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Global Minimum-Variance Portfolios Across All Return Targets

Article Quant Q&A · Author: Richard Hardy
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Summary

The document asks what “global” means in the term global minimum-variance portfolio and how it differs from a minimum-variance portfolio. The accepted answer distinguishes the unconstrained search across all possible return levels from the common optimization that minimizes variance subject to a specified expected return.

Under that distinction, the global minimum-variance portfolio has the lowest variance among portfolios without fixing a target return. The answer also calls the terminology a possible misnomer and offers a tentative historical reference, but does not establish the origin of the term or discuss constraints such as short-sale limits. The exchange is a concise clarification of portfolio optimization terminology rather than a derivation or empirical analysis.

Key ideas

  • A minimum-variance portfolio is often defined subject to a chosen expected return.
  • The global minimum-variance portfolio minimizes variance across all possible return levels.
  • The document characterizes the word “global” as potentially misleading terminology.
  • It does not derive the portfolio weights or address practical portfolio constraints.

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Portfolio constructionStatistics
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# Terminology: "global" in "global minimum-variance portfolio"


# Terminology: "global" in "global minimum-variance portfolio"












I am confused about the meaning of "global" in "global minimum-variance portfolio". The sources that I have encountered so far do not explicitly state what "global" means. So what is the difference between "global minimum-variance portfolio" and "minimum-variance portfolio"? I will appreciate any pointers.

## Answer by Bob Jansen (score 4, accepted)

https://quant.stackexchange.com/a/75962

I think it's just a common misnomer, on Google Scholar I found a 1980 article by R. Roll: "Orthogonal Portfolio's" but I doubt the term was coined there.

I do think I understand why a global minimum variance portfolio is different from a 'regular' minimum variance portfolio. Many texts deal with finding a "minimum variance portfolio" given a level of return. The global minimum variance is then the portfolio with the lowest variance for all possible levels.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.