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10. In your finance courses, you will learn a number of techniques for creating "optimal"
portfolios. The optimality of a portfolio depends heavily on the model used for defining
risk and other aspects of financial instruments. Here is a particularly simple model that is
amenable to linear programming techniques. Consider a mortgage team with
$100,000,000 to finance various investments. There are five categories of loans, each
with an associated return and risk (1-10, 1 best):
Loan/investment
Return (%)
Risk
First Mortgages
9
3
Second Mortgages
12
6
Personal Loans
15
8
Commercial Loans
8
2
Government Securities
6
H
Any uninvested money goes into a savings account with no risk and 3% return. The goal
for the mortgage team is to allocate the money to the categories so as to:
(a) Maximize the average return per dollar
(b) Have an average risk of no more than 5 (all averages and fractions taken over the
invested money (not over the saving account)).
(c) Invest at least 20% in commercial loans
(d) The amount in second mortgages and personal loans combined should be no higher
than
the amount in first mortgages.

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