Management Science Methods

Financial Applications- Portfolio Selection

1. Define the Decision Variables

𝐺𝑖= amount of new investment in government bonds in month i (for i = 1, 2, 3, 4)

𝐶𝑖= amount of new investment in construction loans in month i (for i = 1, 2, 3, 4)

𝐿𝑖= amount invested locally in month i, (for i = 1, 2, 3, 4)

2. Define the Objective Function

Maximize total interest earned in the 4-month period: Max (interest rate on investment) x (amount

invested)

Max .02G1 + .02G2 + .02G3 + .02G4 + .06C1 + .06C2 + .06C3 + .06C4 + .0075L1 + .0075L2 + .0075L3

+ .0075L4

3. Define the Constraints

Month 1's total investment limited to $20 million:

(1) G1 + C1 + L1 = 20,000,000

Month 2's total investment limited to principle and interest invested locally in Month 1:

(2) G2 + C2 + L2 = 1.0075L1

or G2 + C2 - 1.0075L1 + L2 = 0

Month 3's total investment amount limited to principle and interest invested in government bonds in

Month 1 and locally invested in Month 2:

(3) G3 + C3 + L3 = 1.02G1 + 1.0075L2

or - 1.02G1 + G3 + C3 - 1.0075L2 + L3 = 0

Month 4's total investment limited to principle and interest invested in construction loans in Month 1,

government bonds in Month 2, and locally invested in Month 3:

(4) G4 + C4 + L4 = 1.06C1 + 1.02G2 + 1.0075L3

or - 1.02G2 + G4 - 1.06C1 + C4 - 1.0075L3 + L4 = 0

$10 million must be available at start of Month 5:

(5) 1.06C2 + 1.02G3 + 1.0075L4 > 10,000,000

Non-negativity:

Gi, Ci, Li > 0 for i = 1, 2, 3, 4