• Applied neural networks and genetic algorithms to track the Dow Jones Index • Used historical data from January 2005 to March 2010 as training data sets • Developed a portfolio that selected 5 best companies on a weekly basis

1. Alex Camhi Shankar Kar Jason Siegel Financial Market Analysis

2. Agenda Overview DOW Jones Index SP 500 Index Data Collection Objective Function Results DOW Jones Index SP 500 Index

3. Background Information

4. Dow Jones DOW Jones Index: Referred to as “DOW 30” Created by Wall Street Journal Editor – Charles DOW and statistician Edward Jones Second oldest U.S market index index that includes 30 large Blue Chip public owned companies in US that trades in the stock market Index is price weighted , to compensate for effects of stock splits and adjustments – a scaled average. Actual average is calculated by summing the 30 component stock prices and dividing it by a divisor where p are the prices of the component stocks and d is the Dow Divisor. Divisor is adjusted in case of stock splits or spinoff ( a company sells part of its company)

5. Data Collection Dow Jones Index: Historical Data from January 1,2005 to March 24,2010 Obtained from Yahoo! finance website Divisor value Account for holidays and new companies added to the index. Removed: C, AIG, MO, HON Replaced with: BAC, CVX, CSCO, TRV

6. S&P 500 S&P 500 Index: 500 Stock components on NYSE/Nasdaq Owned and maintained by Standard & Poors Components selected by committee Must be commonly traded among general public Representative of all major US industries Float Weighted Market capital of public shares vs. index

7. Data Collection S&P 500: Historical data from Jan 2005 to April 2010 Source: Google Finance Not split adjusted Method of Collection Script to collect historical prices Data compiled and holidays added

8. Genetic Algorithm Specifics

9. Two GAs Buy and Hold Active Management X number best stocks chosen Stocks are held for the duration of the test X number best stocks chosen each period Y stocks swapped at start of each period Data must be renormalized each time stocks are swapped

10. Objective Function Index data normalized Selected stocks are weighted to total $1000 at start of period RMSE – (ΣDifference in value^2)^1/2

11. DJIA Tracking

12. Purpose Individual Investors consider investing in an index for many reasons Tracker manages portfolio for individual investor With advancements in the tracking technology, future market collapses could be seen in advance so that corrective action may be taken prior to the collapse.

13. No Active Management Running GA Script Stock 1 Parameters: (From Jan 1 2005 – Dec 31 2007) Number of stocks to pick = 10 Number of generations = 1000 Population size = 30 Mutation rate = 0.1 Seed number = 2

14. No Active Management

15. Active Management Running GA Script Stock 3 Parameters: (From Jan 1 2005 – Jan 28 2008) Number of days to backtrack = 100 Number of swaps to make = 5 Number of Generations = 1000 Population size = 30 Mutation rate = 0.1 Seed number = 2

16. Active Management

17. Active Management First Swap After 20 Days Sold: AXP, XOM, JPM, KO, MCD Bought: HON, DD, VZ, UTX, MRK Added 20 rows of data representing monthly management through the data to 3/24/2010 Gave the program the option to swap 5 stocks each month GA Optimizes the portfolio Completed 30 iterations of this management process

18. Final Results

19. Final Results

20. Final Results

21. S&P500 Tracking

22. GA Paramters Portfolio Size: 20 Stocks Replications: 3000 Population size: 30 Mutation Rate: 0.1 Number of Swaps: 5/Period Back Data: 100 Days Total time period: 28 months

23. Buy and Hold

24. Active Management Period Length: 1 Month Swap up to 5 stocks on the 1st of Month GA run to optimize portfolio each period Resulting portfolio values calculated and compared to S&P500

25. Active Management Results

26. Active Management Results Percent Error: 1.651%

27. Questions?