dream is not smooth – it is rough. Encounters with financial prices and their behavior would forever be a part of his life.
“The three states of chance—wild, mild, and slow—can be compared to the three states of matter. Are not solid and gas separated by liquid? Absolutely. In my view, the same is true of chance—the counterpart of liquid being “slow” randomness.”Mandelbrot’s The Fractalist, Chapter 22
Enumeration of options is always fascinating, and ‘mild, wild and slow’ are wonderful names.
“We’ve done all we can to make sense of these cotton prices. Everything changes, nothing is constant. This is a mess of the worst kind.”Mandelbrot’s The Fractalist, Chapter 22
There is great freedom in declaring a situation in hopeless. By declaring things a mess, “of the worst kind” the stage is set for Mandelbrot to attempt an explanation. As he benefited from his unique position with Zipf in his PhD, here Mandelbrot benefits from encountering a situation where there is low risk of embarrassment.
“Fractals—or their later elaboration, multifractals—do not claim to predict the future with certainty. But they do create a more realistic picture of market risks than does observation alone.”Mandelbrot’s The Fractalist, Chapter 22
Telling the future with 100% accuracy isn’t yet possible – but telling the future a little bit better tomorrow than was done today is a great improvement for society. Finance had previously lived in the world of smooth trajectories – when everyone knew that this was inaccurate. Through his study of roughness, Mandelbrot improved the understanding of market behavior.
“But not for a moment did I forget that to remain stable and vertical, a bicycle must move sufficiently fast.”Mandelbrot’s The Fractalist, Chapter 22
Bicycles are wonderful, but they are safest when moving. Balance is possible with minimal equipment, provided that motion is part of the equation. Velocity and direction are essential to safe operation with a minimalist approach.
“I was acutely aware that my findings would have devastating consequences for the accepted standard theory of speculation.”Mandelbrot’s The Fractalist, Chapter 22
In Part 1 we watched Mandelbrot’s family deftly maneuver through World War 2 and survive where others misread the political environment and perished. Mandelbrot has recognized that he has done work of great merit, but also sees that the work may not exist in fertile ground. The finance industry’s inertia and resistance to change may prevent this phase of his Keplerian Dream from becoming the early landslide victory that it might have been.
Page by Page, Screen by Screen, Swipe by Swipe
“MY INVOLVEMENT WITH THE BEHAVIOR of financial prices—absolutely unplanned—became a constant of my scientific life.”
“… different states of randomness: the “mild” and the “wild,” and a third state I call “slow.””
“I was acutely aware that my findings would have devastating consequences for the accepted standard theory of speculation.”
“Oh, I am very sorry. I should have started by saying so. The invitation is from Harvard, and their offer is higher than my current salary.”
“If status within IBM had been measurable, mine would have instantly jumped from well under the radar to well above—where it stayed.”
“But not for a moment did I forget that to remain stable and vertical, a bicycle must move sufficiently fast.”
“The sequence that followed, of sociological low points and intellectual highs, could not have been predicted.”
“There were far too many big price jumps and falls. And the volatility kept shifting over time. Some years prices were stable, other years wild. “We’ve done all we can to make sense of these cotton prices. Everything changes, nothing is constant. This is a mess of the worst kind.””
“Moreover, there were too many big price jumps to fit the bell curve.”
“All price charts look alike. Sure, some go up, some down. But daily, monthly, annually, there is no big difference in their overall look.”
“Here, the fractal scaling up and down is not being done to a shape, such as the florets of a cauliflower. Rather, it is being applied to a different sort of pattern, the way prices vary. The very heart of finance is fractal.”
“My first work in finance had brought together two domains of knowledge far removed from one another.”
“By bringing them into all-too-practical finance, I imposed and argued for a deep distinction between “mild” and “wild” states of randomness of chance.”
“The three states of chance—wild, mild, and slow—can be compared to the three states of matter. Are not solid and gas separated by liquid? Absolutely. In my view, the same is true of chance—the counterpart of liquid being “slow” randomness.”
“First, price changes are not independent of each other.”
“Second, the distribution of price changes is not “normal.””
“Fractals—or their later elaboration, multifractals—do not claim to predict the future with certainty. But they do create a more realistic picture of market risks than does observation alone.”
“This left him with a problem that was the bane of my life: my tendency to cross scientific disciplines.”
Mandelbrot encounters current and future greats of finance; Eugene Fama, then a student, and Merton Miller, who would make efforts to recruit him to the University of Chicago.
“Fama conceded, corrected his earlier assertions, replaced the mysterious label “martingale” with “efficient market,” and built his career on becoming its champion.”
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