The Physics of Wall Street

Physics applied to predicting the unpredictable Wall Street - It was 2008 - a housing bubble was about to inelegantly burst. The explosion spread from individuals unable to meet their payments, to banks, and then to financial institutions that had bet that the housing market would right itself and sail on. There was a general feeling that the bets that took down great swatches of traditional Wall Street were based on a misplaced almost mystic trust that mathematical modeling -- some of it derived from the advanced math underlying the work of modern physicists was part of the problem. With this as a backdrop to all this Stevens Institute physics student James Own Weatherall began to write The Physics of Wall Street.

The book takes a journey through the development of mathematical modeling for finance, with many way stations along the historical path. The writer, who has also studied the history of the philosophy of science, makes a pretty enjoyable book as he brings in math personalities like Poincare, Mandelbrot and Shannon, and one I didnt know about named  Bachelier -- a mathly crew who in generations of collaboration set the stage for some brilliant quantitative types --- ones that came out of the physics milieu -- to way lay Wall Street beginning in the 1980s.

Along the way we meet Dr Brown, not the soda pop Dr Brown but the naturalist Dr Brown who saw pollen in a petri dish under a microscope and wondered mightily why they jiggled and wiggled about so. He didnt just wonder, he observed up on it.  But why that erratic woblling? Twas hard to figure?

Such physics and the math to describe it was to come eventually to be considered a diviner of the future of the stock ticker - its ascent or descent or sideways swipes.

The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by the aforementioned Louis Bachelier who in 1900 in his PhD thesis "The theory of speculation" at the ecole, in which he presented a stochastic analysis of the stock and option markets! 

Epitomigm writers wont try to go further to discuss Einstein's work in Brownian motion (or Paul Levy's or Norbert Wiener's) because, well it's above our pay grade and over our head. But its nature made it seem a key to unlocking the satchel of uncertainty and predictability, you might say. The study of Brownian motion brought about the idea of random walks that ,,, serve as a fundamental model for the recorded stochastic activity. 

Simulation of Brownian motion.

Bachelier's work was somewhat known and somewhat unknown. In time to come A mathematician later on, named Maury Osbrone, author Weatherall writes, and looking at some bills, wondered if the math behind the Brownian motion and random walk might bring sense to the stock market, which sat on his cluttered table (he had 11 kids), in the form of Wall St. Journal stock pages replete with numbers that looked like those dancing pollen particles dancing mysterious boogie woogies.

Osborne's work, notably,  a paper entitled "Brownian Motion and Its Applications In The Stock Market," gained some currency among economists in the '50s and later. It is seen by Weatherall as the basis for one of the great stock books of all time, A Random Walk Down Wall Street. Important to the narrative is the role of an Edward Thorpe, author of both How to Beat the Game of 21 and How to Beat the Stock Market, but let's do a sum before we head to the exits. And pick up the Edward Thorpe line a little further down there road...

There you have a bit of random walk up from pollen and down to Wall Street, as I garnered it, from reading The Physics of Wall Street.

What can you learn from this book?  I’d distill the message I took away from the tome thusly: Physicists have improved people’s understanding of financial markets, because they have come to it from a distinctly different place, in terms of methodology and engineering. The steps as recorded by Weatherall are these:

1-One uses simplifying assumptions to make a problem tractable (sounds like a heuristic);
2-One double backs and sees how well the model worked, adjusting, tuning and testing assumptions;
3-This may uncover a model that just doesn’t really work, because its assumptions do not apply in the use case; and,
4-Or the conclusion is that the model works pretty well, and can be improved, especially given certain circumstances.

How many failures flow from misplaced faith in a misunderstood poorly fed model? Writes Weaterall: " Models are at bottom tools for approximate thinking."

The Physics of Wall Street takes considerable interest in the field of probability and gambling, and, as such studies often do, alights briefly on the sport of horseracing. A discussion of Claude Shannon’s work on chance (which, to my surprise, included gambling junkets to Reno and Las Vegas to test out theories) brings up John Kelly.

Kelly is pretty well known among horse handicappers as inventor of a bank roll manager system for gambling. The Kelly Criterion sets bet size based on one’s usual percentage of wins for a given race type, measured against the horses’ odds. It’s intended to ensure that a good day of handicapping also includes a favorable outcome in the wallet – as avowed punters know, the two things do not hand and handy always go. Advantage/Payout = Amount of bankroll to bet. If you have 0 or less advantage, you don’t bet.

[An online calculator automatically computes the Kelly Criterion.
https://www.usracing.com/horse-betting/kelly-advantage-calculator]

What I did not know about Kelly was that a Bell Lab colleague of Shannon’s, and that Shannon showed Kellys work to Edward Thorpe, the mathematician who pioneered use of probability theory in hedge funds that play with small movements in shorts and options on a big scale. Thorpe capitalized on the insight.

More about Kelly – he came out of the oil industry into academia (Bell Labs), was a WWII fighter ace, and, generally, a fun lover.

After completion of The Physics of Wall Street Weatherall shifted attention to include MisInformation studies, a crucial area at the moment, and in time to come. -Baruch Bernardini

Now we'll have fun fun fun fun fun fun fun til her daddy takes her T-Bird away.