Pat McCormack, a financial advisor for Investors R Us, is evaluating two stocks in a particular industry. He wants to minimize the variance of a portfolio consisting of these two stocks, but he wants to have an expected return of at least 9%. After obtaining historical data on the variance and returns, he develops the following nonlinear program:
Minimize portfolio variance = 0.16X2 + 0.2XY + 0.09Y2
subject to X + Y = 1 (all funds must be invested)
0.11X + 0.08Y >=0.09 (return on the investment)
X = proportion of money invested in stock 1
Y = proportion of money invested in stock 2
Solve this using Excel and determine how much to invest in each of the two stocks. What is the return for this portfolio? What is the variance of this portfolio?