* Money flows back in to stocks after weeks of outflows
* Margin loans rise for 6 straight sessions
* Reasons for pick up in market not clear
* Many investors remain sidelined, concerned about economy
By Samuel Shen and Pete Sweeney
SHANGHAI, Oct 19 (Reuters) - After months trying to convince investors to come back to China's battered stock markets, there are signs authorities may be getting their wish as money starts flowing back in.
China's benchmark Shanghai stock index is still a third below its June peak, but there are unquestionable signs of life in the market.
The index hit a seven-week high last week and posted its best weekly performance in four-and-a-half months. Money flowing into the stock market was greater than money flowing out for the first week in six. In fact, weekly volume and turnover broke through 10-day and 100-day averages on Friday.
Investors have resumed borrowing money for margin trading for six straight days of rises, the longest streak in two months; the Shanghai exchange volatility index - China's "fear gauge" - has fallen to six-month lows.
"It's time to buy shares again," said fund manager David Dai. During the slump he cut stocks to just 10 percent of his asset mix.
They are now 70 percent of his 200 million yuan ($31.7 million) fund that he manages for Nanhai Fund Management Co after he invested in such sectors as cloud computing, satellite navigation and pharmaceuticals.
"The market is back to normal. I don't see any systemic risk now," he said.
Still, stock traders said there are no clear reasons for the sudden signs of life in a market that had been flatlining for weeks and plenty of investors are staying away after a tumultuous summer when Beijing rewrote the rules of trading with heavy-handed intervention.
The flurry of measures to stem a full-blown panic stifled trade and spread fear among Chinese-based investors as regulators launched investigations to root out those speculating.
Some analysts believe the buying was aimed at front running fresh stimulus measures from the government to revive an economy that is heading in 2015 for its weakest full-year growth in more than two decades. Reduced prospects for a U.S. rate rise this year could also have spurred buying.
Third-quarter GDP figures are due to be released later on Monday.
"There's no disagreement that the rebound was the result of some investors adding to their stock positions," said a mutual fund manager at Guotai Asset Management.
"But what happens next? Many investors got burnt, or even killed by the market rout, and I doubt they will come back again anytime soon."