$61$B Course Project $3$

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 $0\mathrm{.}05$ for the client. The firm$$s risk

indicators show the risk of the growth fund at $0\mathrm{.}10,$ the income fund at $0\mathrm{.}07,$ and the money

market fund at $0\mathrm{.}01.$ An overall portfolio risk index is computed as a weighted aver$-$ age 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, $12\mathrm{.}5\%$

for the income fund, and $7\mathrm{.}5\%$ 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.

Managerial Report

$1.$ 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?

$2.$ Assume that the client$$s risk index could be increased to $0\mathrm{.}055.$ How much would the

yield increase, and how would the investment recommendation change?

$3.$ Refer again to the original situation, in which the client$$s risk index was assessed to be

$0\mathrm{.}05.$ How would your investment recommendation change if the annual yield for the

growth fund were revised downward to $16\%$ or even to $14\%?$

$4.$ 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?

$5.$ 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?