Management Science Methods

Financial Applications- Portfolio Selection

LP can be used in financial decision-making that involves capital budgeting, make-or-buy, asset allocation,

portfolio selection, financial planning, and more. Portfolio selection problems involve choosing specific

investments – for example, stocks and bonds – from a variety of investment alternatives. This type of

problem is faced by managers of banks, mutual funds, and insurance companies. The objective function

usually is maximization of expected return or minimization of risk.

Example:

Winslow Savings has $20 million available for investment. It wishes to invest over the next four months in

such a way that it will maximize the total interest earned over the four-month period as well as have at least

$10 million available at the start of the fifth month for a high rise building venture in which it will be

participating.

For the time being, Winslow wishes to invest only in 2-month government bonds (earning 2% over the 2-

month period) and 3-month construction loans (earning 6% over the 3-month period). Each of these is

available each month for investment. Funds not invested in these two investments are liquid and earn

0.75% per month when invested locally.

Formulate a linear program that will help Winslow Savings determine how to invest over the next four

months.

Hint 1: You need 12 decision variables for 3 types of investment (government, construction, local) in 4

months. Use index for the month.

Hint 2: Objective function is:

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

Hint 3: one constraint for each of the followings:

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

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

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

in Month 1 and locally invested in Month 2

4. 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

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

Hint 4: Can you invest negative amount of money?