* Markets wait to see if Fed will finally taper stimulus
* Yen bounces back from 5-yr low vs dollar ahead of Fed
* Euro helped by euro zone PMIs, tighter money markets
By Anirban Nag
LONDON, Dec 16 (Reuters) - The euro rose against the dollar on Monday, as data showed business activity picking up in the euro zone and uncertainty over the Federal Reserve's stimulus kept investors away from the dollar.
The euro rose to $1.3773, recovering from a dip to around $1.3745 after a report that French private-sector activity slowed unexpectedly in December. A subsequent report showed German manufacturing activity beat expectations, and the Flash Eurozone Composite Purchasing Managers' Index (PMI) rose to 52.1 in December from 51.7 last month, also beating forecasts.
"Admittedly the French numbers were weak, but both the German manufacturing PMI and the composite euro zone numbers were better than expected and that is a relief for the euro," said Jane Foley, senior currency strategist at Rabobank. "They could have been a lot worse."
The data were not good enough to push the euro to the two-year high around $1.3833 it reached in October, and Foley said a lot would depend on what the Federal Reserve does this week.
The odds are the Fed's policy setting committee will make no major policy change when it meets on Dec. 17-18. But most recent U.S. economic data suggest the Fed's bond-buying programme will start to end sooner rather than later.
Nevertheless, U.S. yields fell on Monday, dragging down the dollar index. The index was trading 0.25 percent lower at 80.010.
Alvin Tan, a currency strategist at Societe Generale, said rate differentials between the euro zone and the U.S. had narrowed, but they remain elevated and that is likely to support the euro.
Euro zone money-market rates have tightened in the past few weeks, improving the euro's appeal. As euro zone banks repay cheaper loans to the European Central Bank, the bank's balance sheet should shrink further. In contrast, the Fed and the Bank of Japan are printing vast sums of money, weakening the dollar and the yen.
Also driving euro strength are European banks repatriating funds to shore up their capital bases before a European Central Bank Asset Quality Review.
The yen rose as investors bought the safe-haven currency amid tepid Chinese manufacturing data that kept alive worries about a global recovery. An uptick in Japanese business sentiment supported the yen at the margins, but most analysts said the gains probably will not last.
"The central bank is printing money and the majority of analysts even expect it to increase the volume of bond purchases in 2014," Lutz Karpowitz, currency strategist at Commerzbank wrote in a note. "The yen has everything required to come under further pressure, and Tokyo also welcomes a weak yen."
The dollar was down 0.2 percent at 103.04 yen. The euro was marginally lower 141.90 yen
Selling the yen has been a popular trade as investors bet the Bank of Japan will maintain its ultra-loose monetary policy and may even ease further next year when a sales tax hike kicks in. The BOJ is widely expected to keep its monetary settings unchanged at its Dec 19-20 review.
Data from a U.S. financial watchdog showed speculators' net yen short positions were near six-year highs last week.