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Link:

A carry trade is a strategy in which an investor borrows money at a low interest rate in order to invest in an asset that is likely to provide a higher return. This strategy is very common in the foreign exchange market. For example, in the period up to 2007 many investors borrowed in Japanese yen or Swiss francs, taking advantage of very low interest rates in Japan and Switzerland, and used the money to take long positions in currencies backed by high interest rates, such as the Australian and New Zealand dollars and South African rand.

This strategy relies on relative stability in asset prices, as an adverse exchange rate movement can easily wipe out the returns from the underlying interest rate differential. This leads some to refer to the carry trade as akin to picking up pennies in front of a steamroller.The yen carry trade reversed sharply in 2007 as global interest rate differentials narrowed, causing the yen to rally against currencies such as the antipodean dollars.

to rally against something obviously means to protest against something. But I don't really understand what that means in the context of foreign currencies. Any idea?

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    When yen rallies against dollar, it means there is a war-like competition between yen and dollar. Literally, yen has declared war on dollar. – MAKZ Apr 10 '15 at 16:57
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See rally sense 9:

9) (finance) to rise in price after having fallen (said of stocks, etc.).

So it is saying the yen increased in price compared to other currencies.

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