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Investment portfolio which occupies the "efficient" parts of the risk-return spectrum
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
.
Overview
[
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]
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.
Among certain universes of assets, academics have found that the efficient frontier (the Markowitz model, more broadly) has been susceptible to issues such as model instability where, for example, the reference assets have a high degree of correlation.
[5]
See also
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References
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