* China April exports tumble sharply
* Bank of America sells $7.3 bln of shares in China bank
* EU to stress test its banking sector - sources
* Bank of France, Bernanke less downbeat
* Nissan, Hitachi and Daiichi Sankyo all post big losses
By Zhou Xin and Jan Strupczewski
BEIJING/BRUSSELS May 12 (Reuters) - Chinese exports dropped sharply and a clutch of Japanese companies registered hefty losses on Tuesday, while central banks expressed some optimism that the worst was over for the world economy.
Banks, the epicentre of the financial crisis, continued to hold the markets' focus with Bank of America raising over $7 billion and the European Union saying it would follow Washington's lead and conduct tests on its banking sector.
A bigger than expected 22.6 percent annual fall in Chinese April exports showed global demand remained subdued at best, with Japanese exporters continuing to suffer.
Analysts took heart from signs that Beijing's efforts to prop up domestic demand, via a $585 billion stimulus, seemed to be bearing fruit, but said global conditions remained difficult.
"The future of the world economy remains uncertain, and it's really hard to be optimistic about China's trade prospects," said Qi Jingmei, an economist with the State Information Centre, a government think-tank in Beijing.
Australia unveiled its largest deficit on record and forecast a decade of debt, starkly demonstrating the price to pay for trillions of dollars of public spending worldwide to tackle the worst economic crisis since World War Two and the damage recession does to government revenues.
Nor did Japan offer much to cling to.
Nissan Motor Co lost $2.4 billion in a quarter and forecast more to come as global car sales slump.
Hitachi Ltd, Japan's biggest electronics maker, lost $8.1 billion, its third straight quarterly net loss, and drugmaker Daiichi Sankyo booked a fourth-quarter net loss of $390.1 million.
In contrast, Thomson Reuters research shows that of the more than 400 major U.S. companies that have reported Q1 2009 earnings to date, 65 percent have reported earnings above analyst expectations and only 28 percent below forecasts.
MORE STRESS TESTS
After Federal Reserve chairman Ben Bernanke gave U.S. banks a vote of confidence, EU sources said the European Union would conduct its own bank stress tests by September, although it would look at the whole sector not individual institutions.
"It is more a highly aggregated stress test, which should show the degree of resilience of the overall EU banking sector," one source familiar with EU finance ministers' deliberations said.
Late on Monday, Bernanke said he was confident in U.S. banks' ability to raise cash following government "stress tests" of 19 individual banks concluded that 10 of them should boost their capital by an aggregated $74.6 billion.
"Many of the banks are well ahead in finding private-sector options for increasing their common equity, and several have announced plans for new equity issues," he said.
To that end, Bank of America sold $7.3 billion worth of shares in China Construction Bank to a group of investors, a source said on Tuesday. Its stress test showed it alone needed to find $34 billion in new capital.
The International Monetary Fund estimates that banks around the globe will need to write down about $2.8 trillion. So far, about one-third of that amount has been written off and Europe is lagging -- in the euro area, write-downs so far have totalled $154 billion, with another $750 billion expected through 2010.
OPTIMISM
Nonetheless, policymakers continued to reflect cautious optimism about a gradual recovery, something that has propelled stock markets upwards in the past two months.
A Bank of France survey on Tuesday predicted the French economy would shrink 0.6 percent in the second quarter, an easing in its rate of decline.
First quarter French GDP data is due on Friday with a Reuters poll pointing to a contraction of 1.2 percent.
The sense of returning confidence was also apparent in Bank of Korea's decision to hold interest rates steady for a third month running on Tuesday and its forecast of "mild growth" in the months ahead.
But mounting job cuts, corporate losses, rising bad debts and mixed economic data still keep investors on guard.
Stocks in Asia retreated, Europe's top shares edged down and U.S. futures pointed to a flat start on Wall Street.
UK data backed the growing consensus that the first quarter of 2009 probably marked the low point for the world economy. The British Retail Consortium said sales jumped 4.6 percent year-on-year in April. A separate survey showed house prices in England and Wales fell at the slowest pace in 15 months in the quarter to April and new buyer enquiries rose at their fastest pace in a decade.
Other data showed British industrial output fell less than expected in March -- the end of the first quarter -- but still posted its biggest annual decline on record. (Writing by Mike Peacock; editing by Ralph Boulton)