(Recasts, adds quotes, updates prices) * MSCI World Index up 0.1%, dollar index flat * U.S. May CPI: seen +0.4% mm, +3.4% yy - Reuters poll * ECB meeting due later in the day LONDON/SYDNEY, June 10 (Reuters) - Global shares hovered near a record high and the dollar also held steady on Thursday, eyeing U.S. inflation data for any sign the Federal Reserve could start tapering its massive stimulus. Risk assets have remained buoyant in recent weeks as central bankers on both sides of the Atlantic signal their willingness to keep the monetary taps on until the post-pandemic recovery takes hold, believing inflationary pressures to be short-lived. Yet April’s surprisingly strong U.S. inflation print spooked some, leading to a cautious run into the May numbers later on Thursday in case of another upside surprise. Lagging in the pace of its recovery from COVID-19, the European Union’s central bank is set to keep rates unchanged when it meets later in the session, despite the most recent inflation print passing the target of just under 2%. Ahead of both key events, market sentiment remained subdued with MSCI’s broadest gauge of global stocks flat at 715.79 points, just off a record high of 718.19 hit last week. In early European trades, the pan-regional STOXX Europe 600 index was down 0.1% following gains overnight in Asia, where MSCI’s broadest index of Asia-Pacific shares outside Japan rose 0.5%. U.S. stock futures pointed to a mixed open on Wall Street, with the S&P called flat and Nasdaq down 0.2%. Ankit Gheedia, BNP Paribas’ head of equity and derivative strategy for Europe, said he expected inflation to pick up “sharply” in the coming months. “Some of the supply chain constraints point to more long lasting pain. So we think there will be higher inflation during summer,” although stock volatility would likely remain low in the coming days, absent a shock on inflation. Overnight, fixed income markets were the big movers, with some analysts pointing to a setback to more U.S. stimulus efforts, while others suggested a likely clearing out of short positions in U.S. government bonds ahead of the May CPI. Short positions in Treasuries were the highest since 2018, according to JP Morgan positioning data last week. The yield on benchmark 10-year U.S. Treasury notes edged higher and was last at 1.4992%, albeit some way off the June high of 1.6270%. Euro zone debt yields, meanwhile, were trading near their lowest levels since April, with Germany’s 10-year debt yield at -0.246%. Ahead of the U.S. CPI data, analysts polled by Reuters said they expected a rise of 0.4% in May, taking the annual pace to 3.4%. “I doubt the Fed will be spooked and I doubt markets will be unless we get the core well above 3.5%. And the less bonds get scared, the greater the chance that risk sentiment is supported and dollar weakness resumes,” Societe Generale analyst Kit Juckes said in a note. Activity was muted in the currency market with the dollar flat against a basket of major currencies, with the euro down 0.1% and the pound down 0.2% The CPI number is also likely to be key for gold as a higher print and the subsequent tapering fears could reduce demand. The yellow metal last traded down 0.3% at $1,882.1 an ounce. Elsewhere, oil prices recovered from early weakness after a gasoline inventory surge in the United States, with Brent crude futures up 0.1% at $72.30 a barrel and U.S. crude futures flat at $69.98 a barrel. Additonal reporting by Swati Pandey in Sydney and Thyagu Adinarayan in London; Editing by Ana Nicolaci da Costa, Christopher Cushing and Angus MacSwan Our Standards: The Thomson Reuters Trust Principles.