Question

The Glorious Company manages approximately $15 million for clients. For each client, Gloria chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund. Each client has different investment objectives and different tolerances for risk. To accommodate these differences, Gloria places limits on the percentage of each portfolio that may be invested in the three funds and assigns a portfolio risk index to each client. Here's how the system works for Dennis Hartmann, one of Gloria's clients. Based on an evaluation of Hartmann's risk tolerance, Gloria has assigned Hartmann's portfolio a risk index of 0.05. Furthermore, to maintain diversity, the fraction of Hartmann's portfolio invested in the growth and income funds must be at least 10% for each, and at least 20% must be in the money market fund. The risk ratings for the growth, income, and money market funds are 0.10, 0.05, and 0.01, respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the three funds, where the weights are the fraction of the portfolio invested in each of the funds. Hartmann has given Gloria $300,000 to manage. Gloria's currently forecasting a yield of 20% on the growth fund, 10% on the income fund, and 6% on the money market fund. Develop: a) a linear programming model to select the best mix of investments for Hartmann's portfolio b) Solve the model you developed in part (a). c) How much may the yields on the three funds vary before it will be necessary for Gloria to modify Hartmann's portfolio? d) If Hartmann were more risk tolerant, how much of a yield increase could he expect? For instance, what if his portfolio risk index is increased to 0.06?

Answer 1

MAX sol; z (a) Given that alet G amount invested in growth stock find s = amount invested in income stock find M= amount invested in money moolast fund 0.20G + 0.105 +0.06M 0.106 +0.0 55+0.01M € (0.05) (360,000) Hartmann's mox risk G2 (0.10)( 300,000) Growth fund menimum sz (0.10) (300,600) Income fund minimum M2 (0.201 (300,000) Money market minimum G +S+MS 300, COO Funds Available G,S,M20 (6) The solution to hold mann's portfolio mie problem is given sbjective function value = 36000.000 value Reduced costs Variable 0.000 120000.000 G 0.000 30000.000 S 0.000 M 150000.000 Dual prices constraint Slack 1 surplus 1-556 1 0.000 2 0.000 90000 1000 0.000 -0.022 3 0.000 90000.000 4 0.044 0.000