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Efficient frontier

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Title: Efficient frontier  
Author: World Heritage Encyclopedia
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Subject: Risk parity, Portfolio optimization, Asset allocation, Chartered Financial Analyst, Mathematical finance
Publisher: World Heritage Encyclopedia

Efficient 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. 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 usually represented by the standard deviation of the portfolio's return).[2] Here, every possible combination of risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The positively-sloped (upward-sloped) part of the left boundary of this hyperbolic region is then called the "efficient frontier." The efficient frontier is the portion of the opportunity set that offers the highest expected return for any given level of risk, and lies at the top of the opportunity set (the feasible set).


  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.  
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