Efficient Set

Now that we know about indifference curves and risk aversion, how can we use that to select from an almost infinite number of portfolios available for investment? The key lies in the efficient set theorem, which states that an investor will choose a portfolio from the set of portfolios that:

1.

Offer maximum expected return for varying levels of risk, and

2.

Offer minimum risk for varying levels of expected return.

We begin by constructing the feasible set, which represents all portfolios that could be formed from a group of N securities. The efficient set can now be located by applying the efficient set theorem to this feasible set. This demonstrates that all the portfolios in the efficient set are located on the "northwest" boundary of the feasible set, often called the efficient frontier. Selecting a portfolio is henceforth easy, by simply plotting the investor's indifference curves on the same figure as the efficient set and then proceed to choose the portfolio that is on the indifference curve that is "furthest northwest." An important property of the efficient set is that it is concave, the proof of which is outside the scope of this paper.

 

Figure: Graph displaying the feasible set (the dark area), the efficient set (the borderline between E and S is ) and some indifference curves. The optimal portfolio is marked with O^*.