Give an Overview of the Case Study 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$$s risk indicators show the risk of the growth fund at $0\mathrm{.}10,$ the income fund at $0\mathrm{.}07,$ and the money market fund at $0\mathrm{.}01.$ An overall portfolio risk index is computed as a weighted average of the risk rating for the three funds, where the weights are the fraction of the client$$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.