Question

Fund	Expected Annual Return	Risk Measure
Izabella Low-priced Stock Fund	8.10%	10.82%
Izabella Multinational Fund	9.25%	13.67%
Izabella Mid-cap Stock Fund	7.23%	14.11%
Izabella Mortgage Fund	3.08%	3.19%
Izabella Income Equity Fund	7.88%	9.19%
Izabella Balanced Fund	4.17%	7.31%

Izabella Investments uses a proprietary algorithm to establish a measure of risk for its funds based on the historical volatility of the investments. The higher the volatility, the greater the risk. The company recommends that no more than $200,000 be invested in any individual fund, that at least $50,000 be invested in each of the multinational and balanced funds, and that the total amount invested in income equity and balanced funds be at least 40% of the total investment, or $200,000. The client would like to have an average return of at least 5% but would like to minimize risk (total risk would be the sum of the dollar amount invested in each fund times each risk measure, divided by the total amount invested. What portfolio would achieve this? Please post excel formulas

Answer 1

We will solve this problem using linear programming. Excel setup with screenshots is shown below:

Go to File-> Options-> Excel Add ins -> Solver Add in

Now go to Data -> Solver and setup Solver with decision variables, objective function and constraints.

Click on Solver to get the optimal solution.

Optimal portfolio to achieve the requirement is:

Fund	Amount invested
Izabella Low-priced Stock Fund	$                                       -
Izabella Multinational Fund	$                               50,000
Izabella Mid-cap Stock Fund	$                                       -
Izabella Mortgage Fund	$                             200,000
Izabella Income Equity Fund	$                             153,934
Izabella Balanced Fund	$                               50,000

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