Extending the existing analysis to include all risky assets, and combinations of risky assets, is restricted by the infinite number of possibilities that must be considered. However, by assuming that investors prefer more return to less, and less risk to more, the set of risky portfolios an investor may consider holding can be restricted to an efficient set of portfolios. This efficient set of portfolios cannot include interior portfolios i.e those in which there exists a portfolio that has more risk for the same return, or less return for the same risk.
As figure 3.4 illustrates, the efficient set therefore consists of the concave2 curve of all portfolios that lie between the global minimum-variance portfolio and the maximum return portfolio: often called the efficient frontier.
2Since a linear relationship is both concave and convex, we can refer to the efficient frontier as concave.