* Euro back at August levels on dollar weakness
* Trade and global growth optimism hurt U.S. currency
* Sterling recovers to $1.31; yen also boosted
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
LONDON, Dec 30 (Reuters) - The euro hit a 4-1/2-month high on Monday as optimism over U.S.-China trade relations and the global growth outlook knocked demand for dollars.
Thin end-of-year volumes exacerbated the broad weakness in the greenback, which has seen it dip for three straight sessions and on Friday suffer its biggest one-day fall since June.
Investor sentiment, which has discouraged buying of the dollar as a safe haven, was boosted during Asian hours when China's central bank unveiled a measure to help lower borrowing costs and boost flagging economic growth. Investors also cheered a report forecasting that China's 2019 retail sales would be up 8%.
The euro climbed as high as $1.1211, its strongest level since Aug. 13, in early Asian trading.
Bleak European economic data had prompted hedge funds to bet on a weaker euro during 2019, but some signs that the euro zone economy has turned a corner have lifted the EU single currency in recent weeks.
The dollar index, which measures the currency against a basket of rivals, weakened 0.1% to 96.821.
With Friday's loss, the index's gains for the year have shrunk to around 0.6%.
The greenback was also on the backfoot against the Japanese yen, losing 0.3% to 109.17.
"The main drivers of the weaker dollar have likely been risk appetite holding up in the wake of comments from the U.S. pertaining to a Phase 1 trade deal recently, as well as the U.S. Federal Reserve's continued repo operations, which have recently been undersubscribed," MUFG analysts said.
Sterling was also a beneficiary, rising 0.2% to $1.3106 . Against the euro, it was down 0.1% at 85.51 pence - concerns that Britain is headed for a disruptive "hard Brexit" at the end of 2020 have hurt the pound since mid-December.
China's yuan strengthened, holding below the key level of 7 per dollar. In the offshore market, the Chinese currency rose to 6.9752, its highest since Dec. 13.
Marshall Gittler, chief strategist at ACLS Global, said it was noticeable how little currencies had moved during 2019, with very low volatility and narrow trading ranges, which he put down to "economic and monetary policy convergence".
"I expect less of both in 2020, for two reasons," he said, noting the expected end of the Sino-U.S. trade war, which should lead to broader economic recovery across the world.
The second reason, Gittler said, was that inflation seemed to have bottomed out and "conceivably some countries could start thinking about hiking rates, which would encourage monetary policy divergence".
Later on Monday, investors will stay tuned for the Chicago Purchasing Management Index for clues about the health of the U.S. economy. (Reporting by Tommy Reggiori Wilkes; Additional reporting by Swati Pandey in Sydney; Editing by Kevin Liffey)