In: Operations Management
Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $35,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240.
(a) | Formulate a linear programming model to find the best investment strategy for this client. | ||||||||||||||||||||||||||||||||||||||||||
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If required, round your answers to two decimal places. If an amount is zero, enter “0”. If the constant is "1" it must be entered in the box. | |||||||||||||||||||||||||||||||||||||||||||
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(b) | Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? | ||||||||||||||||||||||||||||||||||||||||||
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What is the annual return for the portfolio? | |||||||||||||||||||||||||||||||||||||||||||
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(c) | Suppose that a second client with $50,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor? | ||||||||||||||||||||||||||||||||||||||||||
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(d) | Suppose that a third client with $50,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 160. Develop the recommended investment portfolio for the conservative investor. If an amount is zero, enter “0”. | ||||||||||||||||||||||||||||||||||||||||||
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(a): Objective function = 0.12I + 0.09B. This has to be maximized.
Constraints are:
(i): I+B<=50,000
(ii): I<=35,000
(iii): 6/1000I + 4/1000B<=240
(iv) I, B>=0 (i.e. non-negativity)
(b): Excel's spreadsheet model gives the following solution:
Internet fund = $20,000
Bluechip fund = $30,000
Annual return of the portfolio = $5,100
(c): Here the 2nd constraint will change and become: 6/1000I + 4/1000B<=320. The answers are:
Internet fund = $35,000
Bluechip fund = $15,000
Annual return of the portfolio = $5,550
(d): Here the 2nd constraint will change and become: 6/1000I + 4/1000B<=160. The answers are:
Internet fund = 0
Bluechip fund = $40,000
Annual return of the portfolio = $3,600
I am uploading the solver image for the investor in part "b" i.e. with the risk rating of 240 for your reference: