LP Assignment Munchin Investments $($S$5)|$

Muchin 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 client's portfolio to be invested in growth fund, income fund and hedge fund.

To maintain diversity in each client's 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 portfolio's risk index.

A new client, Benjamin Rich should be advised on allocation of $$360,000.$ Based on an evaluation of the client's risk tolerance, the Munchin Investments assigned a maximum risk index of $\mathrm{.}05$ to the portfolio. The firm's risk indicators show the risk rating for the growth stock fund at $\mathrm{.}06,$ while the risk ratings for income fund and hedge fund are at $\mathrm{.}045$ and $\mathrm{.}015$ respectively. An overall portfolio's 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 growth stock 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 growth stock fund should be at least as high $(>)$ as the amount invested in income fund.

The firm is forecasting annual yields $($returns$)$ of $7\mathrm{.}9\%$ for the growth stock fund, $6\%$ for income fund and $3\mathrm{.}5\%$ for the hedge fund.

Based on the information provided, how should the new client be advised to allocate the $$360,000$ 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 Excel's Solver. Generate Answer report and sensitivity reports.