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

capital allocation line is the efficient frontier.

In modern portfolio theory, the **efficient frontier** (or **portfolio frontier**) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum.
Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk).^{[1]}
The efficient frontier was first formulated by Harry Markowitz in 1952;^{[2]}
see Markowitz model.

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Overview

Parametric plot (as a function of weights

$\beta$) of the expected return and the expected risk for different correlations. The efficient frontier is the upper part of the corresponding curves.

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).^{[3]} 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^{[4]} 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. All portfolios between the risk-free asset and the tangency portfolio are portfolios composed of risk-free assets and the tangency portfolio, while all portfolios on the linear frontier above and to the right of the tangency portfolio are generated by borrowing at the risk-free rate and investing the proceeds into the tangency portfolio.