Johnson is a managing partner of a prominent investment firm who is designing a
ID: 3146129 • Letter: J
Question
Johnson is a managing partner of a prominent investment firm who is designing a portfolio for his client Ryan. Ryan has $500,000 to invest. Johnson has identified 11 different investments falling in 4 broad categories that Johnson and Ryan would be potential candidates for the portfolio. The investments and their characteristics are given below:
Investment
Estimated Annual After-Tax Return
Liquidity Factor
Risk Factor
Category
Carson Corporation
9.5%
100
62
Stock
Carson Corporation
7.3%
92
33
Bond
Jefferson REIT
11.5%
100
78
Stock, Real Estate
Certificate of Deposit
8.8%
0
0
Money
SF Power
6.8%
95
19
Bond
Metropolitan Transit
8.2%
79
23
Bond
Money Market Fund
6.2%
100
10
Money
Pixel Electronics
13.0%
100
95
Stock
Cabrera Partnership
10.0%
0
50
Real Estate
Treasury Bills
5.6%
80
0
Money
Taco Loco
11.0%
100
71
Stock
The expected annual after-tax returns account for all commissions and service charges. Note that there are two separate investments in the Carson Corporation and that the Jefferson REIT is a single investment (a stock in a real estate investment company).
Johnson’s objective is to construct a portfolio for Ryan that maximizes his total estimated after-tax return over the next year. Ryan has the following requirements:
1) The average risk factor must be no greater than 55.
2) The average liquidity factor must be at least 85.
3) At least $10,000 is to be invested in the Carson Corporation.
4) At least 20% but no more than 50% of the “non-money” portion of the portfolio (stocks, bonds, and real estate) should be from any one category of investment.
5) With the exception of the money category investments, no more than 20% of the total portfolio should be in any one investment.
6) At least $20,000 should be invested in the money market fund.
7) A minimum investment of $125,000 should be in bonds.
8) No more than 40% of the total portfolio in investments with expected annual after-tax returns of less than 10% is to have risk factors exceeding 25.
9) At least one-half of the portfolio must be totally liquid (i.e., have a liquidity factor of 100).
Formulate a linear program to determine the best investment portfolio distribution, assuming Ryan wants to invest some or all of the $500,000 (general case). Formulation using the specific case for exactly $500,000 will be marked incorrect and no credit given.
Investment
Estimated Annual After-Tax Return
Liquidity Factor
Risk Factor
Category
Carson Corporation
9.5%
100
62
Stock
Carson Corporation
7.3%
92
33
Bond
Jefferson REIT
11.5%
100
78
Stock, Real Estate
Certificate of Deposit
8.8%
0
0
Money
SF Power
6.8%
95
19
Bond
Metropolitan Transit
8.2%
79
23
Bond
Money Market Fund
6.2%
100
10
Money
Pixel Electronics
13.0%
100
95
Stock
Cabrera Partnership
10.0%
0
50
Real Estate
Treasury Bills
5.6%
80
0
Money
Taco Loco
11.0%
100
71
Stock
Explanation / Answer
Let the variables be as follows
Portfolio
a
b
c
d
e
f
g
h
j
k
m
Total
500000
Return
9.50%
7.30%
11.50%
8.80%
6.80%
8.20%
6.20%
13.00%
10.00%
5.60%
11.00%
Category
Stock
Bond
Stock, Real Estate
Money
Bond
Bond
Money
Stock
Real Estate
Money
Stock
Liquidity
100
92
100
0
95
79
100
100
0
80
100
Risk Factor
62
33
78
0
19
23
10
95
50
0
71
Objective function
Maximize
0.95a+0.0730b+ +0.11m,
Subject to
Portfolio
a
b
c
d
e
f
g
h
j
k
m
Total
500000
Return
9.50%
7.30%
11.50%
8.80%
6.80%
8.20%
6.20%
13.00%
10.00%
5.60%
11.00%
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