* Euro's 2-1/2 peak against dollar within sights
* Commodity currencies rally again
* Graphic: World FX rates in 2017 By Tommy Wilkes
LONDON, Jan 2 (Reuters) - The euro climbed to a four-month high against a broadly weaker dollar on Tuesday, the first trading day of 2018, on optimism over a brightening economic picture in the euro zone.
It finished 2017 with its best year against the dollar since 2003 as European economies strengthened and expectations the European Central bank will wind down its monetary stimulus grew, boosting demand for the single currency.
The euro started the year by adding to those gains, climbing 0.3 percent to $1.2046 at 0839 GMT, within sights of the $1.2092 it hit in September, the highest since early 2015.
The single currency was also higher against the Japanese yen at 135.64 , reaching levels not seen since late 2015.
Alvin Tan, an FX strategist at Societe Generale in London, said the end of a dollar funding squeeze typical of December, as well as a rally in commodity prices, had reduced demand for dollars since the holiday season, but the euro was also gaining because of the better economic performance of its member states.
"Fundamentally, what is helping the euro is the brightening economic outlook in the euro area. The momentum should continue," he said.
Euro zone manufacturers ended 2017 by ramping up activity at the fastest pace in more than two decades, a survey showed on Tuesday, and rising demand suggests they will start the new year on a high.
Tan said Societe Generale forecasts the euro will strengthen to $1.25 by the middle of the year.
The dollar's index against a basket of six major currencies slipped to 91.932, its weakest level since September.
For the whole of 2017, the dollar index slid more than 9.8 percent, the greenback's worst annual performance since 2003.
Satoshi Okagawa, senior global markets analyst at Sumitomo Mitsui Banking Corporation in Singapore, said a drop in the benchmark U.S. 10-year Treasury yield toward the end of 2017 was helping to weigh on the U.S. dollar.
With the dollar on the defensive, emerging Asian currencies clawed higher. The Chinese yuan rose to as high as 6.4922 yuan per dollar, its highest level since Sept. 8.
Commodity currencies traded higher after a rally in metal and oil prices and the Australian dollar gained another 0.4 percent to reach $0.7836 , its highest level since October.
Bitcoin, the biggest and best-known digital currency, was flat at $13,496 after earlier falling 2.0 percent on the Luxembourg-based Bitstamp exchange.
Bitcoin soared in 2017, gaining more than 1,300 percent for the year, although it fell at the end of December from its peak.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url= (Additional reporting by Masayuki Kitano in SINGAPORE; Editing by Matthew Mpoke Bigg)Keywords: GLOBAL FOREX/
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