How can I set this question up in Lindo?
Client has 800,000 that must be invested in 3 funds. 20 to 40% invested in growth fund, 20 to 50% in income fund and at least 30% in money market fund. Client has a max risk index of 0.05. Risk indicators - growth fund is 0.10, income fund is 0.07 and money market is 0.01. Portfolio risk index is computed as a weighted average of risk rating for the three funds where the weights are the fraction of the clients portfolio invested in each of the funds.
Yields are growth - 18%, income fund - 12.5% and money market - 7.5%.
I need to determine the annual % yield for each of the investments.
To set up this question in Lindo, you would need to define the decision variables, objective function, and constraints. Here's a step-by-step guide for setting it up:
Step 1: Define the decision variables:
Let's denote the amount invested in the growth, income, and money market funds as G, I, and M, respectively. These variables represent the fractions of the client's portfolio invested in each fund.
Step 2: Set up the objective function:
The objective is to maximize the annual yield of the portfolio. The annual yield for each fund can be calculated as the product of the amount invested in that fund and its corresponding yield. Therefore, the objective function is:
Maximize: 0.18 * G + 0.125 * I + 0.075 * M
Step 3: Define the constraints:
The constraints are as follows:
- The total investment amount must be equal to $800,000:
G + I + M = 800,000
- The fraction invested in the growth fund should be between 20% and 40%:
0.2 * (G + I + M) <= G <= 0.4 * (G + I + M)
- The fraction invested in the income fund should be between 20% and 50%:
0.2 * (G + I + M) <= I <= 0.5 * (G + I + M)
- The fraction invested in the money market fund should be at least 30%:
M >= 0.3 * (G + I + M)
- The risk index of the portfolio should be less than or equal to 0.05:
(0.10 * G + 0.07 * I + 0.01 * M) / (G + I + M) <= 0.05
Step 4: Solve the LP problem:
Use the Lindo software to input the objective function and the constraints defined above. Solve the LP problem using Lindo, which will provide you with the optimal values of G, I, and M.
Step 5: Calculate the annual % yield for each investment:
Using the optimal values of G, I, and M obtained from Lindo, calculate the annual % yield for each investment by multiplying the yield of each fund by the respective amount invested.
That's it! Following these steps should help you set up the LP problem in Lindo and determine the annual % yield for each investment.