(Updates after Fed decision, adds quote) * 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 WASHINGTON, Nov 3 (Reuters) - Shares were mixed as Treasuries rose on Wednesday after the U.S. Federal Reserve, as expected, approved plans to begin scaling back its bond-buying stimulus program this month and end it by June. The pan-European STOXX 600 index rose 0.35% and MSCI’s gauge of stocks across the globe gained 0.14% as investors digested the announcement, taken amid a surge in inflation. U.S. indexes edged slightly higher with the benchmark S&P 500 advancing 0.14% in early afternoon trading. The Dow Jones Industrial Average fell 0.12% while the Nasdaq Composite added 0.42%. The Fed also maintained its assessment that high inflation would prove “transitory” and likely not require a fast rise in interest rates.. The Tokyo bourse was closed for a public holiday while MSCI’s broadest index of Asia-Pacific shares outside Japan closed 0.03% lower. The benchmark 10-year U.S. Treasury yield , which fell to a 2-1/2-week low of 1.519% earlier in the session, climbed to a session high of 1.602%. It was last up 4.9 basis points at 1.5963%. The two-year yield, which hit a 19-month peak of 0.5640% last week, was last 3.6 basis points higher at 0.4916%. Oliver Pursche, a Senior Vice President at New York-based Wealthspire Advisors, said Wednesday’s muted market reaction indicated that the Fed announcement was very much in line investor expectations. “It’s also leading me to think... we can probably expect one, maybe two, rate hikes tops in late 2022, which is less than many had kind of priced in,” said Pursche, adding that he views “a lot of (future Fed) actions are going to be predicated on continued economic improvement and the inflation outlook.” 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. 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. Meanwhile, the U.S. job market may have improved enough by the middle of next year to be considered at “maximum employment,” Fed Chair Jerome Powell said on Wednesday after its policy meeting. Officials did not see “troubling increases” in workers’ wages that might raise the risk of a wage-price spiral developing that could force the Fed to act sooner than expected to contain inflation, he added. Meanwhile, 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, with Germany’s 10-year Bund yield falling to a one-month low of -0.19% . Fixed income investors are also eager to find out whether the Bank of England will on Thursday become the first major central bank to raise borrowing costs after the coronavirus crisis. The dollar index softened after the Fed statement, hitting a session low before reversing some of the losses and was last down 0.045% at 94.068, still within reach of its 2021 peak of 94.563 hit last month. U.S. crude stocks and distillate inventories rose while gasoline inventories fell, the Energy Information Administration said on Wednesday. Crude inventories rose by 3.3 million barrels in the week to Oct. 29 to 434.1 million barrels, compared with analysts’ expectations in a Reuters poll for a 2.2 million-barrel rise. U.S. crude fell 4.31% to $80.29 per barrel and Brent was at $81.42, down 3.9% on the day. Spot gold dropped 0.9% to $1,771.68 an ounce. Reporting by Katanga Johnson in Washington; Additional reporting by Caroline Valetkevitch in New York Editing by Angus MacSwan and John Stonestreet