Question

M3_IND5. An investor wishes to invest all of her $13.5 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 7.20% 15%
Conventional mortgage loans 6.00% 30%
Government sponsored
mortgage loans
8.00% 20%
Bond investments 5.45% 15%
Stock investments 8.90% 20%
Futures trading 9.80% 15%

She wants at least 30% of her total investment in non-mortgage instruments. Furthermore, she wants
no more than 45% 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 5%, how much should be invested
in these low-income mortgage loans based on your new solution?

Answer 1

a. The expected total interest income = 7.48% X 13.5 Mn = $1,009,125. This solution has been reached by using Solver add-in in Excel.

b. 10% must should be invested in Govt. sponsored mortgage loans ie. $ 1.35 Mn.

c. 20% must should be invested in stock investments ie. $ 2.70 Mn.

d. I would chose conventional mortgage loans as of the three options, this is the only one where the optimum solution has used up the maximum limit.

e. Based on new solution, 10% or $1.35 Mn must be invested in these low income mortgage loans.

Please feel free to comment in case you need any further clarifications. Thanks.