Mortgage Portfolio Optimization.
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 Mortgage 9 3
Second Mortgage 12 6
Personal Loans 15 8
Commercial Loans 8 2
Government Securities 6 1
Any uninvested money goes into saving 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 mortgage and personal loans combined should be no higher than the amount in first mortgage.
Questions:
1) Write out the entire linear programming model formulation for this problem.
2) Use Solver or Matlab to solve this problem.
3) What is the optimal solution and optimal value?