In several articles we have explored how the probability of an event can change greatly depending on the value of related parameters. The surprising Monty Hall paradox is one example. Sometimes the accuracy with which we can predict an event changes with the addition of slight bits of information that might not even seem to be relevant to the event. Lewis Carroll’s puzzle about guessing the color of the stone in the bag that I featured last week is another example. The stock market is a major example.

For instance, suppose you want to pick a stock to purchase and you obviously want to buy something that will appreciate in price. How do you do it? Throwing a dart at the financial section is a bad way, regardless of the occasional humorous article about how someone did just that and made a bundle.

The more sophisticated the investors, the more information they will get about the target stocks before purchasing. Parameters such as the overall economic condition, the growth in the targeted industry, the track record of the company, the competition, and new products all enter into the consideration. More sophisticated investors will examine the company’s financial statements and look at esoteric parameters such as the current ratio and debt to equity.

Any measurement of any parameter that correlates in any way with past stock price moves, up or down, could be used in principle to help improve predictions of future performance. Parameters as extreme as sun spots and skirt length have been proposed as key indicators.

The value of information in predicting future performance was recognized by the government many years ago. That is why we have laws against insider trading. If Martha Stewart truly had information about future performance that was not available to the general public, then the rest of the investors were at an unfair disadvantage. The game was fixed in her favor.

But an interesting thing happens when a market is established. From a purely mathematical point of view, the purpose of an open market is to remove randomness from pricing.

Go back and think about that sentence for a moment. Doing business and investing obviously have an element of risk. Predicting the future always involves probability. As we have shown many times, risk can be reduced by correlating relevant parameters to make better predictions. However, when an investor trades based on how the stock is predicted to move in price, then the trade itself is a factor for other investors and it becomes a factor in the direction to reduce the random fluctuations by tending to remove the systemic variation the investor has found.

In an ideal market with ideal communications, all fluctuations in price will be truly random. Deviations from true random behavior is how savvy investors make money.

Enter programmed selling. Very sophisticated programs can quickly assimilate and correlate huge amounts of data and make predictions about future moves in stock. The result is an automated order to buy or sell. That is fine, but suppose a large fraction of the market uses similar algorithms to make similar predictions and they all move at the same time. Unless the algorithms have a specific correction for other programmed trading, the situation at the time of the transaction is not what was assumed in the calculation. So instead of acting to reduce random fluctuations, programmed trading of large blocks of stock can induce sudden changes in price that would not have happened otherwise.

That is, an ideal market really consists of an infinite number of fully informed buyers and sellers. Whenever a substantial block of sellers act in unison, the market is not ideal. Whenever all potential traders are not fully informed, the market is not ideal.

As a side note, for those with an electrical engineering background, in many ways, the government recognizes the difficulties in establishing an ideal market, and so establishes itself as a factor in the role of impedance matching device. Think of simulating an ideal antenna with an impedance load. Of course, I don’t believe anyone in government or most specialists in security law think that way. It’s just an interesting analogy.

In the next piece, I will consider insurance, and then probably get hit with a lot of protests. That’s a prediction based on past measurement of the response of audiences.

For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.