Question

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 $50,000 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 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $35,000 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 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 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 6(10) + 4(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 the constant is "1" it must be entered in the box. If your answer is zero enter “0”. - 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 $50,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor? Internet Fund = $ Blue Chip Fund = $ Annual Return = $ (d) Suppose that a third client with $50,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 160. Develop the recommended investment portfolio for the conservative investor. If your answer is zero enter “0”. Internet Fund = $ Blue Chip Fund = $ Annual Return = $

Answer 1

Decision Variables:

Let,

I is internet fund investment in thousands

B is Blue Chip fund investment in thousands.

Objective Function:

Is to maximize the annual portfolio return

Return from Internet fund = 12%

Blue Chip fund has a return of = 9%

So objective function is:

MAXIMIZE 0.12*I + 0.09*B

Constraints:

Total investment should not exceed the available fund of $50,000

So, I + B <= 50 (as investment in thousands)

Maximum investment in Internet is $35000

I + 0*B <= 35

Risk rating for Internet fund is 6 per thousand dollar.

Risk rating for Blue Chip fund is 4 per thousand dollar.

Maximum risk rating is 240.

6*I + 4*B <= 240

The investments cant be in negative quantity.

I, B >= 0

***

Question – b:

Putting in Excel:

Solver Parameters:

Optimal Solution:

Internet Fund	Blue Chip Fund
I	B
20	30

Internet Fund = $20,000

Blue Chip Fund = $30,000

Annual Return = $5,100

***

Question – c:

Maximum portfolio risk is 320.

The only constraint change is:

6*I + 4*B <= 320

From Excel:

Solver Parameters:

Optimal Solution is:

Internet Fund = $35,000

Blue Chip Fund = $15,000

Annual Return = $5,550

***

Question – d:

Now the maximum risk rating is 160.

6*I + 4*B <= 160

From Excel:

Solver Parameters:

Optimal Solution is:

Internet Fund = 0

Blue Chip Fund = $40,000

Annual Return = $3,600

********

IF YOU HAVE ANY DOUBT, KINDLY COMMENT. I WOULD LOVE TO HELP YOU!!!

IF YOU LIKE THE ANSWER, PLEASE GIVE AN UP-VOTE OR THUMB UP. THIS WILL ENCOURAGE ME TO ANSWER MORE!!