A portfolio manager has developed a list of six investment alternatives for a multiyear horizon. These are Treasury bills, Common stock, Corporate bonds, Real estate, Growth funds, and Savings and loans. These investments and their various financial factors are described below.
In the table, the return is given as an annual percentage, and the length represents the estimated number of years required for the annual return to be realized.
The risk coefficient is a subjective estimate representing the manager's appraisal of the relative safety of each alternative, on a scale of 1-10. The growth potential is an estimate of the potential increase in value over the horizon.
|
|
|
|
Portfolio Data
|
|
|
|
Alternative
|
TB
|
CS
|
CB
|
RE
|
GF
|
SL
|
|
Length (years)
|
4
|
7
|
8
|
6
|
10
|
5
|
|
Annual return (%)
|
6
|
15
|
12
|
24
|
18
|
9
|
|
Risk coefficient
|
1
|
5
|
4
|
8
|
6
|
3
|
|
Growth potential (%)
|
0
|
18
|
10
|
32
|
20
|
7
|
The manager wishes to maximize the return on a $3 million portfolio, subject to the following restrictions:
1. The weighted average length should not exceed 7 years.
2. The weighted average risk coefficient should not exceed five.
3. The weighted average growth potential should be at least 10%.
4. The investment in real estate should be no more than twice the investment in stocks and bonds (i.e., in CS, CB, and GF) combined.
a) Formulate a linear mathematical model to achieve the manager's objective. Clearly define your decision variables, objective and constraints
b) Implement your model using Excel and find the optimal return and the optimal allocation of investment funds? (Give the optimal return in dollars and also as a percentage.). Include in your report a snapshot of the solution
c) What is the marginal rate of return? In other words, what would be the return on the next dollar invested if there were one more dollar in the portfolio?
d) For additional investment beyond the original $3 million, how does the optimal allocation change?