Problem 2: Choosing an optimal investment mix

Some years have now passed, and Jane (from Problem 1) now feels more confident at making investment decisions. She has now accumulated a large amount in savings (partly from the sale of property that her business owned). She has $2 million, which she wishes to invest in some mix of cash, listed property, government bonds, and exchange-traded funds (ETFs). The long-term expected returns for each of these alternatives is as follows:

Investment Type    Expected return (%)

Cash                                3

Property                         5

Bonds                             7

ETFs                               12

Jane wishes to invest for only one year. She realizes that these estimates are long-term averages, and that there can be considerable variability from year to year, particularly with the investment types such as ETFs, so she does not wish to invest all of the $2 million in ETFs.

To reduce the risk, she has come up with the following constraints on how she will invest the $2 million dollars:

 No more than 50% of the funds should be invested in ETFs;

 At least 10% of the funds should be invested in cash;

 The amount in ETFs should be no more than double the amount invested in bonds;

 The combined amount invested in bonds and stocks should not be more than double the combined amount invested in cash and property;

 All of the available $2 million must be invested; and

 Each investment must be in multiples of $1,000.

Set this problem up as a linear programming model in Excel, and use your model to answer the following questions:

 How should the $2 million should be invested?

 What is the overall return (in dollars terms)?

 What is the overall return as a percentage of the $2 million invested?