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8.3 An investor wishes to invest all of her $6.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected annual interest rate for the investment, and the maximum allowed percentage of the total portfolio that the investment can represent are shown in the table below: INVESTMENT EXPECTED INTEREST MAXIMUM ALLOWED (% of total portfolio) Low-income mortgage loans 7.40% 20% Conventional mortgage loans 6.20% 25% Government sponsored mortgage loans 8.00% 25% Bond investments 4.45% 30% Stock investments 7.50% 15% Futures trading 8.90% 10% She wants at least 40% of her total investment in non-mortgage instruments. Furthermore, she wants no more than 35% of her total investment to be in high-yield and high-risk instruments (i.e. expected interest rate of investment is 8% or greater). Formulate and solve this problem in Excel to determine how her money should be diversified in a manner which will meet the requirements and maximize the amount of interest income. (Hint: Make sure that the LHS and RHS of constraints are the same units) a) What is the expected total interest income generated from the investment strategy (the value of the objective function)? b) Based on your solution, how much should be invested in government sponsored mortgage loans? c) Based on your solution, how much should be invested in stock investments? d) If you could increase the maximum allowed for the investments (in order to increase overall return) - which would you choose: conventional mortgage loans, bond investments, or governmental sponsored mortgage loans. e) If the return on low-income mortgage loans was reduced to 4%, how much should be invested in these low-income mortgage loans based on your new solution? X6 X1 X2 0.15 6.2 0.2 7.4 X3 0.25 8 XS 0.15 7.5 X4 0.15 4.45 0.1 8.9 in Sign 1 1 1 Decision Variables Objective Function Coefficient Constraints: X1 X2 X3 O X4 1 X5 2 X6 3. Total Investment Budget 4 Non-Mortage Constraints 5 High-Risk Contsrtaint 1 7.0925 LHS 0.2 0.35 RHS 0.2 0.25 0.25 0.3 0.15 0.1 1 0.4 0.35 1 1 1 1 1 1 1 1 1 1 1 1