Efficient frontier

This article is about the financial mathematical concept. For other frontiers described as efficient, see Production possibilities frontier and Pareto frontier.

The efficient frontier (or portfolio frontier) is a concept in modern portfolio theory introduced by Harry Markowitz^[1] and others in 1952. It is the set of portfolios each with the feature that no other portfolio exists with a higher expected return but with the same standard deviation of return.

Concept overview

A combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk (which is represented by the standard deviation of the portfolio's return).^[2] Here, every possible combination of risky assets can be plotted in risk–expected return space, and the collection of all such possible portfolios defines a region in this space. In the absence of the opportunity to hold a risk-free asset, this region is the opportunity set (the feasible set). The positively sloped (upward-sloped) top boundary of this region is a portion of a hyperbola and is called the "efficient frontier."

If a risk-free asset is also available, the opportunity set is larger, and its upper boundary, the efficient frontier, is a straight line segment emanating from the vertical axis at the value of the risk-free asset's return and tangent to the risky-assets-only opportunity set.

See also

• Modern portfolio theory

References

1. Harry Markowitz (1952). Portfolio-Selection. The American Finance Association. pp. 77–91.
2. Edwin J. Elton and Martin J. Gruber (2011). Investments and Portfolio Performance. World Scientific. pp. 382–383. ISBN 978-981-4335-39-3.