* Yen moves away from lows as investors take profits * New York trade quiet amid major snowstorm * Dollar constrained despite positive data on Thursday * Euro extends slide after second-half rally By Julie Haviv NEW YORK, Jan 3 (Reuters) - The yen rose on Friday as investors shunned risk and took profits after rallies in the dollar and the euro, helping the Japanese currency bounce from recent five-year lows. New York trade was extremely thin with governors of New York and New Jersey declaring a state of emergency as a major snowstorm hammered the northeastern United States. Asian stock markets were under water after a sudden reversal in some very popular trades sparked a bout of global risk aversion. Investors tend to flock to the yen in times of market stress. The dollar last traded 0.3 percent lower at 104.42 yen , down more than a full yen from a five-year high of 105.44 yen set on Thursday. Traders said there had been some stop-loss dollar offers at levels between 104.50 and 104.30 yen. Moves can also be larger when volumes are thin, as they were with Japanese market players out for New Year holidays until next week. The euro, the top-performing major currency of 2013, shed 0.7 percent to 142.24 yen, extending its losses in the wake of its 1.2 percent slide the previous day. The single currency retreated from a five-year peak of 145.67 yen set last Friday. Asian shares outside Japan shed 1 percent as a slower China services survey prompted some caution but European markets made small gains and analysts said thin trade was making currencies more volatile. Growth in China's services sector fell to a four-month low in December as business expectations dropped, a government survey showed, adding to evidence that the world's second-largest economy lost steam into the close of 2013. "January is a bit of a messy month for foreign exchange," said Simon Smith, head of research at FxPro. "Volumes are still thin ... Things are very much driven by flows. "I don't think the yen is a one-way bet in 2014. The easy wins have been had. Always the most run-over people in the markets are yen bears." Smith expects dollar/yen to end the year at 109 yen per dollar. Betting on the dollar against the yen has been a big trade for hedge funds and other investors over the past year, who see the Bank of Japan's ultra-loose monetary policy and potential for more stimulus this year as one of the clearer themes in tricky currency markets. Data on currency futures positions on the Chicago Mercantile Exchange shows that currency speculators had increased their net short position in the yen to 143,822 contracts in the week ended Dec. 24, the largest since July 2007 and up from 62,395 contracts in late October. The dollar index was up 0.1 percent at 80.718, having hit a two-week high on Thursday as a slew of generally positive U.S. economic data reinforced expectations the Federal Reserve will continue to move away from its bond purchases. Looking ahead, next week will include the release of the minutes from the Federal Reserve's December meeting and key labor market data. The Fed's meeting minutes will be closely watched on Wednesday for signs over how far the Fed may further reduce its bond-buying program. Last month the central bank said it would cut the mortgage-backed securities and Treasuries purchases by $10 billion to $75 billion a month. The euro, meanwhile, hit a four-week low against the dollar of $1.3609 and was last at $1.3614, down 0.4 percent. The single currency - whose second-half rally was driven by factors such as euro zone banks repatriating funds to shore up their capital bases and repaying cheap loans to the European Central Bank - has retreated from a two-year high of $1.3894 touched last Friday. Marshall Gittler, head of global FX strategy at IronFX Global, said 2014 had begun with last year's trends reversing. "Looking at the G10 currencies, most of the movement was mean reversion: the currencies that gained in December lost, and those that lost, notably the yen, gained," he said.