* World stock index little changed after hitting 4-month high
* Zuckerberg loses $16 bln in record Facebook fall
* U.S. agrees to refrain from car tariffs on EU for now (Adds oil gains, strategist quote)
By Trevor Hunnicutt
NEW YORK, July 26 (Reuters) - World stock markets struggled to hold on to four-month highs on Thursday as a record sell-off in shares of Facebook Inc offset optimism that the European Union and the United States would settle their differences on trade.
Facebook Inc, the fifth-largest global stock by market capitalization, collapsed 18.89 percent, set for the biggest one-day wipeout in U.S. stock market history, after the social media company's earnings report showed slowing usage in the biggest advertising markets. Executives warned profits would plummet as the company improves privacy safeguards.
That countered optimism over news that U.S. President Donald Trump agreed to refrain from imposing car tariffs while Europe and the U.S. negotiated to cut other trade barriers.
MSCI's gauge of stocks across the globe gained 0.01 percent after earlier rising to the highest level since March 16.
The Dow Jones Industrial Average rose 100.35 points, or 0.39 percent, to 25,514.45, the S&P 500 lost 8.65 points, or 0.30 percent, to 2,837.42 and the Nasdaq Composite dropped 83.64 points, or 1.05 percent, to 7,848.60.
The dollar index rose 0.28 percent.
Liz Young, senior investment strategist at BNY Mellon Investment Management, said investor skepticism of the market's run is leading people to take a close look at corporate earnings and other fundamental factors "rather than jumping on the bandwagon and investing in tech stocks."
"People need to be careful right now to be in those trendy trades," she said.
The heat has eased somewhat over U.S. and European trade issues, allowing markets to return their attention to central banks and their plans to withdraw stimulus.
"The lifting of the threat of tariffs on the auto sector in particular is a major development," said Royal Bank of Canada European economist Cathal Kennedy.
The euro, which initially received the U.S.-EU trade news warmly, sharply lost ground after European Central Bank boss Mario Draghi reaffirmed a commitment to keep interest rates on hold "through" next summer, even though he saw inflation picking up by the end of the year.
The euro was last down 0.59 percent to $1.1659.
Concerns about Facebook's major earnings miss in an otherwise largely positive U.S. corporate results season did little to support bonds, which lost value as yields resumed their climb higher.
Benchmark 10-year notes last fell 8/32 in price to yield 2.9653 percent, from 2.936 percent late on Wednesday.
Progress on trade also helped demand for oil, which is sensitive to economic growth prospects. Crude prices were also helped as Saudi Arabia suspended oil shipments through a strait in the Red Sea after an attack by Yemen's Iran-aligned Houthi movement.
U.S. crude rose 0.51 percent to $69.65 per barrel and Brent was last at $74.37, up 0.6 percent on the day.
Trade is by no means removed from a slate of issues facing investors, with the U.S. still to finalize an agreement with Europe, while it remains in negotiations with China as well as with Canada and Mexico.
China's blue-chip shares lost 1.1 percent. Qualcomm Inc dropped its $44 billion bid for NXP Semiconductors after a deadline for securing Chinese regulatory approval passed.
The breakdown of the deal leaves "investors fearing that the trade war has just turned even more so on China," Citi analysts told clients.
Reporting by Trevor Hunnicutt Additional reporting by Andrew Galbraith in Shanghai, Abhinav Ramnarayan and Tommy Wilkes in London Editing by Nick Zieminski