Mid-Term Report: Dependence of Stock Market Prices
Prof. Larry Wright
The stock market is the financial backbone of the United States. During each day of trading, thousands of trades occur. During each of these trades, stock is sold at a price that tends to fluctuate between trading. This project will test a series of successive stock prices to determine if they are independent or if they depend on previous trade prices and are predictable.
To determine this, we must first determine the reoccurrence of patterns in the prices of stock. Then we must look at the probability that this pattern is predictable. For example, we can examine a series of only positive price increases, and look at the probability that the following price will be positive as the series of previous positive prices increases. The hypothesis is that the probability will increase as the length of series increases or
P(Xi > 0) < P(Xi > 0 | Xi - 1 > 0) < P(Xi > 0 | Xi - 2 > 0, Xi - 1 > 0) < P(Xi > 0 | Xi - I > 0 … Xi - 1 > 0)
where I is the length of the longest series of positive changes in series of successive stock prices Xi. Obviously for this to be true, I must approach some limit though as we all know that no stock’s prices increases at every trade forever. In addition to testing for series of all positive, negative or zero changes, series of combinations of these changes can be tested to provide insight into more unique cases.
The data being used to search for stock price dependence is on a disc which contains all trading prices on all listed stocks on the New York Stock Exchange, the American Stock Exchange, and major NASDAQ listings for 4 days in 2001, a total of 3300 stocks with 2,500,000 price changes.
The analysis of the data will be done through a computer program that will be written in Java. The program will read in the stock prices from text files that include the trade prices data, calculate the change in price, and then add the change to a series of changes. Afterwards, the series of changes will be analyzed to determine if the supplied array of changes occurs and what the probability that is that the series followed by a certain type of change (Positive, Negative, of Zero).
Initial results do show some pattern as I increases in the series. The results from tests on a pair of single random stocks yielded the following results:
I: 1 Prob Pos: 13.67 Prob Neg: 16.59 Prob Zero: 47.79
I: 2 Prob Pos: 14.41 Prob Neg: 14.18 Prob Zero: 50.35
I: 3 Prob Pos: 5.88 Prob Neg: 25.0 Prob Zero: 53.99
I: 4 Prob Pos: 0.0 Prob Neg: 20.0 Prob Zero: 59.49
I: 5 Prob Pos: NaN Prob Neg: 0.0 Prob Zero: 66.38
I: 1 Prob Pos: 20.11 Prob Neg: 9.09 Prob Zero: 64.75
I: 2 Prob Pos: 10.28 Prob Neg: 23.91 Prob Zero: 69.12
I: 3 Prob Pos: 45.45 Prob Neg: 27.27 Prob Zero: 70.8
I: 4 Prob Pos: 60.0 Prob Neg: 33.33 Prob Zero: 74.82
I: 5 Prob Pos: 66.67 Prob Neg: 0.0 Prob Zero: 71.26
These results, although far from conclusive, show a trend in the probability as the length of a series of a certain kind of change increases, so does the probability that the next change will be the same as the previous. This is especially noticeable in the series of zero changes, where the probability increases in almost every case as the length of the series increases.
The program to analyze these results is now complete. The next stage will be to read in and record the results of the analysis. Upon completion of this, the Chi-square test can be used to determine the relevance of these results. After determining the relevance of the results, they then can be summarized and presented.