Linear Programming and Portfolio Selection
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One of its clients has just instructed the Heinlein and Krampt brokerage firm to invest $250,000 that she obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the firm, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm selects whatever stocks and bonds it believes are well rated, but within the following guidelines:
****Municipal bonds, nursing home stock, and drug company stock should constitute at least 20%, 10%, and 10%, respectfully, of the total amount invested.
****At least 40% of the funds should be placed in a combination of electronics and aerospace firms, with each accounting for 15%.
****No more than 50% of the total amount invested in electronics and aerospace firms should be placed in a combination of nursing home and drug company stock, both of which carry high risk.
Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at Heinlein and Kramft, aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return:
Investment Projected Rate of Return
Los Angeles municipal bonds 5.3%
Thomas Electronics, Inc. 6.8%
United Aerospace Corp. 4.9%
Palmer Drugs 8.4%
Happy Days Nursing Homes 11.8%
Formulate this portfolio selection problem using Linear Programming (LP) and solve it by using Excel.
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Solution Summary
The solution provides detailed explanations, discussions including the Excel codes for the optimization problem.
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I have used the Solver tool in Excel for this purpose. If you're not familiar with this tool, use the Help Center in Excel.
It was found that using a combination below, a maximized rate of return for the portfolio was found to be 7.21%.
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