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Unless you are also hedging the local currency return, you cannot also hedge the currency risk completely.

This is because the return on a foreign investment is the sum of:

(1) Return of the investment in it's local currency
(2) The local currency appreciation or depreciation versus the investors domestic currency.
(3) The cross product of 1 & 2 above.

You can normally only hedge (2), which leaves (1) and (3) un-hedged. However, if you also need to hedge (1), you are then enabled to hedge (3) also, because now (1) and (2) are known ex-ante.

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