The U.S. dollar’s thrashing on Thursday after a last-minute European deal to contain the debt crisis may have sealed the currency’s fate.

And it is all downhill from here.

The European agreement, which involves a 50 percent write-down of Greek debt and boosting the euro zone’s bailout fund to as much as 1 trillion euros, has averted a collapse in Europe and spurred a rush to risky currencies and assets once again at the expense of the dollar.

Add in to the mix: a suddenly revitalized U.S. economy that a few weeks ago was teetering on the verge of recession and had fueled speculation about another round of quantitative easing. Almost overnight it leaves a whole new global outlook that appears a little more encouraging.

The dollar, with its near-zero interest rates guaranteed over the next two years, is the first to get sold off in times of global optimism, as investors use the greenback to fund the market’s foray into risky trades.

“When economic conditions are not deteriorating, there is a general risk-loving mode and the dollar will remain the primary funding currency,” said Alessio de Longis, portfolio manager for the Oppenheimer Currency Opportunities fund in New York.

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