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# Fractal Dimension of Stock Price Changes

## Abstract

The purpose of this lab was to determine the fractal dimension associated with stock price changes.

## Introduction

The definition of stock, based on the Encarta Encyclopedia is "in business and finance, a share of ownership in a corporation ….

Shares in a company can be traded publicly on a stock exchange so that the owner can realize a profit if the value of the stock rises above what the owner originally paid for it. Some companies enable stockholders to share in the profits of the company, which are paid out at intervals, in the form of dividends. Besides a claim on company profits, stockholders are entitled to share in the sale of the company if it is dissolved. They may also vote in person or by proxy for corporation officers, inspect the accounts of the company at reasonable times, vote at stockholders' meetings, and, when the company issues new stock, have priority to buy a certain number of shares before they are offered for public sale. Because stocks are generally negotiable, stockholders have the right to assign or transfer their shares to another individual. Unlike a sole proprietor or partner in a business, a stockholder is not liable for the debts of the corporation in which he or she has invested. The most the stockholder can lose if the company fails is the amount of her or his investment.

We used two stocks and aquired the daily stock price data for one year. The stocks we chose for calculations were Coca Cola and Mattel. We then decided to create a program using C++ to the fractal dimension associated with stock price changes.

## Procedure

1. Get closing prices of two stocks for 200 straight days
2. Format the data. Type closing price for each day on its own line. Closing price only nothing else. Use notepad or some other text editor.
3. Download and run FK.stock. The resulting data from FK.stock is saved as output.txt. The format of the output is the fractional change in the stock price in the first column (change in price divided by initial price) and the time interval in the second column (1, 2, 4, 8, 16, 32, and 64 days).
4. Using statistical software, construct a log-log plot of price change vs. time interval.
5. Do a linear regression best fit line for each of the two graphs.

## Data

Raw data before analysis from the C++ program.

Raw data after analysis from the C++ program.

## Conclusion

When linear regressions were performed on the log-log data of price change vs. time, the following values were calculated.

1. For Coca-Cola (CCE), the fractal dimension was 0.634.
2. For Mattel (MAT), the fractal dimension was 0.521.

## Sources of Error

• Fluctuation of stock prices throughout the year are normal, but the economic downswing following 9/11 drove many stocks downward, which interfered with the pattern that we are trying to analyze.

Joby Josekutty, Jane Rubinshteyn, Edward LaValley, David Engel -- 2002

Chaos Project