Question

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?

Answer 1

Investment Conditions:-
1. At least 40% of Total Investment in Non Mortgage Instruments
2. Maximum 35% of Total Investment in High Risk Instruments
Type of Investments	Expected Annual Interest Rate for the Investment	Percentage Investment	Investment Amount in Dollars	Instrument Type	Instrument Type	Interest Income / Year = Investment Amount * Expected Annual Interest Rate
Low income Mortgage Loans	7.40%	20%	1300000	Mortgage		96200
Conventional Mortgage Loans	6.20%	15%	975000	Mortgage		60450
Government Sponsored Mortgage Loans	8.00%	25%	1625000	Mortgage	High Yield / High Risk	130000
Bond Investments	4.45%	15%	975000	Non Mortgage		43387.5
Stock Investments	7.50%	15%	975000	Non Mortgage		73125
Futures Trading	8.90%	10%	650000	Non Mortgage	High Yield / High Risk	57850
			Expected Total Interest Income			461012.50

a) Expected Total Interest Income generated from Investment Strategy: $461012.50

b) Amount of Investment in Govt Sponsored Mortgage Loans: $1625000

c) Amount of Investment in Stock Investment: $975000

d) Govt. Sponsored Mortgage limit should be increased as it yields highest return.

e) If return on Low Income Mortgage Loans are dropped to 4% then based on new investment I would not invest anything in Low Income Mortgage.