LP Assignment Roberts Investments (S2)

Roberts Investments is a financial services firm that manages funds for numerous clients. The company uses a proprietary asset allocation model that recommends the portion of each clients portfolio to be invested in exchange traded fund, income fund and hedge fund.

To maintain diversity in each clients portfolio, the firm places limits on the percentage of a portfolio that may be invested in each of the three funds, and assigns a limit on the portfolios risk index.

A new client, Boris Grey should be advised on allocation of $500,000. Based on an evaluation of the clients risk tolerance, the Roberts Investments assigned a maximum risk index of .05 to the portfolio. The firms risk indicators show the risk rating for the exchange traded fund at .075, while the risk ratings for income fund and hedge fund are at .055 and .01 respectively. An overall portfolios risk index is computed as a weighted average of the risk rating for the three funds, where the weights are the fraction of the portfolio invested in each of the funds. Higher value of the risk index represents a more risky portfolio.

To maintain diversity the following investment guidelines are used:

• The amount invested in exchange traded fund should be between 15% and 40% of the total portfolio value.
• The amount invested in income fund should be between 25% and 40% of the total portfolio value.
• At least 30% of the total portfolio value must be in in hedge fund.

Furthermore, the amount invested in exchange traded fund should be at least as high (>=) as the amount invested in hedge fund.

The firm is forecasting annual yields (returns) of 13.5% for the exchange traded fund, 10.25% for income fund and 6.0% for the hedge fund.

Based on the information provided, how should the new client be advised to allocate the $500,000 among the three funds to maximize the overall yield from the portfolio?

Formulate a linear programming model for this portfolio selection problem (define decision variables, write down the objective function, develop constraints show all steps/calculations) and solve it using Excels Solver. Generate Answer report and sensitivity reports.

This problem is suposed to be an excel sheet I am unsure of how to formulate a linear programming model for tis portfolio. Can someone explain the formula and process to get this information?