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• 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
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Alex Camhi
Shankar Kar
Jason Siegel
Financial Market Analysis
Agenda
Overview
DOW Jones Index
SP 500 Index
Data Collection
Objective Function
Results
DOW Jones Index
SP 500 Index
Background Information
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)
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
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
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
Genetic Algorithm Specifics
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
Objective Function
Index data normalized
Selected stocks are weighted to total $1000 at
start of period
RMSE – (ΣDifference in value^2)^1/2
DJIA Tracking
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.
No Active ManagementRunning 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
No Active ManagementStocks 1 1/3/2005 1/1/2008
TickerOriginal Pivots Weights
Price on 1/1/2008
$ Holdings on 1/1/2008
Price on 3/24/2010
$ Holdings on 3/24/2010
AXP 3 2.1687 52.02 112.815774 41.01 88.938387
XOM 12 1.7997 93.69 168.613893 66.5 119.68005
JPM 19 2.707 43.65 118.16055 44.94 121.65258
KO 10 0.68282 61.37 41.9046634 54.62 37.2956284
MMM 1 1.326 84.32 111.80832 81.61 108.21486
MCD 21 2.0184 58.91 118.903944 66.8 134.82912
HPQ 14 2.4255 50.48 122.43924 53.06 128.69703
GE 13 2.4639 37.07 91.336773 18.45 45.458955
WMT 29 1.5981 47.53 75.957693 55.58 88.822398
HD 15 1.4127 26.94 38.058138 32.32 45.658464
$ Total on 1/1/2008 999.9989884
$ Total on 3/24/2010 919.2474724 % Portfolio Change -8.08%
DJIA on 1/1/2008 13043.96 DJIA on 3/24/2010 10836.15 % DJIA Change
-16.93%
Percent Error -8.85%
No active Management$ Total on 1/1/2008 $1,000.00
$ Total on 3/24/2010 $919.25
Active ManagementRunning 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
0 10 20 30 40 50 60 70 80 90 10096
98
100
102
104
106
108
110
Time
Po
rtf
oli
o h
old
ing
s
Portfolio holding tracker for DOW
RSME = 0.28806
DOW
Tracker
Active ManagementSwap 1 1/1/2008
New Pivots Weights Price on 1/1/2008 $ Holdings on 1/1/2008Price on
2/28/2008$ Holdings on
2/28/2008
1 34 1.504854 61.57 92.65384847 58.92 88.6659859
1 11 4.036599 44.09 177.9736675 44.84 181.0011171
1 28 3.554694 43.69 155.3045721 38.11 135.4693807
1 27 0.99632 76.54 76.2583305 73.73 73.45867139
1 1.326043 84.32 111.8119205 77.44 102.6887467
1 22 1.001714 58.11 58.20958311 49.25 49.33439973
14 2.425475 50.48 122.4379982 43.8 106.2358225
13 2.463909 37.07 91.33711034 34.72 85.54692395
29 1.598051 47.53 75.95537354 48.71 77.84107395
15 1.41268 29.64 41.87182927 29.14 41.16548937
5 $ Total on 1/1/2008 1003.814234$ Total on 1/28/2008 941.4076113 % Portfolio Change -6.22%
DJIA on 1/1/2008 13043.96 DJIA on 1/28/2008 12383.89 % DJIA Change -5.06%
Percent Error 1.16%
Active Management $ Total on 1/1/2008 1003.814234 $ P&L -62.40662
1003.814234 $ Total on 2/28/2008 941.40761
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
Final ResultsSwap 30 3/24/2010
New Pivots Weights Price on 3/24/2010 $ Holdings on 3/24/2010 Price on 4/23/2010 $ Holdings on 4/23/2010
JPM 19 1.393579 44.94 62.62744026 44.94 62.62744026
UTX 27 2.6926242 73.04 196.6692716 76.47 205.9049726
WMT 29 3.037488 55.58 168.823583 54.53 165.6342206
IBM 17 0.8119807 128.53 104.3638729 129.99 105.5493647
1 DD 11 0.9013654 38.77 34.94593578 40.22 36.25291558
1 INTC 16 1.1872023 22.43 26.62894759 24.04 28.54034329
CAT 7 0.8815036 62.06 54.70611155 68.78 60.62981554
PG 25 0.8086214 63.61 51.4364098 63.54 51.3798063
JNJ 18 3.0818363 64.75 199.5489004 65.04 200.442633
HPQ 14 1.6989863 53.06 90.14821308 53.9 91.57536157
