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minimum-variance portfolio and the glbal minimum-variance

Really basic question:
What’s the difference between the  minimum-variance portfolio and the glbal  minimum-variance portfolio.

all the points on the efficient frontier are MVPs. The MVP with minimum Variance is the global minimum variance portfolio.
All thumbs are fingers but not all fingers are thumbs. All Global min var portfolios are MVPs but not all MVPs are Global min var portfolios.
As far as i know GMVPs are 100% invested in the asset/asset class that has the lowest variance.

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Or as Frank would say, all Kardashians have huge butts, but not all huge butt ladies are Kardashians…

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