• Rana Basheer

Physics of Wall Street

This book chronicles the trials and tribulations of those who toiled hard, despite being ostracized by mainstream scientist, to develop a  formal mathematical foundation for one of our fundamental human activity.. trading.  Even great minds like Sir Issac Newton who invented calculus and was instrumental in developing the theory of gravity stayed well clear of this task. He is quoted as having quipped “I can calculate the movement of stars, but not the madness of men” [1] after he lost 20,000 pounds in a stock bubble called the south sea bubble.

This book begins in the late 19th century with the thesis of a french mathematician called Louis Bechelier. He was the first mathematician who attempted to explain the nature of randomness in stock price. He hypothesized that the changes in price for a stock or commodity can be explained as a sort of random movement that is commonly found in nature called the Brownian motion (the same randomness that defines the motion of a speckle of dust under sunlight). His argument was that in a Laissez-faire economy, the price of a commodity such as cotton, for e.g., is a tug-of-war between two competing entities: the buyer and seller. So at any time instance t, all possible information that a buyer or seller could use to push/pull the price for cotton up or down has attained a delicate equilibrium. Consequently, he argued that the chance of price going up or down is the same as that of winning a coin toss. Now the question was how much would it shift up or down from the current price? Since he worked at the Paris Bourse (stock exchange) in 19th century, whose day-to-day activity is quite slow compared to the rough and tumble of our modern stock exchanges, he posited that a normal distribution (where extreme price jumps are very very rare) would account for fluctuations in price.

Roll forward 100 years and several people began suspecting that normal distribution was not enough to account for price variations observed in stock exchanges. So around 1950, a astrophysicists named Maury Osborne posited an alternate pricing model where traders are assumed to be more interested in rate of change of price rather than the absolute dollar amount by which the price increased or decreased. For e.g. a person who lost $100 on a commodity that he was planning to sell at $1000 feels more pain than a person who lost $100 on a $100,000 priced item. Osborne hypothesized that the logarithm of the loss is a better indicator of the pain felt by a trader. So in this model if a trader loses $10,000 for a commodity that was priced at $100,000 will feel a pain coefficient of  log($100,000) – log($10,000) = log($10) and another trader who lost $100 for a $1000 ticketed item will feel a pain coefficient log($1000) – log($100) = log($10) thereby making them partners in pain. This lead to the log-normal distribution that has become the corner stone for much of the financial statistics in the last 50 years including the maligned Black-Scholes formula for option pricing. This book also explores the contributions made by Benoit Mandelbrot of the Mandelbrot fractal fame in attempting to model the stock prices under extreme conditions such as those observed under stock bubbles using random distribution models (levy stable distributions) where large jump in stock prices have a higher likelihood.

In my personal opinion this book does a good job of laying out the history behind these mathematical innovations in layman terms that should appeal to a broader audience. Though this book’s story telling might not reach the level of sophistication as Michael Lewis’s The Big Short: Inside the Doomsday Machine


Additionally, this book shines the spot light on some very novel method for predicting bubbles and the subsequent market crash based on ideas that cross pollinated from the field of material engineering. For ages, physicists have been studying the properties of materials under extreme fatigue and their subsequent catastrophic failures. They observed that if minute fissures starts occurring in a material with logarithmic periodicity, then a catastrophic failure is on the horizon. They were applying these theories for the altruistic task of predicting earthquakes. However, Didier Sornette applied this log-periodic technique to predict the market crash of 1997 and 2008 and was extremely successful in reaping the riches from his insight. There is also some discussion on the tricks of the trade employed by hedge fund managers such as pair trading and arbitrage opportunities arising from the lag experienced by a commodity price which might appeal to students of financial statistics.

However, an important aspect that this book failed to explore in depth is the emerging field of behavioral economics pioneered by Daniel Kahneman and the late Amos Tversky called the Prospect Theory. Dr. Kahneman won the 2002 Nobel prize in economics for his work where he sought to bring human psychology into financial statistics. He hypothesized that any human endeavors should reflect the foibles of its practitioners, and consequently has to account for all our subconscious biases. His 2011 book Thinking, Fast and Slow

The main take away from this book is that if you are smart enough to develop a new mathematical model that better reflects the price fluctuations, then you better keep it secret inside lead walls. Often scientists are looking for approval for their new ideas from peers. The formal process to do this is to publish their idea on peer reviewed journals. This is an excellent method for benign fields like engineering and physics where this form of feedback helps straightens the chinks in your original idea. However, in the cut throat field of economics, the success of your new idea becomes the impetus for its failure. Once the new pricing model idea percolates into the larger audience of hedge fund managers and individuals looking to make a quick buck, they will become more risk taking or cautious based on your theory’s recommendation and consequently the price of the underlying stocks or commodity will reflect this new information. Subsequently, any advantage that your idea had from the status-quo is effectively neutralized. There is a field of engineering that deals on a daily basis with this sort of complex feedback systems: Control System. If last century saw the pollination of ideas from the field of physics, perhaps, this century would witness the deluge of control system theorists into this alluring field of financial statistics. Control system theorists could probably figure out the poles (bull market) and zeros (bear market) of our economy and device checks and balances that will keep us chugging along happily like an inverted pendulum problem as in this video 🙂

#distributions #physics #random


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