1. An individual investor has $70,000 to divide among several investments. The alternative investments are municipal bonds with an 8.5% return, certificates of deposits with a 10% return, Treasury bill with a 6.5% return, and income bonds with a 13% return. The amount of time until maturity is the same for each alternative. However, each investment alternative has a different perceived risk to the investor; thus it is advisable to diversify. The investor wants to know how much to invest in each alternative in order to maximize the return. The following guidelines have been established for diversifying the investment and lessening the risk perceived by the investor.
No more than 20% of the total investment should be in an income bonds.
The amount invested in certificates of deposit should not exceed the amount invested in other three alternatives.
At least 30% of the investment should be in treasury bills and certificates of deposits.
The ratio of the amount invested in municipal bonds to the amount invested in treasury bills should not exceed one to three.
2 / 2
The investor wants to invest the entire $ 70,000
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An individual investor has $70,000 to divide among several investments. The alternative investments are municipal bonds with an 8.5% return, certificates of deposits with a 10% return, Treasury bill with a 6.5% return, and income bonds with a 13% return. The amount of time until maturity is the same for each alternative. However, each investment alternative has a different perceived risk to the investor; thus it is advisable to diversify. The investor wants to know how much to invest in each alternative in order to maximize the return. The following guidelines have been established for diversifying the investment and lessening the risk perceived by the investor.
No more than 20% of the total investment should be in an income bonds.
The amount invested in certificates of deposit should not exceed the amount invested in other three alternatives.
At least 30% of the investment should be in treasury bills and certificates of deposits.
The ratio of the amount invested in municipal bonds to the amount invested in treasury bills should not exceed one to three.
2 / 2
The investor wants to invest the entire $ 70,000
To maximize the return while diversifying the investment, we can solve this problem using linear programming. Linear programming is a mathematical technique that helps find the optimum solution given certain constraints.
Let's assign variables to represent the amount invested in each alternative as follows:
x1: amount invested in municipal bonds
x2: amount invested in certificates of deposits
x3: amount invested in Treasury bills
x4: amount invested in income bonds
We can set up the following objective function to maximize the return:
Maximize: 0.085x1 + 0.1x2 + 0.065x3 + 0.13x4
Now, let's set up the constraints based on the given guidelines:
1. No more than 20% of the total investment should be in income bonds:
x4 <= 0.2 * ($70,000)
2. The amount invested in certificates of deposits should not exceed the amount invested in the other three alternatives:
x2 <= x1 + x3 + x4
3. At least 30% of the investment should be in treasury bills and certificates of deposits:
x2 + x3 >= 0.3 * ($70,000)
4. The ratio of the amount invested in municipal bonds to the amount invested in treasury bills should not exceed one to three:
x1 <= 3x3
5. The total investment should equal $70,000:
x1 + x2 + x3 + x4 = $70,000
With these constraints in place, you can use a linear programming solver or a spreadsheet program with optimization capabilities to find the values of x1, x2, x3, and x4 that maximize the objective function while satisfying the constraints.
By solving this optimization problem, you will find the optimal allocation of the $70,000 investment among the different alternatives, considering the given guidelines.