ENTROPY ANALYSIS OF US BONDS AND STOCKS

In general, since WWII, whenever the feeling of uncertainty or fear arises, money flows into US dollars, US bonds, and gold. As uncertainty decreases, money flows out of these assets and into other assets, such as stocks. A look back at the two charts I created yesterday shows how the level of volatility in both the US stock market and the US bond market went up and came down over the last few years. How can we analyze this in terms of entropy and dissipative systems?

In terms of entropy, the entropy of each individual market participant increased as the news and reality of the economic collapse spread. This resulted in a higher individual level of entropy, and consequently, a higher level of entropy for all market participants viewed as a group. For purposes of this analysis, and in terms of open and dissipative systems, each market, and all market participants together as a group, can be considered as three open and dissipative systems all interacting with one another.

Mr. Prigogine suggested that open and dissipative systems import matter, mass, energy, or information into their systems in order to reduce the increased entropy within the system. These systems then process whatever it is that was imported and export entropy into their surroundings. Entropy that is exported is also called negentropy. It is not a big step to state that after individuals imported information and processed it, they exported entropy back into stock and bond prices. This higher level of entropy in the markets was reflected in the higher standard deviation of prices. So how do the markets reduce higher levels of entropy? I would argue that both markets used money to reduce their heightened levels of entropy. Once the money was “churned” and the process played itself out, the markets exported negentropy to some other system. The exporting of entropy by the markets is reflected by the lower calculations of volatility.

Obviously this is a simplified example, but it may help one appreciate the enormous complexity of many open and dissipative systems working out their entropic differences.

ENTROPY

I have been studying the Second Law of Thermodynamics. One example of the Second Law is how particles in a gas, when heated, tend towards increasing randomness and disorganization as they move towards a state of equilibrium. A generalization of the Second Law is that entropy increases.

Scientists define systems as closed or open and moving towards equilibrium or not. Measuring the movement and position of particles in a gas was viewed from the perspective of a closed system. In contrast, measuring the movement and position of financial prices in a market can be thought of from the perspective of an open system that does not move towards equilibrium. What is equilibrium in the market anyway? Sideways price movement? Narrow range price bars or range trading over a particular time period? A price where seller and buyer agree?

One can make the argument that entropy is similar to information content. If we have less information, then we have more uncertainty, and vice versa, the more information we have, the more we know, the less uncertain we are. Thus the amount of entropy in a system is similar to the amount of uncertainty that exists. What I find very interesting is that if maximum entropy occurs in a closed system when equilibrium is reached, then maximum uncertainty would also occur at equilibrium. Somehow, this seems counter-intuitive. One would think that as equilibrium is reached, that things “settle down,” stabilize, and should theoretically be more known or certain. I need to think more about this.

On a different note, there were no trades this week. These three trading models can be quite boring sometimes.