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Case Problem 2 INVESTMENT STRATEGY 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 rec- ommends 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 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 ad just 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 cli ent'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 pro- vided, 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 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?

Answer 1

1. Let X1, X2, & X3 be the investment in growth fund, income fund & monetary fund.

Therefore we have Objective function as:-

Maximize Z = 1.18X1+1.125X2+1.075X3

Subject to constraints :

X1+X2+X3 < 800000

0.01X1+0.07X2+0.01X3 < 0.05 (requirement of overall risk to be not more than 0.05)

0.20 < X1 < 0.40

0.20 < X2 < 0.50

0.30 < X3

After solving all these equation we will get optimum solution as

X1 = $248800

X2 = $160000

X3 = $39120

Therefore allocation of fund should be as follows :-

Growth fund = $248800

Income fund = $160000

Money market fund = $391200

Annual yield = 248800x18%+160000x12.5%+391200x7.5% = $94124.

2. If the risk of client is increased from 0.05 to 0.055, then the annual yield would also be increased by $4676. Total annual yield will increase from $94124 to $98800.

Investment recommend will change as follows :-

Fund allocation	projected annual yield
Growth fund = $293333	$293333x0.18 = $52800
Income fund = $160000	$160000x0125 = $20000
Money market fund = $346667	$346667x0.075 = $26000
Total = $800000	total = $98800