Is the Equity Market in its Statistical Infancy?

"The trend is your friend." ~Wall St. Maxim

There exists a near-universal belief by folks on Wall Street that the stock market trends higher over time. The spread of capitalism, global growth, secular trends, these things form the foundation of the "buy and hold" strategy that undermines much of investment strategy. History has been the de facto guide to growing capital. Hold stocks for 10 years and they will appreciate in value.

I would like to raise a new question. What if the equity market were in its statistical infancy? In other words, what if the markets are still young compared to the timescale on which they operate? I realize this question is pedantic (I don’t think the world is going to sit on its trillions in cash and wait for my question to pan out), but it could mean investors in future are in store for some interesting times.

Suppose we examine the market as a scientist would. We input a number of variables into the system, such as news events, interest rates, investor psychology, consumer preferences, and out comes a price, the fair value of a stock. These myriad inputs and indicators of the market are collectively called the "state space".

As thousands of mathematicians will attest, it’s very hard to find a correlation between the state space and the movement of equity prices. Predicting stock prices is not just a matter of predicting future news and trends (though one could make a pretty penny if one could). One must also swallow the fact that the state space is huge. How huge? Factorially huge. Perhaps a simple example will illustrate.

Suppose we have 100 economic numbers which determine the price of the markets (yes, a gross, disgusting underestimate). Let’s further assume that these numbers can fall between 1 and 100. Now I ask the question, how many ways can I order this state space (in business-speak, how many different states can our economy have?)? The answer is frightening. The answer is not 10000. You see, we have to include the temporal order of these numbers (it matters, economically, if all the subprime slime hits the fan at once). So, we now ask how many ways to order one of 10000 economic states over a given timespan. That, my friend, is a factorial-sized number, and it is much, much larger than 10000.

Where am I headed with this mathematical poppycock? Does it matter that state space is so big? After all, there is good evidence that the markets are not deterministic (the same state-space input does not necessarily lead to the same valuation). The answer is a resounding maybe. In the hundred or so years of modern financial markets, we have probed only a minuscule portion of our economical state space. It is statistically possible (perhaps even probable) that we await history-defying events in the markets. Hundred-year bull markets, six-sigma swings, periods of record-breaking volatility, lifespans of sideways-trending stock prices, all of these events may await the markets (assuming the heat death of the universe doesn’t get there first) if they are still in their statistical infancy. It is the age of the markets compared to the timescale of their behavior that matters. Since nobody - I am justified in using the sweeping generality - knows the timescale, nobody knows the true "age" of the market.

Just as the ant on the basketball thinks his world is rather flat, the upward-trending market could be a local patch on a more global manifold of market behavior. Consider the process of evolution, whose state space is thousands of DNA pairs. Evolution spits on a hundred years; it is a paltry period of time for the true process to show its workings. There is no a priori reason to assume the equity markets are any different. It’s a pedantic point, perhaps, but it may be increasingly less pedantic in a few hundred years.

Disclosure: none

Comments

[gembree:]

The valuation of the stock market is determined by human nature more than fundamentals. Human nature is never "different this time" and has robust capability to hedge chaos into tedium and leverage tedium into chaos.

2007 Aug 23 09:36 AM