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.

  • $\begingroup$ I don't know, but I've seen "global" refer to "all developed markets" or even "all developed and emerging markets", as opposed to some specific country like the U.S. or some region like Western Europe or North America. The universe of possible univestments is restricted to this geographical region, and then the optimizer selects a portfolio. I haven't seen it used to describe multiple asset classes. $\endgroup$ Commented Jun 26, 2023 at 17:53
  • $\begingroup$ @DimitriVulis, yes, I have seen it in that context, too, but not only. In many cases it seems that global has nothing to do with geography. Within that, in some (many?) cases it has nothing to do with the set of assets under consideration (the entire set versus some subset thereof) either. $\endgroup$ Commented Jun 26, 2023 at 19:48

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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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    $\begingroup$ I also think it's simply the global as opposed to local optimum (true for the entire set whereas local means it is true in some vicinity.) See for example CFA prep. $\endgroup$
    – AKdemy
    Commented Jun 26, 2023 at 18:48
  • $\begingroup$ Regarding Many texts deal with finding a "minimum variance portfolio" given a level of return: as in mean-variance optimization and in contrast to variance minimization (the latter regardless of the mean)? $\endgroup$ Commented Jun 26, 2023 at 19:10
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    $\begingroup$ Indeed, and maybe a bit broader as well: you can have a minimum variance given for a required return rate but you can also think of other constraints such as no short selling or 0 beta that have lead to an achievable minimum that is higher than the global minimum. $\endgroup$
    – Bob Jansen
    Commented Jun 26, 2023 at 19:23

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