Blair & Rosen, Inc. (B&R) is a brokerage firm that
specializes in investment portfolios designed to meet the specific
risk tolerances of its clients. A client who contacted B&R this
past week has a maximum of $55,000 to invest. B&R's investment
advisor decides to recommend a portfolio consisting of two
investment funds: an Internet fund and a Blue Chip fund. The
Internet fund has a projected annual return of 17%, while the Blue
Chip fund has a projected annual return of 8%. The investment
advisor requires that at most $25,000 of the client's funds should
be invested in the Internet fund. B&R services include a risk
rating for each investment alternative. The Internet fund, which is
the more risky of the two investment alternatives, has a risk
rating of 5 per thousand dollars invested. The Blue Chip fund has a
risk rating of 5 per thousand dollars invested. For example, if
$10,000 is invested in each of the two investment funds, B&R's
risk rating for the portfolio would be 5(10) + 5(10) = 100.
Finally, B&R developed a questionnaire to measure each client's
risk tolerance. Based on the responses, each client is classified
as a conservative, moderate, or aggressive investor. Suppose that
the questionnaire results classified the current client as a
moderate investor. B&R recommends that a client who is a
moderate investor limit his or her portfolio to a maximum risk
rating of 240.
| (a) |
Formulate a linear programming model to find the best
investment strategy for this client. |
|
| Let I |
= Internet fund investment in thousands |
| B |
= Blue Chip fund investment in thousands |
|
|
If required, round your answers to two decimal places. If an
amount is zero, enter “0”. If the constant is "1" it must be
entered in the box. |
|
| - Select your answer -MaxMinItem 1 |
I |
+ |
B |
|
|
|
| s.t. |
|
|
|
|
|
|
|
I |
+ |
B |
- Select your answer -≤≥=Item 6 |
|
Available investment funds |
|
I |
+ |
B |
- Select your answer -≤≥=Item 10 |
|
Maximum investment in the internet fund |
|
I |
+ |
B |
- Select your answer -≤≥=Item 14 |
|
Maximum risk for a moderate investor |
|
|
|
I, B |
- Select your answer -≤≥=Item 16 |
|
|
|
|
|
| (b) |
Build a spreadsheet model and solve the problem using Solver.
What is the recommended investment portfolio for this client? |
|
| Internet Fund |
= |
$ |
| Blue Chip Fund |
= |
$ |
|
|
|
|
What is the annual return for the portfolio? |
|
$ |
|
|
| (c) |
Suppose that a second client with $55,000 to invest has been
classified as an aggressive investor. B&R recommends that the
maximum portfolio risk rating for an aggressive investor is 350.
What is the recommended investment portfolio for this aggressive
investor? |
|
| Internet Fund |
= |
$ |
| Blue Chip Fund |
= |
$ |
| Annual Return |
= |
$ |
|
|
|
| (d) |
Suppose that a third client with $55,000 to invest has been
classified as a conservative investor. B&R recommends that the
maximum portfolio risk rating for a conservative investor is 150.
Develop the recommended investment portfolio for the conservative
investor. If an amount is zero, enter “0”. |
|
| Internet Fund |
= |
$ |
| Blue Chip Fund |
= |
$ |
| Annual Return |
= |
$ |
|
The correlation coefficient will always take values
The College Board originally scaled SAT scores so that the
scores for each section were approximately normally distributed
with a mean of 500 and a standard deviation of 100. Assuming scores
follow a bell-shaped distribution, use the empirical rule to find
the percentage of students who scored less than 400.