Asset Allocation Problem Investment advisory firms offer investment advice and provide their clients with the best mix of financial assets to invest in with different risk tolerance levels. Assume that you work for XYZ investment advisory firm that uses an asset allocation model to recommend the portion of each client's portfolio to be invested in three funds, Alpha, Bravo, and Charlie. Table 1 shows XYZ's general guidelines of the minimum and maximum percentage of the total portfolio value invested in these three funds. For example, if a client has $100,000 to invest, the amount of Alpha fund in the portfolio will be between $20,000 to $40,000 ($100,000*20% to $100,000*40%.) In addition, XYZ attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. Table 1. Min/Max percentage of the total portfolio Fund Alpha Bravo Charlie Minimum Percentage Invested Maximum Percentage Invested 20% 45% 15% 30% 50% Now you have a new client Mr. Smith who has $800,000 to invest. Based on an evaluation of Mr. Smith's risk tolerance, you assign a maximum risk index of 0.05 for him. Table 2 shows the individual risk rating of the funds based on XYZ's risk indicators. 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, annual yields forecasted by XYZ are also shown in Table 2. Based on the information provided, how should Mr. Smith be advised to allocate the $800,000 among Alpha, Bravo, and Charlie funds? What is the annual yield you anticipate for the investment recommendation? Table 2. Risk ratings and yields of the funds Fund Alpha Bravo Charlie Risk Rating 0.1 0.06 0.02 Annual Yields 18% 12.5% 7.5% You are asked to develop a linear programming model that will provide the maximum yield for the portfolio. Create a spreadsheet model to develop an optimal feasible solution of the investment portfolio to present to Mr. Smith. Write up a report to recommend how much of the $800,000 should be invested in each of the three funds and what the annual yield is. Additionally, use the model to do some analysis and answer the following questions: 1. Assume that Mr. Smith's risk index could be increased to 0.06. How much would the yield increase, and how would the investment recommendation change? 2. Refer again to the original situation, in which Mr. Smith's risk index was assessed to be 0.05. How would your investment recommendation change if the annual yield for the Alpha were revised downward to 17.5% or even to 16 %? 3. Assume that the client expressed some concern about having too much money in the Alpha. How would the original recommendation change if the amount invested Alpho is not allowed to exceed the amount invested in Bravo?