In discussions regarding the effect of the presidential election on the stock market, the favorite line of argument appears to be that: there is much more randomness in the markets than most people recognize: and, people have a tendency to become comfortable with the perceived patterns even though the patterns are nothing more than random noise. Some have even suggested that the works of Mr. Nassim Nicholas Taleb are definitive on the issue.

I have carefully read the volume “The Black Swan” by Nassim Nicholas Taleb, the seminal work “Statistical Mechanics of Financial Markets” by Johannes Voit as well as many other works on the mathematical theory of the stock market. I also have also studied statistical mechanics in a number of disciplines for more than 20 years. Based upon my understanding of statistical mechanics, the aforementioned works, and several years of studying the stock market data, it is my observation that the two fatal flaws in the works by both Taleb and Voit, as well as the plethora of others who claim that the market is “random”, are embedded in the assumption that the incremental change in the either the share price of a company or the stated level of an index is either a stationary levy process or a quadratic brownian process. Both of these processes lead to a normal probability density function for the incremental price change, which has been demonstrated to be incorrect. From the flawed basic assumption, the standard argument arises that the market is “random” and, therefore, unpredictable.

If the market were to be truly “random” process, then it will return to its starting point, because it is a one-dimensional random walk in time, an infinite number of times and the recurrence time diverges to infinity. Before diverging to infinity, the infinity minus one times that the random walk returns to the starting part has a finite and predictable recurrence time. That means that the market will return to precisely zero, or any other number that you choose, an infinite number of times and will do so with a finite recurrence time until the recurrence time diverges to infinity.

Now, let us look at the data: never, in the history of the stock market, has the market returned to zero. Over the history of the stock market, the average annual return has been greater than zero and a significant number of large incremental price changes have happened. Even a cursory examination of the data leads to the conclusion that the stock market, as measured by any index you might wish, is a stochastic process with a non-zero drift and “fat-tail” price changes in continuous time. If that were not true, then there would not be a single sane investor in the market and the market would not exist. The immediate response is whether the price of a share can be predicted at any moment in the future. The answer is no unless all the factors that affect the share price can be determined with any certainty. In the absence of complete knowledge of the factors affecting the price, it is sufficient and necessary to predict the distribution of the share price and hedge against the probability of of being incorrect about the selected price.

I hope that this helps.

Nathan A. Busch