Yellen: We hope to offer a revised exit strategy later this year

Fed Chair Yellen: Unemployment remains elevated

U.S. stocks climbed on Wednesday, with the S&P 500 on track for a record finish, after the Federal Reserve continued to taper its asset purchases, as expected, and said the economy is rebounding.

Read MoreFed tapers and cuts outlook

Fed Chair Janet Yellen told a news conference that inflation was expected to move gradually back to the central bank's 2 percent target.

Some traders said they were surprised the Fed did not say more about inflation, after Wednesday's CPI showed inflation running at 2.1 percent over last year. Bonds yields rose on the inflation data but were lower Wednesday.

"The Fed is deathly afraid of a rise in rates stomping out the recovery. It's clear they will allow inflation to run higher than it should be in order to achieve that," said Peter Boockvar, market strategist with Lindsey Group. "What's going to be the end result is the bond market is going to start dictating policy."

The CBOE Volatility Index, one measure of investor uncertainty, dropped to its lowest level in 7 years.

—With reporting by CNBC's Patti Domm and Kate Gibson