An investor wishes to invest all of her $6.5 million in a diversified portfolio through acommercial lender. The types of investments, the expected annual interest rate for theinvestment, and the maximum allowed percentage of the total portfolio that the investmentcan 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 sponsoredmortgage 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, shewants 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 inExcel to determine how her money should be diversified in a manner which will meet therequirements and maximize the amount of interest income. (Hint: Make sure that the LHS andRHS of constraints are in terms of dollars not ratios)a) Formulate the problem.b) What is the expected total interest income generated from the investment strategy(the value of the objective function)?c) Based on your solution, how much should be invested in each investment option? Speak
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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 in terms of dollars not ratios)
a) Formulate the problem.
b) What is the expected total interest income generated from the investment strategy
(the value of the objective function)?
c) Based on your solution, how much should be invested in each investment option?
Speak