Please show me how to do this in excel. Pat McCormack, a financial advisor for I

Question

Please show me how to do this in excel.

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 + 009Y2 subject to (all funds must be invested) X + Y = 1 0.08Y 0.09 (return on the investment) 0.11X X, Y20 where 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?

Explanation / Answer

X + Y = 1                 .......(i)

0.11X + 0.08Y >= 0.09             .......(ii)

X,Y >= 0                                 ......(iii)

Substituting value of Y from (i) in (ii),

0.11X + 0.08(1-X) >= 0.09            

0.11X + 0.08 - 0.08X >= 0.09

0.03X >= 0.01

X >= 0.33

Y <= 0.67

Return on Investment = 0.11x0.33 + 0.08x0.67 =0.0363 + 0.0536 =0.0899 i.e. 8.99%

Minimum Portfolio Variance = 0.16X2 +0.2XY + 0.09Y2

                                        = 0.16x0.33x0.33 + 0.2x0.33x0.67 + 0.09x0.67x0.67

= 0.102

Hence, the portfolio variance is 10.20%                                        

                                          

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