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

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 63P
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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 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:

   

9X1 + 13X2 + 8X3 ≥ 12

   

[(9X1 + 13X2 + 8 X3)/(X1+ X2+ X3)] + d2- - d2+ ≥ 12

   

[(9X1 + 13X2 + 8X3)/(X1+ X2+ X3)] + d2- - d2+ ≤ 0

   

-3X1+ X2 - 4X3 + d2- - d2+ ≥ 12

   

-3X1 + X2 - 4 X3 + d2- - d2+ = 0

 

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