Project Proposal

Senior Project Proposal

Lu Wang

December 17, 2012

1. Title of Project:

Prophesying Prices: A Basic Predictive Model for Stock Index Prices

2. Statement of Purpose:

This project will study trends in the financial market’s indices using mathematical software to determine if and how different indices correlate with one another and to create a model (or models) in Matlab that uses the relationship between different indices to predict their future prices. I intend to prove that accessible mathematical software can be used by a home investor to make more accurate predictions in the stock market. In order to do this, I need to answer a few questions: How are these indices calculated and what is the relationship between them? and How can current price trends be used to make a mathematical model that can predict future prices?

3. Background:

As a potential finance major in college, I’ve always been interested in investment theory. Since my linear algebra and vector calculus class has been dealing extensively with matrices, I feel like now is an opportune time to use the basics I’ve learned in that class along with new techniques I will research to learn more about financial markets as well as possibly produce something of practical use. Though I know that the real predictive models companies use to determine their investment strategies are infinitely more complex than anything I can produce at the moment, I want to familiarize myself with the possibilities of predictive modeling, mathematical programs and models, and financial markets.

4. Prior Research:

Predictive modeling is commonly used as a tool in finance and economics. In particular, predictive analytics is commonly applied to risk management techniques. Entire companies are based on this, for example, SAP Predictive Analysis. Extended further, in high-frequency trading, computers use complex algorithms to make trading decisions before humans can analyze the data themselves. Such techniques are used by Renaissance Technologies, an example of a highly successful firm that trades this way. However, such tools are not available and are too complex for the average person.

Similarly, the basics of stock markets and indices can be researched on the Internet. For example, the website letslearnfinance.com offers a variety of articles that explain basic financial concepts. The information I find on these concepts from the Internet and other sources will be integral for my understanding of my project.

The software I’ll be using to conduct my research, Matlab, is also easily researched. Though I am unfamiliar with its use at the moment, numerous online resources, such as the “Matlab Tutorial and Learning Resources” page on mathworks.com, will allow me to familiarize myself with the program. The Matlab program has also been used previously in relation to financial and stock markets. For example, Sebastian Musielak of Worcester Polytechnic Institute used Matlab and various mathematical techniques to evaluate different techniques for predicting the short term changes in stock prices for his college thesis.

5. Significance:

The results of this project may have practical applications and become a tool that my family and I could potentially use in our investment decisions. Unlike the abstruse tools used by professionals, my model would be readily available and understandable to the average person. Furthermore, I would be looking at this issue from a teenager’s perspective, and my analysis could be explained to my classmates, who have undergone the same math education I have. My model could be shared with and used by my peers and their families, and I think I can get some of my peers to become more interested in learning about economics and investing while opening their eyes to the possibilities in mathematical software.

6. Description:

For this project, I will be collecting data, making observations, and doing Internet research primarily. Then I will be using Matlab and mathematical techniques like auto-regressive moving-average models and proper orthogonal decomposition to reach my conclusion.

7. Methodology:

My research for this project can be divided into 4 sections: Data Collection and General Research, Programming and Model-building, Testing, and Analysis.

Data Collection and General Research:

I will collect the daily prices of the DJ Industrials, S&P 500, NASDAQ Comp, NYSE Composite, NYSE U.S. 100, NYSE Market Comp, NYSE TMT, NYSE World Leaders, NYSE Financial, NYSE Energy, NYSE Healthcare, and NYSE Intl 100 for 20 days. This data will be entered into an Excel spreadsheet. To complement this data, I will also research records of historical prices of these indices to give me more numbers to work with. Meanwhile, I will research these indices on the Internet, discovering what they measure and how they are calculated. I will also conduct general research on stock market, learn about the Matlab program, and learn more about the mathematical techniques I plan to use.

Programming and Model-building

I will enter the data collected into Matlab. The data will be graphed and analyzed using proper orthogonal decomposition to produce an autoregressive moving-average model that should be able to predict future data sets, i.e. indices’ prices. This will involve putting the data into a matrix and using orthogonal transformation to devise a model that takes the possibly correlated prices and transforms them so that future prices can be predicted by multiplication with a common variable. This section involves a lot of trial and error, and I will most likely go through several models.

Testing

Using my new model, I will attempt to predict future prices and compare them to the real prices set by the New York Stock Exchange. My predictions and the actual prices will be collected and recorded in Excel for 20 days. In addition, I will “back-test” my model with the historical prices I gathered to evaluate if and how my model would have performed differently at different times.

Analysis

Based on how the testing period went, I will compare my predictions to the actual prices and see how close the two are. Due to the naturally erratic nature of the stock market, I will consider my model a success if it can predict prices with some accuracy around 55% of the time. If I find ways to improve my model or discover that my model was completely inaccurate, I will return to the third stage. Ultimately, I will determine how successful my experiment is.

8. Problems:

The greatest problem I think could happen is if I am unable to devise a model that can predict future prices with some accuracy. If this should occur, I will instead research why my model could not work. Or, rather than attempting to predict future prices of indices, I could research what drives these indices up and down. Perhaps this research would help me determine why I could not devise a suitable model. Other more minor issues could occur. For example, the sources from which I plan to learn about stock markets and Matlab may become unavailable, but then I will simply resort to other sources, which exist abundantly on the Internet. Additionally, I may make errors in my calculations that would lead to a faulty model. In this case, I would have to redo my calculations.

9. Bibliography:

"Analytics Services" SAP.com. http://www.sap.com/services-and-support/business-analytics/business-intelligence.epx (accessed November 18, 2012).

Carlberg, K "A Compact Proper Orthogonal Decomposition Basis for Optimization-Oriented Reduced-Order Models" Academia.edu. http://www.academia.edu/239313/A_Compact_Proper_Orthogonal_Decomposition_Basis_for_Optimization-Oriented_Reduced-Order_Models (accessed November 18, 2012).

Harris, D. "Check Out the Big Data Expert You've Never Heard Of" Gigaom. http://gigaom.com/cloud/meet-the-big-data-expert-youve-never-heard-of/ (accessed November 18, 2012).

Let's Learn Finance. http://www.letslearnfinance.com/ (accessed November 18, 2012).

"MATLAB Tutorials and Learning Resources" MathWorks. http://www.mathworks.com/academia/student_center/tutorials/launchpad.html (accessed November 18, 2012).

Musielak, S "Short Term Stock Market Analysis", Worcester Polytechnic Institute , 2008. http://www.wpi.edu/Pubs/E-project/Available/E-project-082908-095710/unrestricted/IQP_Report_Draft.pdf

Pandey, A and Marcus Tan. "How Stock Indices Work" WikiInvest. http://www.wikinvest.com/wiki/How_Stock_Indices_Work (accessed November 18, 2012).

Renaissance Institutional. https://www.renfund.com/vm/index.vm/ (accessed December 17, 2012)

Teasley, B. "Using Predictive Models, Part 1" ClickZ Marketing News & Expert Advice. http://www.clickz.com/clickz/column/1707212/using-predictive-models-part (accessed November 18, 2012).

"Understanding Shares" TD Direct Investing. http://www.tddirectinvesting.co.uk/get-started/understanding-shares/indices/ (accessed November 18, 2012).

"Why You Should Take Time to Learn" The American Institute for Financial Education. http://www.investmenteducation.org/whyyoushouldlearn.html (accessed November 18, 2012).