1. Artificial Neural Networks in Engineering Conference
St. Louis, MO
Application of Taguchi Methods to
Manage an Investment Portfolio
Vivek K. Jikar, PhD candidate
Kenneth M. Ragsdell, Professor
Design Engineering Center
Engineering Management and Systems Engineering
Missouri University of Science & Technology
4th November 2009

2. Outline
• Introduction
• Signal-to-Noise ratio-based screening metric
• Optimal screening strategy using product
parameter design
• Stock market index prediction using Taguchi
method
• Questions and discussion
Nov 4, 2009 2009 ANNIE Conference 2

3. Introduction
What, when
Investor and how Robust
Preferences much to buy Portfolio
or sell?
• Investors would like their investments to consistently
appreciate in price and value over time.
• Screening for investments is a first critical step to successful
investment portfolio management.
• Forecasting enables us to choose right strategies for managing
an investment portfolio.
• Quality engineering can help!
Nov 4, 2009 2009 ANNIE Conference 3

4. Signal-to-Noise ratio1
St*=S0(1+MARR)t St*=S0 (1+MARR)t
A St B St
Desired Stock .. .. β2
Price β2 Actual Stock β3 βt
S2 * S2 β1
β1 βt = β1=β2=β3=… Price
S1 S1
s0
s0 t1 t2 t t1 t2 t
Holding Time Holding Time
n
* 2 2
( t t ) log(1 r ) 2 log(1 r )
SN Bull SN (3) 10 log n
SN Bear SN (4) 10 log n
t 1 * 2 * 2
Volatility ( t t ) ( t t )
n t 1 t 1
n n
1
(Sβ Ve ) β2
SN(1) 10log r SN(2) 10log
Ve σ2
1Jikar,
Vivek K., and Kenneth M. Ragsdell, “Signal-to-Noise Ratio Based Algorithm for Stock
Screening”, Proceedings of the 2009 Industrial Engineering Research Conference, Miami FL.
Nov 4, 2009 2009 ANNIE Conference 4

5. Application: Screening a small sample
Nov 4, 2009 2009 ANNIE Conference 5

6. Did we do it right??
Up 65%
Down 35%
Nov 4, 2009 2009 ANNIE Conference 6

7. Application: Screening from NYSE
(Backtesting period: April 4 – October 21, 2008)
Strategy Comparison
50.00%
41.99%
40.00%
30.00%
Cummulative Return
20.00%
10.00%
0.00%
-1.40%
-10.00% -4.80%
-20.00%
-30.00%
-30.25%
-40.00%
Zack’s
Zack’s Relative Dynamic
Upgrades and
Valuation Signal to Noise S&P 500 Index
Revisions
Screen Ratio
Screen
% Return -4.80% -1.40% 41.99% -30.25%
Nov 4, 2009 2009 ANNIE Conference 7

8. Optimal Screening Strategy2
Up-market Down-market
Investment Portfolio
Portfolio return
Screening Metric (S/N1, S/N3, S/N4)
Price History (30-day, 90-day, 200-day)
Holding Period (7-day, 15-day, 30-day)
Number of stocks in the portfolio (10,20,30)
2Jikar,Vivek K., and Kenneth M. Ragsdell, “Optimal Strategy for Building an Investment Portfolio
Using Product Parameter Design”, Journal of Quality Engineering Society (accepted for
publication).
Nov 4, 2009 2009 ANNIE Conference 8

9. Portfolio Return
300.00% 20.00%
10.00%
250.00%
S&P 500 Return (%)
Portfolio Return (%)
0.00%
200.00%
-10.00%
150.00% Up-market -20.00%
-30.00%
100.00%
Down-market -40.00%
50.00%
-50.00%
0.00% -60.00%
10/10/2006 4/28/2007 11/14/2007 6/1/2008 12/18/2008 7/6/2009
Portfolio Return S&P 500
Portfolio Return is a cumulative return from an equally weighted portfolio of
ten stocks selected using bull signal-to-noise ratio. The portfolio was balanced
weekly.
Nov 4, 2009 2009 ANNIE Conference 9

10. Findings
• A portfolio of long positions needs to be
managed differently than the portfolio of
short positions.
• High returns does not necessarily mean high
risk.
• Quality engineering principles can be used to
augment the screening strategy.
Nov 4, 2009 2009 ANNIE Conference 10

11. Forecasting using T-method
Noise states
Unknown y Predictive Model Actual y
ˆ
y f(x1 , x 2 , x 3 , x 4 ....xp )
Control factors
(explanatory variables)
1400
S&P Signal Space
1200 Unknown space
500 1183
Unit Space
926
Time
Nov 4, 2009 2009 ANNIE Conference 11

12. T-method steps
• Step 1: Select a unit space, a signal space, and an unknown
space.
• Step 2: Normalize the signal space and the unknown space
using the average and the standard deviation of the unit
space data.
• Step 3: Calculate the performance statistics and dynamic S/N
ratio for each leading indicator in the signal space.
• Step 4: Predict the S&P 500 for the signal space and verify the
predictive model.
• Step 5: Repeat steps 3 and 4 for the unknown space.
Nov 4, 2009 2009 ANNIE Conference 12

13. Predictive power comparison
S&P 500 Unknown space
1600
1500
1400
S&P 500 Index ($)
1300
1200
1100
1000
900
800
700
600
10/10/2006 1/18/2007 4/28/2007 8/6/2007 11/14/2007 2/22/2008 6/1/2008 9/9/2008 12/18/2008 3/28/2009
Actual S&P 500 Predicted (Scaled) S&P 500
Nov 4, 2009 2009 ANNIE Conference 13

14. Predictive power comparison
Sr. Prediction Method Mean Squared Error
1 T-Method 1067.22
2 Linear Regression 20634.30
3 Principle Component Regression 3.67191E+11
4 ARIMA 1577.33
Nov 4, 2009 2009 ANNIE Conference 14

15. Remarks
• The principles of the Taguchi System of Quality
Engineering can be used to perform screening,
investment portfolio management, and
forecasting.
• Stock price stability has the same importance
in an investment portfolio management
process as the design stability of a concept in
an advanced product development process.
Nov 4, 2009 2009 ANNIE Conference 15

16. Nov 4, 2009 2009 ANNIE Conference 16