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. Similar percentages for the other two funds stipulate that between 20 and 50%
of the total portfolio value must be in the income fund and that 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 computed as a weighted average of the risk rating for the three
funds, where the weights are the fraction of the client’s portfolio invested in each of the funds.
Additionally, 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 be advised to allocate the $800,000 among the growth, income, and
money market funds? Develop a linear programming model that will provide the maximum yield
for the portfolio. Use your model to develop a managerial report.
Recommend how much of the $800,000 should be invested in each of the three funds.
What is the annual yield you anticipate for the investment recommendation?
Assume that the client’s risk index could be increased to 0.055. How much would the yield
increase, and how would the investment recommendation change?
Assume that the client expressed some concern about having too much money in the
growth fund. How would the original recommendation change if the amount invested in
the growth fund is not allowed to exceed the amount invested in the income fund?
The asset allocation model you developed may be useful in modifying the portfolios for
all of the firm’s clients whenever the anticipated yields for the three funds are periodically
revised. What is your recommendation as to whether use of this model is possible?
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