* Stocks gains 1-2% after strong Chinese factory data
* Some signs virus infection rates slowing
* Many investors cautious about recent rally given lockdowns
* Oil price bounces off 18-year lows
* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh
By Tommy Wilkes
LONDON, March 31 (Reuters) - World stocks looked set to close their worst quarter since 2008 on a brighter note on Tuesday, as strong Chinese factory data held out hope for an economic revival even as much of the rest of the world shut down to fight the coronavirus.
Stocks have rallied since the start of last week but remain down more than 20% for the quarter. European shares have had an even worst time, suffering their worst three months since 1987.
But with trillions wiped off global markets in March and policymakers responding with more than $10 trillion and counting of fiscal and monetary stimulus packages, a semblance of calm has returned this week.
Some analysts have been bold enough to call a bottom in stocks and say the lows of early last week are unlikely to be revisited.
That followed gains in Asia after China's official manufacturing purchasing managers' index (PMI) rose to 52.0 in March from a record-low 35.7 in February, topping forecasts of 45.0. cautioned that underlying activity probably remained below par, since the improvement measured the net balance of companies reporting an expansion or contraction, but markets cheered the news.
S&P 500 futures rose 0.6% ESc1 , pointing to a stronger open on Wall Street after a rally on Monday lifted the U.S. index towards a 20% gain since the lows of last week.
Despite the more positive mood, not everyone is convinced the current rally has legs.
"In spite of the significant sell-off of most growth-oriented assets since mid-February, we are concerned there is further downside ahead," said Salman Baig, an investment manager at Unigestion.
"The violent market action should not be understated, but the underlying cause – an accelerating pandemic requiring large parts of the economy to shut down – is still with us."
The pace of coronavirus infections globally was heading towards 800,000. But Deutsche Bank (DE: DBKGn ) analysts noted that for two consecutive days the global growth in new cases was 10%, after being well above that for most of the past two weeks.
Health officials are much more cautious. A World Health Organisation official warned on Tuesday that even in the Asia-Pacific region the epidemic was "far from over".
"This is probably the most embarrassing statistic for the West that China could possibly release. Not only did China stop the virus with just 3,309 deaths, they also appear to have done it with just a one-month shutdown of the economy," Charlie Robertson, the chief economist at Renaissance Capital, said on Twitter.
Some analysts dispute China's figures, however.
Elsewhere, oil prices rose off the 18-year lows hit on Monday after the United States and Russia agreed to talks to stabilise energy markets.
Oil prices have been hit by a double whammy, with U.S. crude at one point falling below $20 a barrel on Monday, as the virus outbreak cut demand worldwide and Saudi Arabia got into a price war with Russia.
Brent crude LCOc1 was up 43 cents, or 1.9%, at $23.19 a barrel, after closing on Monday at $22.76, its lowest finish since November 2002. nL4N2BO131
U.S. crude Clc1 was up $1.21, or 6.0%, at $21.30 a barrel, after settling in the earlier session at $20.09, its lowest since February 2002.
The dollar rose for a second day, although the gains were more controlled than the jumps of earlier this month that put severe stress on funding markets for the U.S. currency.
The dollar, measured against a basket of currencies, was up 0.3% at 99.493 =USD .
Analysts say investors rebalancing their portfolios at month-end and quarter-end were probably behind some of the dollar's moves over the next 24 hours.
There was little respite for emerging-market currencies, however. The South African rand ZAR= was near record lows and Latin American currencies were falling once again.
Bond market moves were more measured than in recent weeks. Italian government bond yields IT10YT=RR were steady before an auction of debt, amid hopes the country's efforts to contain the spread of the coronavirus may be starting to work. benchmark 10-year yields rose 5 basis points to -0.474% DE10YT=RR . U.S. Treasury yields gained 2 to 4 bps, as investors sold safer bonds and bought into equities.
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