Money trade, Inc. Moneytrade, Inc. is an investment advisory firm that manages m

Question

Money trade, Inc. Moneytrade, Inc. is an investment advisory firm that manages more than S120 million in funds for its numerous clients. The company uses an asset allocation model that recommends the portion ofeach client's portfolio to be invested in a growth stock fund, an income fund, equity fund and a money market fund. To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each ofthe four funds. General guidelines indicate that the amount invested in the growth fund must be between 15 and 35% of the total portfolio value. Similar percentages for the other three funds stipulate that between 25 and 50% ofthe total portfolio value must be in the income fund, 10 and 20% of the total portfolio value must be in the equity -funds and that at least 35% of the total portfolio value must be in the money market fund. In addition, the company attempts to assess the risk tolerance ofeach client and adjust the portfolio to meet the needs ofthe individual investor. For example, Money trade just contracted with a new client who has $1,100,000 to invest. Based on an evaluation of the client's risk tolerance, Money trade assigned a maximum risk index of 0.05 of the total invested by the client. The firm's risk indicators show the risk of the growth fund at 0.105, the income fund at 0.07, the equity fund at .055 and the money market fund at 0.02. An overall portfolio risk index is computed as a weighted average of the risk rating for the four funds, where the weights are the fraction of the client's portfolio invested in each of the funds. Additionally, Moneytrade is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, 10.1% for the equity and 7.5% for the money market fund. Based on the information provided, how should the new client be advised to allocate the si,100,000 among the growth, income, equity and money market funds? Develop a linear ming model that will provide program

Explanation / Answer

A. Maximise the yield from the total investment, with the constraint that the overall portfolio risk index is less than or equal to 0.05. Also the investments should be such that the distribution across various funds must be as mentioned, that is for example it must be between 15 and 35% in growth funds, must be at least 35% in market fund and such. Here the decision variables are distribution of investment across various funds, like investment in growth fund, investment in market fund, investment in income fund and investment in equity fund.

B. Let a denote the % investment in growth funds, b investment in income fund, c investment in equity fund and finally d investment in market fund then the problem is to

maximise: 18/100 a + 12.5/100 b + 10.1/100 c + 7.5/100 d;

subject to

15 <= a <= 35;
25 <= b <= 50;
10 <= c <= 20;
35 <= d <= 100;
a + b + c + d = 100;
and
(a 0.105 + b 0.07 + c 0.055 + d 0.02)/100 <= 0.05;

The following solution was obtained for this LPP using Lp_solve (a Mixed Integer Linear Programming (MILP) solver)

a                         16.4706
b                              25
c                              10
d                         48.5294

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