# Thread: Portfolio Linear Programming problem

1. ## Portfolio Linear Programming problem

Michael Frazier, has $120,000 available to invest. he wants to invest in an index fund and in an Internet stock fund. He has also decided that the proportion of the dollar amount he invests in the index fund relative to the Internet fund should be at least one-third, but that he should not invest more than twice the amount in the Internet fund that he invests in the index fund. The price per share of the index fund is$175.

The price per share for the Internet fund is \$208.

The average annual return during the last 3 years for the index fund has been 17% and for the Internet stock fund it has be 28%.

He anticipates that both mutual funds will realize the same average returns for the coming year that they have in the recent past; however, at the end of the year he is likely to reevaluate his investment strategy anyway. Thus he wants to develop an investment strategy that will maximize his return for the coming year.

• Implement a spreadsheet model for this problem and solve it using Solver. Your formulated linear programming model for Michael should indicate how much money he should invest in each fund and show the client how this is illustrated graphically. What is the optimal solution?

• Suppose Michael decides to change his risk balancing formula by eliminating the restriction that the proportion of the amount he invest in the index fund to the amount that he invest in the internet fund must be at least on-third. What will the effect be on his solution?

• Suppose instead that he eliminates the restriction that the proportion of money he invests in the Internet fund relative to the stock fund not exceeds a ratio of 2 to 1. How will this affect his solution?

• If Michael can get one more dollar to invest, how will that affect his solution? Two more dollars? Three more dollars? What can you say about his return on his investment strategy given these successive changes?

2. "Implement a spreadsheet model for this problem and solve it using Solver. "

Did you do that?

I did but I did not know how to put the constraint as a formula

4. I'm puzzled by these two statements:

"the proportion of the dollar amount he invests in the index fund relative to the Internet fund should be at least one-third"

and

"not invest more than twice the amount in the Internet fund that he invests in the index fund."

Does the first mean $\frac{Index}{Internet} \ge \frac{1}{3}$?

Does the second mean $\frac{Index}{Internet} < \frac{1}{2}$?

See if you can think this through carefully and clearly before we get started.

5. yes it is correct this is what I did, and it worked on the solver, and the result are correct thank you so much for your help.