* Global stocks on all-time highs * European stocks reach fresh milestone * Oil falls as data shows stock build up in U.S. * Dollar ticks down against major peers, gold slips LONDON, Nov 3 (Reuters) - Global stock markets traded at fresh record-high levels on Wednesday while U.S. Treasury and euro zone government bond yields ticked down as investors braced for the world’s largest economy to start cutting pandemic-era monetary stimulus. The U.S. Federal Reserve is expected to announce the tapering of its $120 billion-a-month asset purchase programme in its policy statement at 1800 GMT, a move widely seen as marking a new chapter in the world’s policy response to COVID-19. European stock markets rose to a new all-time high for a second day in a row after Wall Street’s main indexes also scored new records on Tuesday. U.S. futures were pointing to a mixed open while MSCI’s all-country world index, which tracks equity performance in 50 nations, was up 0.02%, just a whisker from a new milestone. The Tokyo bourse was closed for a public holiday while MSCI’s broadest index of Asia-Pacific shares outside Japan lost 0.05%. Boosted by fiscal and monetary stimulus, global stocks have thrived during the economic rebound after the recession triggered by the first wave of COVID-19 infections in 2020. “From a pure macro perspective, negative real rates mean there is no alternative to stocks, while at the same time the earnings cycle is very strong,” said Salman Ahmed, global head of macro at Fidelity International. “Negative real rates is a very powerful force,” he added, as investors wonder whether equities are at risk of losing their edge against other asset classes with the direction of travel for interest rates firmly on the rise. Markets are almost certain the Fed will taper but are looking to see if policymakers will give hints about the possibility of rate hikes next year. Fed officials are trying to maintain a difficult balancing act by giving the economy as much time as possible to recover while tightening policy soon enough to contain inflation. ‘PATIENCE’ “Fed Chairman Jay Powell, who is seeking renomination for another four-year term, will likely renew his calls for patience before hiking interest rates,” argued Thomas Costerg, senior economist at Pictet wealth. “We remain of the view that the Fed will seek to keep its interest rates below the rate of inflation in the long run, as it remains implicitly focused on the high level of debt in the U.S. economy,” he added. Meanwhile in Europe, European Central Bank President Christine Lagarde pushed back on market bets on an interest rate hike as soon as next October, saying it was “very unlikely” such a move would happen in 2022. Euro zone government bond yields retreated and Germany’s 10-year Bund yield fell to a one-month low of -0.19% . At the same time, U.S. benchmark 10-year Treasury yields were also lower at 1.5296%, off last month’s recent top of 1.7%. Fixed income investors are also eager to find out on Thursday whether the Bank of England will become the first major central bank to raise borrowing costs after the coronavirus crisis. Moves in currency markets were limited on Wednesday with the U.S. dollar index losing 0.12% at 94 points against a basket of major peers. The Aussie dollar picked up 0.15% after having dropped 1.2% against the dollar a day earlier following more dovish remarks from the Reserve Bank of Australia, even as it abandoned its short-term yield target. Oil prices fell as industry data pointed to a big build in oil stocks in the United States, the world’s largest oil consumer, and as pressure mounted on OPEC to increase supply. Brent crude fell 2.08% to $82.96 a barrel while U.S. crude tumbled 2.4% to $81.90 a barrel. Spot gold slipped 0.13%. Reporting by Julien Ponthus, Alun John and Sujata Rao; Editing by Catherine Evans and Andrew Cawthorne