* Fed jolts markets by not tapering bond purchases * Bonds yields drop in Japan, Germany * Dollar lower vs euro * Emerging market stocks, currencies rally By Ryan Vlastelica NEW YORK, Sept 19 (Reuters) - Stocks in Asia and Europe rose and bond yields fell on Thursday after the Federal Reserve's decision to stick with its easy money policy, but Wall Street's rally the day before faded as investors digested the Fed's comments about the economy. The Fed announced its decision before the close of U.S. markets on Wednesday, sending Wall Street to record highs. Asian and European markets were closed at the time of the statement. Investors celebrated the prospect of continued stimulus in the world's largest economy, even though the Fed said it was sticking with the current pace of bond purchases because of concerns about the strength of U.S. recovery. The Fed also cut its growth outlook for both 2013 and 2014. MSCI's world share index, which tracks equities in 45 countries, jumped 0.9 percent and hit a five-year high as large gains in Asian markets were followed by a 0.6 percent rise in European shares. The Dow Jones industrial average was down 32.41 points, or 0.21 percent, at 15,644.53. The Standard & Poor's 500 Index was down 3.56 points, or 0.21 percent, at 1,721.96. The Nasdaq Composite Index was up 2.60 points, or 0.07 percent, at 3,786.25. "After the substantial move yesterday and people digesting the fact that tapering is put on hold, I don't expect a big move today," said Ryan Detrick, senior technical strategist at Schaeffer's Investment Research in Cincinnati, Ohio. In emerging markets, which have been suffering as higher yields in the developed world attracted much-needed foreign capital, stocks and currencies rose as the Fed decision meant delayed U.S. rate hikes. The chance that U.S. interest rates could stay low for longer was further raised after a White House official said that Janet Yellen, the Fed's vice chair and a noted policy dove, was the front-runner to take over the Fed when Ben Bernanke steps down in January. "The bottom line is that the (Fed) meant to send an extremely dovish message, not only through the lack of tapering, but also with its 2016 forecasts," analysts at Barclays wrote, adding that they now expected the first rate hike to occur in June 2015 rather than March 2015. In fresh forecasts, the Fed cut its projection for 2013 economic growth to a 2.0 percent to 2.3 percent range from a June estimate of 2.3 percent to 2.6 percent. The downgrade for 2014 was even sharper. Other markets that reacted favorably to the Fed's decision were those of developing nations. The main emerging market stock index jumped 2.3 percent. The Turkish lira and Indian rupee leapt while Indonesia's main stock index climbed 4.7 percent. "Markets are thrilled, and a much-needed reprieve for battered EM investors is on its way," said Frederic Neumann, co-head of Asian economics research at HSBC. "With Chinese data having turned up, and the Bank of Japan running at full speed, it looks like Asia might get its mojo back." Australian shares jumped 1.1 percent and Japan's Nikkei added 1.8 percent. TREASURY YIELDS The Fed's decision to keep its asset buying at $85 billion a month was partly a reaction to the sharp rise in Treasury yields over recent months, which was proving a headwind for the housing market and the U.S. economy in general. Ten-year Treasury bonds were down 16/32, with the yield at 2.7482 percent. Overseas, Japanese debt yields dropped to four-month lows while in Europe German Bund yields fell as low as 1.827 percent after their biggest drop in over a year. Against a basket of currencies, the dollar was up slightly, recovering from earlier losses of more than 1 percent that took the index to its lowest level since February. The euro was flat at $1.3527, after rising 1.2 percent on Wednesday to its highest level in almost eight months. In the commodities market, Brent crude fell 1.9 percent to $108.55 per barrel, while U.S. crude futures slid 1.5 percent. Gold was up 0.1 percent after a 4.2 percent surge in Wednesday's session. Oil prices dropped after Iran's president said his country was not seeking war with any other nation, helping unwind a risk premium and foster speculation of a recovery in oil exports to the West.