Problem 8-3 Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in in
ID: 2721832 • Letter: P
Question
Problem 8-3
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 $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. - Select your answer - Max Min Item 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 0 (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. Internet Fund = $ Blue Chip Fund = $ Annual Return = $Explanation / Answer
This is linear programming problem with two decision variables which are the amount invested in internet funds and amount invested in Blue chip fund. We have to maximise the profit made from the investment, subjected to the constrains. The resources are limited and include money available in hand and maximum risk rating. This problem can be formulated in excell and can be solved using the solver module. The sansitivity analysis as well as the shadow prices of all variable is available in the excel solver module.
Decision variables
I = Amount invested in Internet Funds
B=Amount invested in Blue chip Funds
Constraints:
1. A client who contracted B & R this past week has maximum of $50,000 to invest.
I +B <= 50,000
2. the Investment advisior requires that at most $35,000 of the client's fund should be invested in the internet fund.
I <= 35,000
3. A client who is a moderate investor limits hi or her portfolio to maximum risk rating of 240
(6/1000)*I +(4/1000)B <= 240
Objective Function:
Maximise z =(12/100)I +(9/100)B
b) Soving th above linear programming using excel solver we getthe optimum investment for maximum profit given the consrainn in this question I = 20,000 B= 30,000 Annual return =5100
c) Seconf client is aggresive investor hence the question remains same except the third constraint which now becomes:
(6/1000)I +(4/1000)*B <= 320
Now we solve this linear programming in excel to get the values as I =35000 ,B= 15,000 and Annual Return is $5500.
Under the aggressive investor Annual Return is increased to $5500 from $5100, Consequently the risk increases to 270.
d) The third client is conservative investor and hence the question remains same except the third constraint which now becomes:
(6/1000)I +(4/1000)*B <= 160
Now we solve this linear programming in excel to get the values as I =0 ,B= 40,000 and Annual Return is $3600.
Under the aggressive investor Annual Return is increased to $3600 from $5100, Consequently the risk decreases to 160..