Borrowing the dollar cheaply to fund purchases of higher-yielding assets was a no-brainer in 2009, thanks to the Federal Reserve's repeated assurances that U.S. interest rates would stay low for an extended period.

The carry trade, as this strategy is known, may not be as sure a bet in 2010, though, particularly if fears of deflation in Japan and unsustainable deficits in Europe escalate, making the dollar's path unclear.

Investors received a sneak preview this month when the euro retreated from a 16-month high above $1.51 to a 3-1/2-month low below $1.43.

That was in sharp contrast to the sell-the-dollar trend that persisted for most of 2009, as the greenback shed over 15 percent against major currencies between March and November. The trend gave rise to the carry trade, as investors are more likely to engage in such transactions if they're confident in low volatility in the funding currency.

Some of the December move is surely tied to profit-taking as the year winds down, but analysts have been quick to flag a subtle shift in the psychological landscape as well.

This is a preview of what we expect to see later in 2010, said Brown Brothers Harriman strategist Win Thin. Dollar weakness will resume in the first quarter, but the economy will improve, and that will sow the seeds for a dollar turnaround.

The problem is uncertainty, which is radioactive to the carry trade, and analysts agree that uncertainty looks to be the only certain feature of 2010.

Will a nascent U.S. recovery pick up steam and become sustainable? Will the risk of sovereign defaults around the world increase? Can emerging markets continue to drive growth?

After a schizophrenic 2009, which began with the world in the depths of the worst crisis in 70 years and ended with the S&P 500 headed for its best year since 2003, few know what to expect in 2010.

While the Fed reiterated its intention to hold rates low well into the new year, recent employment and consumer spending data have suggested the economic recovery is starting to gain traction.

The U.S. central bank also said it intends to shutter most of its emergency lending programs by February, another sign of confidence in the economy and a potential boon for the buck.

And even if U.S. interest rates do nothing more than edge up from zero to 0.5 percent next year, they are still seen as likely to be moving more quickly than those in Japan or Europe. The Bank of Japan this week, after months of studiously avoiding the mere mention of deflation, abruptly changed course and recognized deflation as a critical challenge.

That suggests low Japanese interest rates for as far as the eye can see, which analysts said could make the yen a more attractive carry trade currency than the dollar.

The idea of the dollar as a funding currency was always fleeting at best. As soon as you have central banks pulling on the monetary policy levers, you'll see the yen left behind, said Samarjit Shankar, managing director of global FX strategy at BNY Mellon in Boston.

Investors favored the yen as a funding currency for the first half of the decade, and Shankar said the trade is much bigger -- and more stable -- than the dollar carry trade.

While Pi Economics estimated recently that the size of the dollar carry trade may have swelled to between $250 billion and $550 billion in the first half of 2009, analysts say the yen carry trade grew as large as $1 trillion between 2004 to 2007.

Of course, a sustained dollar rally will require evidence of sustained U.S. expansion, and the jury's still out on that.

Record U.S. public debt and budget deficits do not look set to fade away soon, either, even if the Fed starts winding down emergency lending and shrinking its balance sheet in 2010.

The euro could trade all the way down to $1.40, said Firas Askari, head of FX trading at BMO Capital Markets. But given the massive U.S. debt, I think it will bounce back.

But UBS strategist Mansoor Mohi-uddin said higher U.S. interest rates, fiscal worries in weak euro zone countries and an overvalued euro all argue for more dollar gains.

(Additional reporting by Gertrude Chavez-Dreyfuss; Editing by Leslie Adler)