(CNBC) — Stocks traded in a wide range on Tuesday, alternating between gains and losses, as volatility continues to grip Wall Street.

As of 2:35 p.m. ET, the Dow Jones Industrial Average was up 24 points. At its high of the day, it rose as much as 368 points. It also fell as much as 202 points. The S&P 500 traded 0.2 percent higher sliding 0.6 percent earlier in the day. The Nasdaq Composite rose 0.3 percent.

Stocks initially rose more than 1 percent across the board amid signs that U.S.-China trade relations could be improving.

Note: Read our discussion guidelines before commenting.