The dollar and the yen fell sharply against the euro on Friday as a rally in stocks around the world and fresh government aid for U.S. banks revived investor optimism and some risk appetite.

The euro also was recovering from a sell-off in the previous session as traders reassessed European Central Bank President Jean-Claude Trichet’s comments following the ECB’s decision to cut rates by a half percentage point to 2 percent.

“We have a much healthier risk appetite. That’s definitely helping the euro,” said Boris Schlossberg, director of currency research at GFT Forex in New York.

The market was re-thinking the implications of comments on Thursday by Trichet, who said any further ECB rate cuts will be postponed until March at the earliest and dismissed the idea of cutting rates close to zero, as the United States and Japan had, analysts said.

“Essentially, there’s going to be a floor on European rates…which will leave the euro with a moderately higher yield than the dollar and the yen,” Schlossberg said.

In early trading in New York, the euro gained 1.2 percent to $1.3314 , rebounding from a five-week low of $1.3025 hit on Thursday, according to Reuters data.

The euro rallied 2.1 percent to 120.52 yen , while the dollar gained 0.8 percent to 90.51 yen .

Risk appetite picked up on Friday with stocks rallying after Bank of America received a $20 billion government capital injection, overshadowing signs of more fallout from the credit crisis for the financial sector.

Those measures along with the prospect of another bank lending package in Britain eased investor concerns and boosted higher-yielding currencies such as the Australian and New Zealand dollars.

“The fact that we are now seeing the U.S. and even UK authorities looking at further help for the financial and banking system have provided some relief,” BNP Paribas senior currency strategist Ian Stannard said in London.

“While the equity market rebound continues, we’re likely to see euro/dollar maintain its current recovery,” he added.

The dollar lost more ground against the euro after a Treasury Department report showed investors sold U.S. Treasury bonds in November for the first time since August 2007, when the credit crunch began. Foreign selling of U.S. Treasuries amounted to $22.88 billion compared with inflows $32.87 billion the previous month.

Net capital inflows into the United States fell to $56.8 billion in November from a revised inflow of $260.6 billion in October, according to the report.

MORE AID

The aid for Bank of America followed the U.S. Senate’s decision to allow the second half of a $700 billion bank bailout program, handing an early political victory to President-elect Barack Obama, who will be sworn in next Tuesday.

Also, Democratic leaders in the House of Representatives have unveiled an $825 billion tax cut and spending bills they hope will help Obama reverse the economic slump, offsetting fears of soaring losses at the top three U.S. banks.

The Australian and New Zealand dollars gained 1.8 percent and 2 percent versus the U.S. currency respectively .

Sterling also surged, rising 2.1 percent to $1.4953.

Despite the boost from the news about government aid,worries about the banking sector were not far from investors’ minds, as Citigroup and Bank of America both reported a fourth quarter loss. Citigroup also said it would split into two operating units.

Meanwhile, Ireland nationalized its third largest lender, Anglo Irish Bank .

NEW YORK, Jan 16 (Reuters)