Submitted to J. D. Williams, Inc.
Industrial Engineering Department
Southern Polytechnic State university
February 20, 2008
This report is our recommendation for an optimal investment strategy that would allow J. D. Williams, Inc. to maximize the annual yield of an investment of $800,000 in a diversified portfolio of funds.
To find the investment that would result in the greatest annual yield we have formulated a linear program that takes into account the requirements for the client of J. D. Williams, Inc. The requirements for the investment portfolio can be found on the section titled “Problem Description”
The greatest annual yield that can be expected while subject to the requirements of the different funds and the prospective client is $94,133.33. The money has to be invested in the following manner to achieve this result: The amount to be invested in the growth fund must be $ 248,889. The income fund must have an investment of $ 160,000 and the money market fund must have an investment of $ 391, 112.
J. D. Williams, Inc. has a client who wishes to invest $800,000 with the firm in order to maximize his yield after a period of one year. The firm wants to allocate the funds while accommodating some requirements related to portfolio composition and the risk index of the funds as well as the client. The portfolio must have investments in 3 funds: a growth fund, an income fund, and a money market fund. There are also several requirements as to the composition of the investment. There are also several requirements as to the composition of the investment. The amount invested in the growth fund must be between 20% to 40% of the total portfolio value. The amount invested in the income fund must be between 20% to 50% of the total portfolio value. The amount invested in the money market fund must be greater than 30% of the total portfolio value. J. D. Williams, Inc. has assigned a maximum risk index for their client of .05. The firm must additionally take into account the risk indexes assigned to the different funds. The risk index for the growth fund is .10, the risk index for the income fund is .07, and the risk index for the money market fund stands at .01. The expected annual yields of the different investments are 18% for the growth fund, 12.5% for the income fund and 7.5% of the money market fund.
Based on the information provided by J.D. Williams, Inc. we can use linear programming to evaluate the best investment portfolio which will minimize risk and maximize annual yield.
Since the final criteria for evaluating the portfolio will be annual yield maximization we can create our objective function using the respective coefficients to get our final answer. The coefficients will be .18 for the growth fund, .125 for the income fund, and .075 for the money market fund. Our objective function is as follows
.18 x1 + .125 x2 + .075 x3
The money invested in the three funds must equal the total amount of the investment, which will give us our first constraint.
x1 + x2 + x3 = 800, 000
We also need to accommodate all the requirements listed by J. D. Williams, Inc in order to maximize profit while following the portfolio composition is kept within the guidelines. These are the constraints which tell us how the portfolio must be made up. x1 > 160, 000
x1 < 360, 000
x2 > 160, 000
x2 < 400, 000
x3 > 240, 000
Finally to finish our linear programming model we must turn our last requirement into an inequality. The last requirement is to have the corresponding risk indexes of the funds be less than the risk index assigned by the J. D. Williams, Inc. to their client. The constraint to represent this requirement is: .05 x1 + .02 x2 - .04 x3 < 0
Our complete linear programming model is as follows
Max .18 x1 + .125 x2 + .075 x3
x1 + x2 + x3 = 800, 000...