1. Risky Business: Glen Bradford Amanda Fricke Thor Brown Brandon Kelly
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).

2. 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).

3. Gathering Data
The Dow Jones Industrial Average Components

4. Get Historical Price Information

5. Compile Statistics In Excel
Standard Deviation over last 24 months
Slope/Price over last 24 months
Percent Change in Price over next Quarter

6. Program GAMS Model 2 Models 1 Year Model 7 Year Model
Quarterly Analysis, 10 Stocks, 1 Year
7 Year Model
Quarterly Analysis, 30 Stocks, 7 Years

7. Results – 1 Year Model $10,000 $10,079 $10,511 Total Rotation
Beginning
$10,000
6/1/2006-8/31/2006
$10,079
$10,511
9/1/ /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

8. Our optimization solvers represent the state-of-the-art in optimization software.

10. Analysis

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