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In practice, when one takes on a large equity ETF position, I would imagine it's not necessarily "optimal" to hedge using a basket of all the constituents even though that should be a perfect hedge. What's the common approach to picking an optimal hedge basket given constraints on its size?

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    $\begingroup$ In statistics, I would run PCA analysis to determine constituents that define 90%, 95% or any desired level volatility of the underlying. $\endgroup$ – Sergey Bushmanov Oct 14 '15 at 17:29
  • $\begingroup$ That seems reasonable - I feel naive approach of truncating off smallest constituents wouldn't be optimal but not 100% on why. $\endgroup$ – Palace Chan Oct 14 '15 at 17:37
  • $\begingroup$ My strong feeling, approximating ETF returns with a pruned basket of underlyings is a statistical exercise. And the commonly accepted approach to this problem in statistics is PCA, as i said. In fact, I saw this suggestion in some "python for finance" books, do not remember the name. As to pruning constituents with smallest weights.... what if a company with 1% weight has unusually high volatility thus impacting returns of the total ETF??? $\endgroup$ – Sergey Bushmanov Oct 14 '15 at 17:44
  • $\begingroup$ That makes sense. It's the best approximation with less dimensions where metric is return difference. Doesn't seem like you can get away with something simple to run "real-time" $\endgroup$ – Palace Chan Oct 14 '15 at 17:52
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    $\begingroup$ to clarify a bit on my earlier hasty statement #1 : PCA will return new "factors" (PC1, PC2, PC3 ... PCN, where N is the number of constituents in ETF) with their contribution to return volatility, NOT constituents volatility. So, you would need to look at the loadings of the several PC's that deliver desired level of approximation. $\endgroup$ – Sergey Bushmanov Oct 14 '15 at 19:09

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