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Suppose want to long an inverse of an ETF, rather than short the ETF itself. Is there a way to determine some mix of component stocks that would mimic the returns of such an inverse ETF (where also have the constraint that don't want any of the weights of the component stocks of this inverse to be negative either)? Also, what would be a better way to phrase this problem as to give some better google results to look into?

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    $\begingroup$ In practice it is very difficult or impossible to find a set of stocks that are highly negatively correlated to another group of stocks. So inverse ETFs have to be short. $\endgroup$ – Alex C Dec 22 '18 at 14:44
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A basket of stocks which is long-only will always have a positive beta to the market.

Shorting this basket will therefore mean you seek another portfolio with a negative beta.

As per the first remark this impossible to achieve synthetically with a long only portfolio.

Q.E.D.

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