* S&P has ended higher 11 times in past 13 sessions
* CBOE Volatility index remains near lowest since 2007
* Achillion Pharma jumps in heavy premarket volume
* Futures down: Dow 17 pts, S&P 3.2 pts, Nasdaq 6.25 pts
By Ryan Vlastelica
NEW YORK, June 10 (Reuters) - U.S. stock index futures edged lower on Tuesday, as investors found few reasons to keep buying with the Dow and S&P 500 just off the latest in a string of records.
* Equities have been strong lately, with the S&P ending at records for the past four sessions, and rising in 11 of the past 13. While Wall Street's upward trend is still seen as intact, it may be harder to continue notching solid gains in the absence of big catalysts. There are no major economic indicators on tap for Tuesday.
* Investors continue to watch the level of trading volume, which has been below average of late, potentially making the market more susceptible to big swings. The CBOE Volatility index , which typically moves inversely to the S&P, rose 3.9 percent on Monday despite the market's advance. The "fear index" recently fell to its lowest since February 2007, and remains at levels that are very low from a historical perspective.
* S&P 500 futures fell 3.2 points and were below fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures fell 17 points and Nasdaq 100 futures lost 6.25 points.
* The benchmark S&P 500 index has advanced 5.6 percent this year, with the strongest group being "low beta" names like utilities, which tend to move less dramatically than the overall market.
* Achillion Pharmaceuticals Inc surged 40 percent to $5.95 in heavy premarket trading, building on a jump of almost 48 percent on Monday. The company early Tuesday commented on an ongoing Phase 1 clinical trial, and was upgraded to "market outperform" from "market perform" by JMP Securities.
* Another volatile name of late, Spherix Inc, rose 13 percent to $1.95 before the bell. Earlier, one of the company's wholly owned subsidiaries said it had commenced patent litigation against Huawei Device USA Inc.
* Microsoft Corp will work with Chinese Internet security specialist Qihoo 360 Technology Co on mobile Internet and artificial intelligence technology, Chinese state media reported late Monday, as the U.S. software giant fights security concerns in the country.
Editing by Bernadette Baum