In the March 1952 issue of Journal of Finance, Harry M. Markowitz published an article titled Portfolio Selection. In the article, he demonstrates how to reduce the risk of asset portfolios by selecting assets whose values aren't highly correlated. The concepts behind the Markowitz portfolio model were discussed in detail in the previous chapter in section Markowitz Portfolio Selection Model.  The basic idea is that, given a desired level of expected return, one should select a basket of assets that minimizes risk (i.e., variance in return).  Any other basket of assets would be inefficient in that it entails taking on extra risk without extra compensation.

The Markowitz model allows you to evaluate tradeoffs between risk and return.  By running the model for a series of different levels of return, you can see how portfolio risk must increase as desired return increases.  The return/risk tradeoff may be graphed, and this graph is known as the efficient frontier.  If we place risk on the vertical axis and return on the horizontal, then portfolios to the left of the efficient frontier are inefficient. This is because portfolios exist with the same amount of return but less risk.  Conversely, all (return,risk) pairs that lie to the right of the curve cannot be achieved given the current available asset pool.  Finally, all portfolios with (return,risk) combinations that lie on the curve are efficient—no portfolio can be found with the same level of return and lower risk.

We will now demonstrate how you can use the programming capabilities in LINGO to generate points along the efficient frontier by repeatedly solving the Markowitz model for a series of portfolio return values.