Question

LP Assignment

Derinx Investments is a financial services firm that manages funds for numerous clients. The company uses a proprietary asset allocation model that recommends the portion of each client’s portfolio to be invested in exchange-traded fund, income fund and hedge fund.

To maintain diversity in each client’s portfolio, the firm places limits on the percentage of a portfolio that may be invested in each of the three funds, and assigns a limit on the portfolio’s risk index.

A new client, Loretta Jobs should be advised on allocation of $800,000. Based on an evaluation of the client’s risk tolerance, the Derinx Investments assigned a maximum risk index of .05 to the portfolio. The firm’s risk indicators show the risk rating for the exchange traded fund at .1, while the risk ratings for income fund and hedge fund are at .07 and .01 respectively. An overall portfolio’s risk index is computed as a weighted average of the risk rating for the three funds, where the weights are the fraction of the portfolio invested in each of the funds. Higher value of the risk index represents a more risky portfolio.

To maintain diversity the following investment guidelines are used:

The amount invested in exchange-traded fund should be between 20% and 40% of the total portfolio value.
The amount invested in income fund should be between 20% and 50% of the total portfolio value.
At least 30% of the total portfolio value must be in in hedge fund.

Furthermore, the amount invested in exchange-traded fund should not exceed the amount invested in income fund.

The firm is forecasting annual yields (returns) of 16% for the exchange-traded funds, 10.25% for income fund and 7.5% for the hedge fund.

Based on the information provided, how should the new client be advised to allocate the $800,000 among the three funds to maximize the overall yield from the portfolio?

Formulate a linear programming model for this portfolio selection problem (define decision variables, write down the objective function, develop constraints – show all steps/calculations) and solve it using Excel’s Solver. Generate Answer report and sensitivity reports.

Answer 1

Exchange traded fund, x,

Income fund, y

Hedge fund , z

Allocation of $800,000

x+y+z <= 800,000 - Constraint 1

Risk Rating : Exchange traded fund, x – 0.1 , Income fund, y – 0.07, Hedge fund , z - 0.01

Derinx Investments assigned a maximum risk index of .05 to the portfolio. An overall portfolio’s risk index is computed as a weighted average of the risk rating for the three funds, where the weights are the fraction of the portfolio invested in each of the funds.

0.1(x/(x+y+z)) + 0.07(y/(x+y+z)) + 0.01 (z/(x+y+z)) <= 0.05

0.1x + 0.7 y + 0.01z <= 0.05(x+y+z)  - Constraint 2

The amount invested in exchange-traded fund should be between 20% and 40% of the total portfolio value.

X >= 20% *(x+y+z)  - Constraint 3.a

X <= 40% (x+y+z) -  Constraint 3.b

The amount invested in income fund should be between 20% and 50% of the total portfolio value.

Y >= 20% *(x+y+z) -  Constraint 4.a

Y <= 50% (x+y+z) -  Constraint 4.b

At least 30% of the total portfolio value must be in in hedge fund.

Z >= 30% (x+y+z) - Constraint 5

Amount invested in exchange-traded fund should not exceed the amount invested in income fund.

X<= y  

x-y <= 0 - Constraint 6

The firm is forecasting annual yields (returns) of 16% for the exchange-traded funds, 10.25% for income fund and 7.5% for the hedge fund.

Maximise : 16% x + 10.25% y + 7.5% z

Enter the data in Excel :

Report :