* S&P 500, Nasdaq, German DAX stock indexes hit record highs
* Wall Street's "fear gauge" hits historic lows
* Bond yields on the rise, gold falls
* Oil buckles as concern grows over battle of OPEC vs shale
By Dion Rabouin
NEW YORK, May 9 (Reuters) - Stock markets touched record highs on Tuesday, with the S&P 500 and Nasdaq hitting all-time intraday peaks, tracking European stocks and global bond yields with investor sentiment bolstered by historically low U.S. equity volatility, the French presidential election result and solid corporate earnings.
The S&P 500 opened at a record-high 2,401 points and the VIX index of implied volatility - known as the Wall Street "fear gauge" - fell to 9.56, the lowest since late 2006.
While the market appeared buoyant, analysts urged caution against investor complacency, especially after the market's strong run since Donald Trump's election as U.S. president.
"In the short term, investors can enjoy this run, but they should start to hedge their positions and look for safety," said Christian Magoon, chief executive at Amplify ETFs in Chicago, Illinois.
"Given world events, common sense would say there should be at least average volatility in daily price movement on the S&P 500. The index seems to be very lethargic."
In early afternoon U.S. trading, the Dow Jones Industrial Average was off 13.51 points, or 0.06 percent, to 20,998.77, the S&P 500 lost 0.67 point, or 0.03 percent, to 2,398.71 and the Nasdaq Composite added 21.00 points, or 0.34 percent, to 6,123.66.
Europe's index of leading 300 shares rose to a near-two-year high, Germany's DAX hit a record high, and Britain's FTSE 100 closed up 0.57 percent.
The benchmark 10-year U.S. Treasury note yield rose to its highest in five weeks with German 10-year yields rising and the 10-year British gilt yield up around 6 basis points from late Monday.
"It's calm sailing today for stock markets," ETX Capital senior markets analyst Neil Wilson said.
Victory for business-friendly centrist Emmanuel Macron in France and earnings were also supportive for equities, he said, adding: "So far, there is precious little to halt the rotation from bonds to stocks."
Fed funds futures pricing shows investors are almost universally expecting the Federal Reserve to raise U.S. overnight interest rates at its next meeting, with close to a 90 percent perceived chance of an increase next month. Yields on U.S. two-year notes, the tenor most sensitive to rate-hike expectations, also advanced on Tuesday, climbing to eight-week highs.
"While the U.S. economy saw a marked deceleration in the first quarter, the overall outlook remains solid and the Fed is still widely expected to raise U.S. lending rates in June and likely again in September," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
The positive sentiment and rising U.S. Treasury yields also boosted the dollar. The dollar index, which tracks the greenback's value against six major currencies, rose to a three-week high, in line with the gains in yields. It was last up 0.54 percent.
Oil prices fell, surrendering earlier gains, rattled by concern over slowing demand and rising U.S. crude output that has shaken investors' faith in the ability of the Organization of the Petroleum Exporting Countries to rebalance the market.
Brent crude futures were last down 1.8 percent at $48.47 a barrel while West Texas Intermediate was off 1.8 percent at $45.58.
Copper bounced from a four-month low touched on Monday after data showed a sharp drop on imports by China, the world's biggest consumer. London copper rose 0.5 percent to $5,514 a tonne, having fallen to as low as $5,462.50 on Monday.
Gold prices touched a nearly eight-week low on Tuesday, indicating a shift in investor preference for riskier assets.
Asian stocks fell, with China's seventh consecutive decline - the longest losing streak for four years - weighing on the region more broadly. (Reporting by Dion Rabouin in New York; Additional reporting by Amanda Cooper in London, Yashaswini Swamynathan in Bengaluru and Gertrude Chavez-Dreyfuss in New York; Editing by Nick Zieminski and James Dalgleish)