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is there an financial product linked to the GDP of the US (or other countries)?

There are plenty of derivatives and certificates whose underlying equity is the Dow Jones, which makes it possible to speculate on the performance of the Dow Jones.

I am looking for a product that allows me to speculate on the growth of the GDP.

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    GDP can only be imperfectly measured and normally with a lag. In principle you could construct a contract on announced GDP estimates, but normally broad market performance is a close enough proxy that it is preferred. – farnsy May 17 '15 at 23:05
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The closest thing that you are looking for would be FOREX exchanges. Currency value is affected by the relative growth of economies among other things, and the arbritrage of currencies would enable you to speculate on the relative growth of an individual economy.

  • A lot of things will be positively correlated with GDP, but I think the OP is looking for something that tracks GDP and nothing else. – Ganesh Sittampalam May 17 '15 at 21:28
  • I can't think of any way to construct something linked only to GDP unless it was operated as a pure betting pool with no intrinsic value. – keshlam May 17 '15 at 22:21

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