Risky Business:

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• Risky Business
• Mathematical Analysis of
• Minimizing Variance in Stock Portfolios
• Glen Bradford
• Amanda Fricke
• Thor Brown
• Brandon Kelly

• For an efficient frontier, it is necessary to
  have expected returns in a covarience matrix for
  the securities in the universe (Winston 28).

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Modern Portfolio Theory

• Markowitz Efficient Frontier
• Minimize Variance
• Maximize Return
• Minimal Turnover
• One method of estimating future values of
  parameters is to use the past sample values of
  these parameters (Winston 29).

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Gathering Data

• The Dow Jones Industrial Average Components

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Get Historical Price Information
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Compile Statistics In Excel

• Standard Deviation over last 24 months
• Slope/Price over last 24 months
• Percent Change in Price over next Quarter

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Program GAMS Model

• 2 Models
• 1 Year Model
• Quarterly Analysis, 10 Stocks, 1 Year
• 7 Year Model
• Quarterly Analysis, 30 Stocks, 7 Years

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Results 1 Year Model
Total Rotation
Beginning 10,000 10,000
6/1/2006-8/31/2006 10,079 10,511
9/1/2006-11/30/2006 10,902 11,739
12/1/2006-2/28/2007 11,049 12,492
3/1/2007-5/31/2007 11,697 12,678
6/1/2007-8/31/2007 11,569 12,264 695
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• Our optimization solvers represent the
  state-of-the-art in optimization software.

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Analysis
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Conclusion

• Modern Portfolio Theory
• Lower Risk Investment Strategy
• Possibly Beats Market Indicies
• Dow Jones, SP, Russell 2000
• Historically beats the Dow Jones
• See our Analysis
• Sept. 11, 2001 seems to be an outlier
• Rotation Portfolio usually wins