A bank is attempting to determine where its assets should be invested during the current year. At present, $4,000,000 is available for investment in municipal bonds, U.S. Treasury bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be: municipal bonds = 3.5%, U.S. Treasury bonds =3%; home loans =4%; auto loans =4.5%; personal loans =11%. To ensure that the bank's portfolio is not too risky, the bank's investment manager has placed the following restrictions on the bank's portfolio:
*The amount invested in personal loans cannot exceed the amount invested in U.S. Treasury bonds.
*The amount invested in auto loans cannot exceed the amount invested in home loans.
*No more than 20% of the total amount invested can be in personal loans.
Part a. Use Excel Solver to obtain the optimal investment portfolio. Obtain an Answer Report and a Sensitivity Report. What is the optimal investment portfolio? What is the annual rate of return for the optimal portfolio?
Part b. Recent events in the real estate and mortgage markets have prompted the Board of Directors to impose a new restriction that no more than 25% of the bank’s portfolio can be invested in home loans. Use Excel Solver to obtain the optimal investment portfolio in this case. Obtain an Answer Report. How much lower would the annual rate of return be for this portfolio compared to the portfolio found in Part a?
Part c. Furthermore, in order to ensure that the bank maintains a diversified portfolio, the Board of Directors has added yet another requirement that at least 10% of the portfolio must be invested in each investment type (i.e., municipal bonds, U.S. Treasury bonds, home loans, auto loans, and personal loans). Use Excel Solver to obtain the optimal investment portfolio with the new requirement. Obtain an Answer Report. How much lower would the annual rate of return be for this portfolio compared to the portfolios found in Parts a and b?