* Dollar bounce after Fed meeting short-lived
* Greenback pares gains against yen
* Euro strengthens
(New throughout, updates prices, market activity and comments)
By Stephanie Kelly
NEW YORK, Feb 1 (Reuters) - The dollar fell on Thursday against a basket of currencies, with the euro rising due to growing investor optimism in the economies that use the single currency.
In January, the dollar fell 3.25 percent, its biggest monthly decline since March 2016. On Wednesday it got a bump up after the Federal Reserve said it expected inflation to rise this year, making investors hopeful that more interest rate hikes were way. "Unless there's any sort of significant news or development that would suggest a reason to start buying dollars, I think the market is content in buying euros for the time being, or at least remaining long on euros," said Mazen Issa, senior FX strategist at TD Securities in New York.
The dollar index , which tracks the greenback against six major currencies, rose briefly after the Fed announcement and climbed again overnight in Asian trading.
However, the index later pulled back and was down 0.62 percent at 88.583 at 3:51 p.m. EST(2051 GMT). It hit its lowest on Thursday since Jan. 26, when the dollar hit a three-year low.
"From a very short-term point of view, it just seems like the dollar is lacking inspiration and it can't catch a break," TD's Issa said.
Against the Japanese yen the dollar rose 0.08 percent to 109.26 yen. Last Friday, the dollar hit 108.27 against the yen, its lowest since September.
Traders are looking ahead to the U.S. government's jobs report on Friday, which will include data on nonfarm payrolls and average hourly earnings.
The dollar has struggled this year as expected monetary policy-tightening in other parts of the world, along with stronger global economic growth, encouraged investors to put more of their money elsewhere, particularly the euro zone.
Meanwhile, the euro rose against the dollar by 0.76 percent to $1.2514, supported by a survey on Thursday that showed euro zone manufacturing was booming. The single currency reached a three-year high above $1.25 in January and ended the month up 3.54 percent amid expectations that the European Central Bank would begin normalizing monetary policy this year.
That prospect got a boost earlier on Wednesday after last month's underlying euro zone inflation picked up pace. Sterling rose 0.56 percent to $1.427.
The Australian dollar fell 0.15 percent to $0.8042, after its recent run-up came to an end.
On Thursday bitcoin slipped to its lowest since November 2017 on the Luxembourg-based Bitstamp exchange as a Facebook ban on cryptocurrency advertisements and a growing regulatory backlash against the nascent market rattled investors. It last fell 11.56 to $8,976.12.
<^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Fairly valued World FX rates in 2018 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^>(Reporting by Stephanie Kelly; Editing by Lisa Von Ahn and David Gregorio)
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