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The problem lies in the definition of risk. It seems that in the cited paper, the authors treat risk as a concept connected with the uncertainty of the out-of-sample performance of the portfolio. In that way portfolios constructed using the proposed robust estimators would be what they call minimum-risk portfolios. Contrasted with minimum-variance ...

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Risk is a broader concept than variance. That paper is specifically focused on robust estimators (i.e., estimators that are less sensitive to outliers) of dispersion. A robust estimator of dispersion is not the same thing as variance (which may be a dispersion parameter for some classes of distributions). Nevertheless, these robust estimators could be used ...

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For academic references, you will likely have to look in the very early optimization literature. Uniqueness of the MV portfolio follows immediately from the lemma that a strictly convex function on a convex set has no local minima. The standard textbook reference is Convex Optimization by Boyd and Vandenberghe. See section 4.2.2 in particular. A free ...

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Answering "No" to the title question, I'll mention that variance is a rather poor measure of risk, even if convinient and nicely behaving. Variance is not even a risk measure, with the standard deviation eventully being a deviation risk measure, while not necessarily for downside risk (see David Nawrocki-"A Brief History of Downside Risk Measures" for ...

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This article by Eric Falkenstein is exactly what you are looking for: Early Low Vol Literature Now Everywhere EDIT Falkenstein has a new post out on the academic origins of the approach: Here

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