* Graphic: World FX rates in 2020 tmsnrt.rs/2egbfVh
* Reuters Live Markets blog on European and UK stock markets: (Updates prices, adds comment)
LONDON, June 3 (Reuters) - World shares hit three-month highs on Wednesday and the dollar fell for the sixth day running as easing lockdowns and hopes for more monetary stimulus gave investors confidence, despite civil unrest in the United States and rising COVID-19 tolls.
The MSCI world equity index, which tracks shares in 49 countries, rose to its highest since March 6, having gained throughout the Asian session.
The index is down more than 8% year-to-date, amid pandemic lockdowns that have pushed many economies into contraction.
MSCI’s main European Index also held near three-month highs and European bourses opened higher, with the STOXX 600 up around 1.2% and back to levels not seen since March 6 .
In China, Japan and South Korea, where COVID-19 is relatively contained, stock indexes have recovered substantially to be only about 5-6% below this year’s peaks .
There are some signs of recovery in business activity as governments restart their economies, albeit in the knowledge that easing lockdowns too early could trigger a second wave of infections.
A closely-watched survey of service sector activity in China recovered to pre-epidemic levels in May.
“If we look at what’s going on in China, for sure, we have more data now and the improvement of the activity is for real. It’s quite easy to extrapolate this Chinese trend to other countries,” said Benjamin Melman, global CIO at Edmond de Rothschild Asset Management.
Euro zone businesses suffered another devastating contraction in activity in May. While there are signs the worst is over, it could be months before there is a return to growth, a survey showed on Wednesday.
But broader economic optimism supported risk-sensitive currencies and pushed down the dollar, which hit a three-month low against a basket of comparable currencies at around 0730 GMT . It then recovered around 0.2% during the morning, reaching 97.52 at 1100 GMT.
Oil rose on Wednesday, with Brent above $40 for the first time since March, as optimism mounted that major producers will extend output cuts and a recovery from the pandemic will spur demand for fuel.
Brent crude futures for August were up around 1.2% at $39.11 a barrel, having hit as high as $40.53 earlier in the session . U.S. West Texas Intermediate (WTI) crude futures rose to the highest since March 6 before erasing gains, down 1% on the day at $36.45.
Spot gold fell 0.6% to around $1,717 per ounce.
STEEPENING U.S. YIELD CURVE
Germany’s ten-year government bond yield rose to its highest since mid-April as the global risk-on mood saw demand for safer debt decline, but then slipped back slightly to -0.399 by 1100 GMT.
The European Central Bank is expected to ramp up stimulative bond purchases when it meets on Thursday.
The euro, which rose above $1.12 for the first time in 11 weeks in early London trading, is on track for a seven-day winning streak against the dollar - its longest streak since December 2013.
The safe-haven Japanese yen hit a two-month low of 108.85 to the dollar before bouncing back to around 108.70 per dollar .
The U.S. Treasury yield curve steepened, partly reflecting the sale of more government debt to finance massive stimulus efforts.
The 30-year U.S. Treasuries yield rose to as high as 1.532% , its highest since mid-March, as expectations of central bank policy support kept shorter yields in check.
The yield gap between five- and 30-year Treasuries rose to 118 basis points, the highest since early 2017.
Tens of thousands of people defied U.S. curfews to take to the streets on Tuesday for an eighth night of protests over the death of a black man in police custody.
“The disconnect between what the average person sees happening in the world and what they see happening in the financial markets is getting wider and wider,” Marshall Gittler, head of investment research at BDSwiss, wrote in a note to clients.
Reporting by Elizabeth Howcroft; Editing by John Stonestreet and Andrew Cawthorne
Our Standards: The Thomson Reuters Trust Principles.