Problem 11-3 Blair & Rosen, Inc. (B&R;) is a brokerage firm that specializes in
ID: 3359670 • Letter: P
Question
Problem 11-3 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 7%. The investment advisor requires that at most $30,000 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 220Explanation / Answer
This problem is a linear programming problem with two decision variables which are the amount to be invested in internet fund and the amount to be invested in Blue chi fund.We have to maximize the profit made from the investment ,Subjectedto the constraints. This problem can be formulated in excel and can be solved using the solver module.
a) Decision variables:
I=Amount invested in Internet fund
B=Amount invested in blue chip fund
A client who contacted B&R this past wek has maximum of $55000 to invest.
I+B<=55000
The investment advisor requires that at most $30,000 of the clients funds should be invested in the internet fund.
I<=30000
b) A client who is a moderate investor limits his or her portfolio to a maximum risk rating of 220.
(6/1000)*I+(4/1000)B<=220
Objective function:
Maximize Z=(17/100)*I+(7/100)*B
Solving the above linear programming using excel solver we get the optimum investment for maximum profit gien in the question.
Internet fund=I=0,
Blue chip fund+B=$55000
Annual return=$3840
c) The second client is an aggressie investor and hence the question remains same except the third constraints which becomes:(6/1000)*I+(4/1000)*B<=310
Now we sove the equation we can get the values.
Internet fund=I=$45000
Blue chip fund=B=$10000
Annual return =$8350
Under the aggressive investor strategy the annual return increase from $3850 to $8350
d) The third client is a conservative investor and hence the question remains same except the third constraint which now becomes:
(6/1000)*I+(4/1000)*B<=150
Internet fund=I=-$35000
Blue chip fund=B=$90000 Annual return=$350