2 $ Total on 3/24/2010 989.898686 $ total on 4/23/2010 1008.536873 % Portfolio Change 1.88%
DJIA on 3/24/2010 10836.15 DJIA on 4/23/2010 11204.28 % DJIA Change 3.40%
Percent Error -1.51%
Average Error 0.69%
Final Results
Buy and Hold DJIA Value on 1/1/2008 Value on 3/24/2008 % Change
DJIA 13043.96 10836.15 -16.93%
$1,000 invested $1,000.00 $830.74 -16.93%
Buy the Tracker
$1,000 invested $1,000.00 $836.48
Total Trades Transaction Fees Total Fees
108 $0.25 $27.00
Follow the Tracker Value after Fees
$1,000 invested $836.48 $809.48
Final Results
-20.00%
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
1/1
/2008
2/1
/2008
3/1
/2008
4/1
/2008
5/1
/2008
6/1
/2008
7/1
/2008
8/1
/2008
9/1
/2008
10
/1/2
00
8
11
/1/2
00
8
12
/1/2
00
8
1/1
/2009
2/1
/2009
3/1
/2009
4/1
/2009
5/1
/2009
6/1
/2009
7/1
/2009
8/1
/2009
9/1
/2009
10
/1/2
00
9
11
/1/2
00
9
12
/1/2
00
9
1/1
/2010
2/1
/2010
3/1
/2010
% C
han
ge
Tracker VS. DJIA
% Portfolio Change
% DJIA Change
Percent Error
S&P500 Tracking
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
Buy and Hold
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
Active Management ResultsPeriod # Start Date End Date Port. Start Port. End
% Change Portfolio S&P Start S&P End
% Change S&P500 % Error
0 1-Jan-08 1-Feb-08 1000 995.556 -0.00444 1468.36 1395.42 -0.04967 -0.04523
1 1-Feb-08 3-Mar-08 999.493 1145.35 0.145931 1395.42 1331.34 -0.04592 -0.19185
2 3-Mar-08 1-Apr-08 1006.13 1010.34 0.004184 1331.34 1370.18 0.029174 0.024989
3 1-Apr-08 1-May-08 1010.35 1017.21 0.00679 1370.18 1409.34 0.02858 0.02179
4 1-May-08 2-Jun-08 1013.98 969.142 -0.04422 1409.34 1385.67 -0.0168 0.027425
5 2-Jun-08 1-Jul-08 999.324 931.81 -0.06756 1385.67 1284.91 -0.07272 -0.00516
6 1-Jul-08 1-Aug-08 989.389 1019.97 0.030909 1284.91 1260.31 -0.01915 -0.05005
7 1-Aug-08 1-Sep-08 993.233 908.657 -0.08515 1260.31 1282.83 0.017869 0.103021
8 1-Sep-08 1-Oct-08 1000 790.565 -0.20944 1282.83 1161.06 -0.09492 0.114512
9 1-Oct-08 3-Nov-08 996.832 848.592 -0.14871 1161.06 966.3 -0.16774 -0.01903
10 3-Nov-08 1-Dec-08 1147.79 1251.88 0.090687 966.3 816.21 -0.15532 -0.24601
11 1-Dec-08 1-Jan-09 1003.86 1020.44 0.016516 816.21 903.25 0.106639 0.090123
12 1-Jan-09 2-Feb-09 1000 1063.15 0.06315 903.25 825.44 -0.08614 -0.14929
13 2-Feb-09 2-Mar-09 1010.08 932.356 -0.07695 825.44 700.82 -0.15097 -0.07403
14 2-Mar-09 1-Apr-09 1023 1098.13 0.073441 700.82 811.08 0.15733 0.083889
15 1-Apr-09 1-May-09 1110.44 1191.13 0.072665 811.08 877.52 0.081915 0.009251
16 1-May-09 1-Jun-09 1004.2 1017.73 0.013473 877.52 942.87 0.074471 0.060998
17 1-Jun-09 1-Jul-09 1040.6 989.969 -0.04866 942.87 923.33 -0.02072 0.027932
18 1-Jul-09 3-Aug-09 1001.02 1136.69 0.135532 923.33 1002.63 0.085885 -0.04965
19 3-Aug-09 1-Sep-09 994.411 1053.9 0.059823 1002.63 998.04 -0.00458 -0.0644
20 1-Sep-09 1-Oct-09 1094.66 1263.71 0.154432 998.04 1029.85 0.031872 -0.12256
21 1-Oct-09 2-Nov-09 1003.85 1021.42 0.017503 1029.85 1042.88 0.012652 -0.00485
22 2-Nov-09 1-Dec-09 860.552 881.989 0.024911 1042.88 1108.86 0.063267 0.038356
23 1-Dec-09 1-Jan-10 1008.54 1032.69 0.023946 1108.86 1115.1 0.005627 -0.01832
24 1-Jan-10 1-Feb-10 1000 1002.17 0.00217 1115.1 1089.19 -0.02324 -0.02541
25 1-Feb-10 1-Mar-10 973.935 992.138 0.01869 1089.19 1115.71 0.024348 0.005658
26 1-Mar-10 1-Apr-10 1004.55 1048.53 0.043781 1115.71 1178.1 0.05592 0.012139
Mean -0.01651
Active Management Results
Percent Error: 1.651%
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
14-Nov-07 22-Feb-08 1-Jun-08 9-Sep-08 18-Dec-08 28-Mar-09 6-Jul-09 14-Oct-09 22-Jan-10 2-May-10
Perc
en
t C
han
ge
Date
Percent Change: Jan 2008-Mar 2010
% Change Portfolio
% Change S&P500
Questions?
