Does the traditional mean-variance optimization paradigm — to the extent that it holds for individual securities, such as stocks — hold also for, say, broad index tracking ETFs?

Are there any theoretical implications to the fact that these are already diversified portfolios? Statistically, ETF returns can, of course, be described by their means and by a covariance matrix, but is there a difference in interpretation economically?

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    $\begingroup$ In fact optimization applied to a small number of ETFs is much more realistic and useful than attempting to apply it to thousands of individual securities. $\endgroup$ – noob2 Jan 22 '18 at 15:38
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    $\begingroup$ On the other hand, there may be more multicollinearity. Multiple ETFs may hold the same instruments thereby increasing redundancy and overlap. $\endgroup$ – AlRacoon Jan 22 '18 at 16:01
  • $\begingroup$ Yes. The way to get around multicollinearity is to choose the ETFs judiciously (one US stock ETF, one bond ETF, one emerging market ETF, etc). You must avoid including two nearly identical ETFs. $\endgroup$ – noob2 Jan 22 '18 at 16:15
  • $\begingroup$ Even if you avoid look alike ETFs, if you select ETFs that are not market cap weighted (or other suboptimal selection method). You may be optimizing on baskets of suboptimal instruments and therefore not getting an efficient portfolio vis-a-vis one comprising the individual investable assets. $\endgroup$ – AlRacoon Jan 22 '18 at 16:28

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