In: Operations Management
Problem 5-09
The table below shows data on the returns over five 1-year
periods for seven...
Problem 5-09
The table below shows data on the returns over five 1-year
periods for seven mutual funds. A firm's portfolio managers will
assume that one of these scenarios will accurately reflect the
investing climate over the next 12 months. The probabilities of
each of the scenarios occurring are 0.1, 0.3, 0.1, 0.1, and 0.4 for
years 1 to 5, respectively.
RETURNS OVER FIVE 1-YEAR PERIODS FOR SEVEN MUTUAL
FUNDS |
|
Planning Scenarios for Next 12
Months |
Mutual Funds |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
Large-Cap Stock |
35.3 |
20.0 |
28.3 |
10.4 |
-9.3 |
Mid-Cap Stock |
32.3 |
23.2 |
-0.9 |
49.3 |
-22.8 |
Small-Cap Stock |
20.8 |
22.5 |
6.0 |
33.3 |
6.1 |
Energy/Resources Sector |
25.3 |
33.9 |
-20.5 |
20.9 |
-2.5 |
Health sector |
49.1 |
5.5 |
29.7 |
77.7 |
-24.9 |
Technology Sector |
46.2 |
21.7 |
45.7 |
93.1 |
-20.1 |
Real Estate Sector |
20.5 |
44.0 |
-21.1 |
2.6 |
5.1 |
- Develop a portfolio model with Excel Solver for investors who
are willing to risk a portfolio with a return no lower than 2%.
Round your answers to one decimal place. For subtractive or
negative numbers use a minus sign even if there is a + sign before
the blank. If the constant is "1" it must be entered in the
box.
To determine the percentage of the portfolio that will be invested
in each of the mutual funds we use the following decision
variables:
|
LS = proportion of portfolio invested in a large-cap
stock mutual fund |
|
MS = proportion of portfolio invested in a mid-cap
stock fund |
|
SS = proportion of portfolio invested in a small-cap
growth fund |
|
ES = proportion of portfolio invested in an energy
sector fund |
|
HS = proportion of portfolio invested in a health
sector fund |
|
TS = proportion of portfolio invested in a technology
sector fund |
|
RS = proportion of portfolio invested in a real estate
sector fund |
Max |
s.t. |
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
|
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
≥ |
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
≥ |
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
≥ |
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
≥ |
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
≥ |
|
LS |
+ |
MS |
+ |
SS |
+ |
ES |
+ |
HS |
+ |
TS |
+ |
RS |
= |
|
LS, MS, SS, ES, HS, TS, RS |
≥ |
0 |
- Solve the model in part (a) and recommend a portfolio
allocation for the investor with this risk tolerance. Round
portfolio return to three decimal places and other answers to one
decimal place. If your answer is zero, enter "0".
The recommended allocation is to invest as follows:
% |
of the portfolio in the large-cap stock mutual fund |
% |
of the portfolio in the mid-cap stock fund |
% |
of the portfolio in the small-cap stock fund |
% |
of the portfolio in the energy sector fund |
% |
of the portfolio in the health sector fund |
% |
of the portfolio in the technology sector fund |
% |
of the portfolio in the real estate sector fund |
The expected portfolio return is %.
- Modify the portfolio model in part (a) and solve it to develop
a portfolio for an investor with a risk tolerance of 0%. Round
portfolio return to three decimal places and other answers to one
decimal place. If your answer is zero, enter "0".
The recommended allocation is to invest as follows:
% |
of the portfolio in the large-cap stock mutual fund |
% |
of the portfolio in the mid-cap stock fund |
% |
of the portfolio in the small-cap stock fund |
% |
of the portfolio in the energy sector fund |
% |
of the portfolio in the health sector fund |
% |
of the portfolio in the technology sector fund |
% |
of the portfolio in the real estate sector fund |
The expected portfolio return is %.