First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return.
Investment Opportunity Rate of Return
Municipal Bonds 0.095
High Tech Stock 0.146
Blue Chip Stock 0.075
Federal Bonds 0.070
The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock.
(a) Formulate this portfolio selection problem using linear programming.
(b) Solve using LP software such as Excel QM or QM for windows. Write out answer step by step if you can't use QM.
This solution creates a linear program to formulate the selection problem and shows step-by-step calculations to determine municipal bonds, high tech stock, blue chip stock, federal bond and total returns on investment.
Linear Programming Modeling
A Brokerage firm has just been instructed by one of its clients to invest $250,000 for her money obtained recently througn the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines: a) Municipal bonds should constitute at least 20% of the investment. b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. c) No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock. Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at the brokerage firm, aware of these guideline, prepare a list of high-quality stocks and bonds and their corresponding rates of return:
Investment Protected Rate of Return %
Los Angeles municipal bonds 5.3
Thompson Electronics, Inc. 6.8
United Aerospace Corp 4.9
Palmer Drugs 8.4
Happy Days Nursing Home 11.8
a) Formulate this portfolio selection problem using LP.
b) Solve this problem.