Yellen re-emphasized Thursday that the Fed could hike rates this year and said that she was personally in agreement with that. Those and other remarks helped clarify her comments from the week earlier when the Fed held off on a rate hike, and spooked the markets by highlighting its concerns about a slowing China.
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Stocks bounced on Yellen's comments but were mixed by the end of the day Friday, as biotechs sold off. For the week, the S&P 500 was down 1.4 percent at 1,931. Futures markets were still pricing in low odds for an October Fed rate hike, at less than 20 percent, while the odds for December were just below 50 percent, as of Friday, according to RBS.
"For years, we obsessed about how the Fed was going to hike rates and that's going to be bad. And they had a chance to hike rates, they didn't do it, and now that's bad," Canally said.
Markets will also be focused on Washington, where House Speaker John Boehner Friday announced his resignation as speaker and from Congress. Boehner was facing "turmoil" within the Republican Party over whether funding for Planned Parenthood should be tied to the federal budget. If the budget does not pass, the government would shut down as of Thursday.
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"The government shutdown will be less likely, but what it does is it raises the prospect of a much harder deal because this is a three-month extension of the budget," said Dan Clifton, head of policy research at Strategas. "You go into the fall and they have to raise the debt ceiling…. This is what the new house leadership is going to deal with, a conservative group of members that removed the speaker of the House."
Clifton said the best scenario for markets would be if Boehner could get the debt ceiling issue resolved before he leaves at the end of October.
"The record of market trading with government shutdowns, it's not entirely clear that it is an unequivocal market negative. If people perceive that it puts pressure on the Republicans to get something done, both in the near term and more importantly in December, it will be a positive," said Julian Emanuel, equity and derivatives strategist at UBS.
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Important for markets, too, will be economic reports, especially the jobs data, expected to show creation of 203,000 jobs, up from 173,000 last month.
"I think if we get another print below 200,000, (the market) might look a lot like this week," Canally said, adding that investors might think the Fed knows something negative about the economy. "That's what this week was about. 'The Fed knows something we don't.' "
Emanuel said Yellen managed to improve the message on the U.S. economy Thursday, so it's important the jobs number does not miss expectations. "I think at this point, the market would not take that well," he said.
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Other data in the coming week includes personal consumption data Monday, with the PCE, the Fed's preferred measure of inflation. ISM manufacturing data and vehicle sales are Thursday.
"The China spillover story is big next week," said Canally. "For ISM, vehicle sales, even the jobs report, were people spooked by what happened in August: the first 10 percent (stock market) selloff in four years. Did that slow hiring?"
Traders will also stay hyperfocused on any economic or market news out of China, as well as the action in emerging markets, where currencies continued to weaken against the dollar in the past week. China does have PMI manufacturing data Wednesday.
As for the Fed speakers, Yellen makes opening remarks at a St. Louis Fed conference Wednesday, and Fischer speaks on monetary policy at a Boston Fed conference Friday. Dudley speaks Monday on monetary policy and again on Wednesday.