* FTSEurofirst 300 down 0.5 percent after eurozone data * Hopes rise for ECB stimulus; euro at more than 4-yr low * Trading activity seen muted throughout day * RBS shares fall on report of new fines By Lionel Laurent LONDON, Jan 2 (Reuters) - A modest New Year rally quickly fizzled out on Friday after subdued manufacturing data from the eurozone and muted trading. The pan-European FTSEurofirst 300 index was down 0.5 percent by 0909 GMT, with benchmark indexes in France, Germany and Britain all reversing early gains after a survey showed eurozone output, new orders and employment all recorded sluggish growth at the end of 2014. French factory activity shrank at the fastest rate for four months in December and Italy's at the fastest in 19 months. Although all national bourses were open except Switzerland and Hungary, traders said quiet trade exaggerated price swings. "Markets have taken a turn for the worse, with the French and Italian data worse than expected," Sanlam Securities' head of execution trading, Mark Ward, said. "But volumes are almost non-existent ... I don't think any people would want to open up any positions now heading into the weekend," he said. Markets had gained ground after the European Central Bank (ECB) fanned expectations it would take bolder steps on stimulus this month, driving the euro down to its lowest in 4-1/2 years. That prospect had helped European shares post an annual gain for 2014, with pan-European equity indexes ending Wednesday in positive territory after a turbulent year. Among standouts, Royal Bank of Scotland was down 1.8 percent after The Times newspaper reported the lender might face fines over the sale of toxic mortgage-backed debt in the U.S. of more than 5 billion pounds ($7.76 billion). The bank declined to comment. Elsewhere, BG Group shares rose after news it had received $350 million from the Egyptian government for outstanding debts.

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