Stocks were higher, but some of the more dramatic moves were in the bond market where yields were lower except for the 30-year bond. The dollar, sensitive to interest rate hikes, slid.
In the Treasury market, buying was stronger at the short end, where expectations for Fed interest rate hikes are reflected. The decline in two-year note yields suggested a slower move by the central bank. "The market trades like there was more expectation that the Fed would indicate more of a September lean," said Briggs.
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The Fed's outlook for 2015 GDP growth shifted to 1.8 to 2 percent, from 2.3 to 2.7 percent. It also provided officials' latest views on the course of interest rates.
"It looks like the leadership is split between one and two hikes this year," said Briggs. "If we have good employment figures and good data like we've had in the last one or two weeks, they'll probably go in September."
John Canally, economist and strategist at LPL Financial, said based on the shift in Fed rate projections for 2015, it appears the Fed could go with just one hike this year, and he expects it to be in December.
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"The Fed came to the markets (view) so that's good," said Canally. "The statement changes were really around just taking account of the first quarter being transitory, but no suggestion of a rate hike in July. That leaves September or December."
Yellen stressed that the Federal Open Market Committee does not yet see the appropriate labor market conditions or signs of an inflation pickup that would justify a rate hike.
"Clearly most participants are anticipating that a rate increase this year will be appropriate. That assumes, as you can see that they are expecting a pickup in growth in the second half of the year and further improvement in labor market conditions," Yellen told a press briefing after the meeting.
Lindsey Group market strategist Peter Boockvar said the Fed wasn't clear enough in what it's looking for from the economy, which has begun to pick up lately and is expected to be growing at about 3 percent in the second quarter.
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"She keeps saying: 'Don't pay attention to when they'll first raise rates. Pay attention to the big picture of where rates go.' After six years, it matters when they'll raise rates," said Boockvar.
"She's just remaining open-ended. The market didn't expect her to raise rates anyway," he said. "But I think they're clueless. They keep laying out the criteria for raising rates, and I'm of the opinion they keep meeting the criteria and saying they're not meeting the criteria. I don't think she's providing any clarity."