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).

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).

Gathering Data The Dow Jones Industrial Average Components

Get Historical Price Information

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

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

Results – 1 Year Model TotalRotation 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

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

Analysis

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