# Probability of Stock Trade Using Standard Deviation

by Walter Johnson

Economic science is an attempt to mollify the uncertainty of human financial behavior. Markets are presumed to be rational on the basis of the human drive to promote their own self interest. People invest in what they think they will be able to make a profit from. On this fundamental postulate about human action, markets can be analyzed based on statistical probability theory.

## Probability Theory

Probability theory, in general terms, deals with bounded rationality. This means that for any major human decision concerning investment, the variables under consideration exist in a context. This context is largely what is possible in a given situation. Therefore, economic decisions are bound by present realities and institutions that limit possible options in important ways. Probability of stock price movements, for example, is based on what economic elites will do under circumstances that can alter this price. It is not what these elites will do in general, or what they would like to do, but what they can do given the constraints of the present time.

## Standard Deviation

Trying to predict the future requires a detailed record of the past. If you are trying to research what stock splits, for example, will do for future earnings, you need to collect as much data as possible on firms in the past that have split their stocks to lower their price. This data is then analyzed by a statistical regression software system, and a line is plotted on the graph. This line represents the average change in stock earnings after the split. Of course, many occurrences will be above or below this line, and these are called deviations. When you average out these deviations, using squares to eliminate all negative numbers, you get the standard deviation. This reveals how much of a change in the average to expect in any given instance of stock splitting.

## Market Applications

If a firm in which you are heavily invested is going to split their stocks, the research into the standard deviation in the average change in earnings after the split can give you an indication of what to do. If the basic average says that earnings fall after the split, you might want to take your money out. The standard deviation in this average tells you how useful this average is. The deviation might be very high in either direction, suggesting near randomness. If the deviation is very low in either direction, then the average is very accurate, and you should divest.

## Randomness and Policy

The standard deviation is a measure of the usefulness of that specific statistical model. The higher this deviation, the less useful the model. It could also be that you did not collect sufficient data in building the model. For example, if you only have two data points, 100 and 0, your average is 50. In itself, this average says nothing. The larger the sample — referred to as an “n” in statistics textbooks — the lower your standard deviation in most cases. This is because the more data you have, the more information the program has for calculating averages and deviations. The more information, in other words, the less randomness. Complete and total information, if that were possible, would lead to exactly zero deviation and zero randomness.