Efficient frontier

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This article is about the financial mathematical concept. For other frontiers described as efficient, see Production possibilities frontier and Pareto frontier.
Efficient Frontier. The hyperbola is sometimes referred to as the 'Markowitz Bullet', and its upward sloped portion is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight line is the efficient frontier.

The efficient 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[edit]

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[edit]


  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.