The promise of accelerating economic growth overseas is propelling investor funds into the yen, euro and many emerging-market currencies, intensifying a yearlong siege on the U.S. dollar.

The ICE Dollar Index hit its lowest level in more than three years on Friday, extending a nearly 10% decline last year that marked the dollar’s steepest annual fall since 2003. The index tracks the value of the currency vs. a basket of U.S. trading partners.

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