Question

J.D. Williams, Inc. is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client’s portfolio to be invested in a growth stock fund, an income fund, and a money market fund. To maintain diversity in each client’s portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value, the amount invested in the income fund must be between 20% and 50% of the total portfolio value, and at least 30% of the total portfolio value must be in the money market fund.In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. For example, Williams just contracted with a new client who has $800,000 to invest. Based on an evaluation of the client’s risk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm’s risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is calculated as a weighted average of the risk rating for the three funds, where the weights are the fraction of each client’s portfolio invested in each of the funds.Williams is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, and 7.5% for the money market fund.Based on the information provided, how should the new client allocate the $800,000 among the three funds in order to provide the maximum annual return for the portfolio?Summarize your findings and recommendations. Include the following:

a. Recommend how much of the $800,000 should be invested in each of the three funds. What is the annual return for this recommendation?

b. Assume the client’s risk index could be increased to 0.055. How does this change your recommendation? What is the new annual return?

c. If the client insists that the risk index should be 0.05, how would your recommendation change if the annual yield for the growth fund is 14% instead of 18%?

d. Go back to a 18% yield for the growth fund. Now the client thinks there’s too much money in the growth fund. How would your recommendation change if the amount in the growth fund cannot exceed the amount invested in the income fund?

Answer 1

Fund	Risk Index	Weightage constraints	Expected return
Growth stock	0.1	20%-40%	18%
Income	0.07	20%-50%	12.5%
Money market	0.01	>= 30%	7.5%

Maximum risk tolerance = 0.05

Objective to maximize annual returns based on the above constraints

a)

Step 1) First we will allocate equal weights to all the funds i.e 100%/3

Step 2) Setup the constraints in the solver

Step3) Solve using the solver

Investments

Growth stock = 31.11%*800000 = $248,888.89

Income = 20%*800000 = $160,000

Money market = 48.89%*800000 = $391,111.11

Annual return = 11.767%

(b) Change the constraint of weighted average risk tolerance to 0.055 in solver

(c)

(d)

Add constraint that F2 <= F4