* Wall Street opens higher, MSCI world index stuck near 4-month low * European shares pare losses; Nikkei has worst day since June * Dollar bobs higher from two-month low against yen * Aussie rallies after RBA drops easing bias By Marc Jones LONDON, Feb 4 (Reuters) - World shares steadied after falling to a near four-month low on Tuesday as a bounce in battered emerging market currencies and a positive start for Wall Street helped lift some of the recent gloom. A weaker-than-expected report on U.S. factory activity had hit global equity markets and the dollar hard on Monday but European shares had clawed back most of their morning losses by the time Wall Street reopened. After the previous session's pounding, the S&P 500 and Dow Jones Industrial indexes opened 0.6 and 0.4 percent higher while many hard-hit emerging currencies rose from their recent lows. U.S. factory orders released shortly after Wall Street open bolstered the fragile mood, nevertheless, there remained plenty to keep traders on edge. The market volatility had seen Russia cancel a bond auction for the second week running, while another round of stock market bloodletting, particularly in Asia, has left MSCI's world index at its lowest level since October. "This emerging crisis does matter if it worsens because it will have an impact on global growth," said Daniel McCormack, a strategist at Macquarie in London. "The other thing that is that earnings are just not coming through. The market was jittery before this crisis came along, in the sense that it was worried about earnings, and this has just been the catalyst that crystallises those worries." Early losses for Europe's top shares had been all but erased but the time U.S. markets opened, but it was the 4 percent plunge in Japan's Nikkei, cementing its position as 2014's worst performing major index, that hogged attention. The recent turbulence has spread from vulnerable emerging markets as major economies like the United States begin to pull back the throttle on stimulus programmes undertaken following the global financial crisis. The promise of a gradual exit from ultra-loose monetary policy has boosted likely returns in developed markets but driven investors out of the emerging countries they favoured while returns on U.S. and European assets fell to near-zero. EMERGING HOPES The earlier flight to safety had seen yields on German government bonds, considered to be one of Europe's most secure investments, hit their lowest in six months but signs the sell-off was easing nudged them up. Emerging market stocks also pared losses, while hard-hit currencies including Turkey's lira, Russia's rouble, Hungary's forint and the South African rand all moved away from their recent lows. "Experienced emerging market investors would be looking at this sell down with great interest, looking to pick up quality names on the dip, but they are still in the minority for now," said Erwin Sanft, Standard Chartered's Hong Kong-based China equity strategist. Among larger currencies, the Australian dollar jumped after its central bank appeared to shut the door on further rate cuts, while another round of strong UK construction data left sterling looking sprightly. Much of the focus remained on the U.S. dollar's contest with the yen, where two factors were at play. The dollar was hit initially after the weak data had pushed down U.S. bond yields, while the Nikkei's plunge pushed up the yen, against which it often see-saws. The U.S. dollar appeared to be recovering, however, and it was last up 0.4 percent at 101.40 yen, after hitting its lowest level since November on Monday at 100.77 yen. 10 PERCENT CORRECTION? The stock market gyrations saw the VIX, the market's fear seismograph, jump to its highest since June. The Nikkei's 4 percent dive meant it has now shed 14 percent of last year's 50 percent boom. By comparison, the U.S. benchmark S&P 500 is down 5.8 percent and the FTSEurofirst 300 has dropped 3.3 percent. "With the main European indices down around 7 percent (since peaks), chatter on trading desk is about whether we are in for a '10 percent' correction," Jonathan Sudaria, a dealer at Capital Spreads in London, said in emailed comments. With risk appetite gradually beginning to seep back into stock and currency markets, the safe-haven appeal of gold waned to leave it down 10 cents at $1,258.84 an ounce. Among other perceived safe assets, the yield on benchmark 10-year U.S. Treasury notes rose to 2.611 percent as U.S. trading began. It fell as low as 2.582 percent on Monday, its lowest since Nov. 1. Three-month copper, a metal highly attuned to global growth, also shrugged off its early gloom. It climbed to $7,060 on the London Metal Exchange, as it looked to dodge its 10th straight loss and its longest run of falls in 37 years. "There's some buying interest because the emerging market crisis is going to be temporary and is not going to include a meltdown in China," said Jesper Dannesboe, senior commodity strategist at Societe Generale.