An investment manager is considering stocks X1, X2, and X3 for investment. Market research shows the following information (per stock) X1 X2 X3 cost $100 risk measure 8 price annual growth rate: 9% annual return: $14 cost $120 risk measure 10 price annual growth rate: 13% annual return: $15 cost $80 risk measure 7 price annual growth rate: 8% annual return: $20 Based on his experience, the manager has set the following priorities for the investment: (1) The total amount invested should be at least $90,000. (d1) (2) The minimum annual average growth rate in stock prices is 12%. (d2) (3) The risk factor of all stocks
An investment manager is considering stocks X1, X2, and X3 for investment.
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X1 |
X2 |
X3 |
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cost $100 risk measure 8 price annual growth annual return: $14 |
cost $120 risk measure 10 price annual growth rate: 13% annual return: $15 |
cost $80 risk measure 7 price annual growth rate: 8% annual return: $20 |
Based on his experience, the manager has set the following priorities for the investment:
(1) The total amount invested should be at least $90,000. (d1)
(2) The minimum annual average growth rate in stock prices is 12%. (d2)
(3) The risk factor of all stocks should not exceed a total of 5,000. (d3)
(4) The total annual return should be $15,000. (d4)
The constraint for the annual growth rate can be written as:
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9X1 + 13X2 + 8X3 ≥ 12 |
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[(9X1 + 13X2 + 8 X3)/(X1+ X2+ X3)] + d2- - d2+ ≥ 12 |
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[(9X1 + 13X2 + 8X3)/(X1+ X2+ X3)] + d2- - d2+ ≤ 0 |
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-3X1+ X2 - 4X3 + d2- - d2+ ≥ 12 |
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-3X1 + X2 - 4 X3 + d2- - d2+ = 0 |
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