The big hairy question that Yellen didn't answer Wednesday

The Federal Reserve said Wednesday it would leave its benchmark interest rate unchanged, a widely expected outcome, and announced it would begin unwinding its multitrillion-dollar balance sheet next month, which appeared to rattle the markets very little.

Now, much of the focus around the central bank will shift to whether President Donald Trump will reappoint Fed Chair Janet Yellen, as her term is set to expire next February.

Speculation has swirled around the prospect of Trump's forgoing her reappointment and instead going with a pick of his own, such as his economic advisor Gary Cohn (though the likelihood of a Cohn appointment is seen as having dwindled).

When asked on Wednesday at the press conference about her term expiration, Yellen did not offer much detail on her intentions to serve another term.

"I have said that I intend to serve out my term as chair and that I'm really not going to comment on my intentions beyond that. I will say that I have not had a further meeting with President Trump. I met with him early in my term, and I've not had a further meeting with him," she said.

In a report published Wednesday evening, Deutsche Bank chief economist Peter Hooper and senior economist Matthew Luzzetti wrote that it appeared evident from her responses on Wednesday that Yellen would serve a second term if offered.

Specifically, they pointed to comments Yellen made Wednesday during the press conference and at Jackson Hole about financial regulation, stress testing and fiscal policy, as well as her willingness to work with the new vice chair for regulation, Randall Quarles, should the Senate approve his appointment.

"Summing up Yellen's various comments in these areas, it strikes us that this is a person who would accept a second term as Fed chair if the Administration chooses to move in that direction," the economists wrote.

Whoever Trump appoints may alter the central bank's intended policy going forward, said Chad Morganlander, portfolio manager at Washington Crossing Advisors. If Cohn were indeed appointed, Morganlander said, he would likely "stay with a consistent, measured approach" to normalizing monetary policy going forward.

Another potential candidate reportedly floated for the position is Stanford economist John Taylor. He may be more hawkish in his approach, Morganlander said, which "may disrupt the financial markets in the short run, but overall, he's another prudent candidate."


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Michael Santoli

Michael Santoli joined CNBC in October 2015 as a Senior Markets Commentator, based at the network's Global Headquarters in Englewood Cliffs, N.J.  Santoli brings his extensive markets expertise to CNBC's Business Day programming, with a regular appearance on CNBC's “Closing Bell (M-F, 3PM-5PM ET).   In addition, he contributes to CNBCand CNBC PRO, writing regular articles and creating original digital videos.

Previously, Santoli was a Senior Columnist at Yahoo Finance, where he wrote analysis and commentary on the stock market, corporate news and the economy. He also appeared on Yahoo Finance video programs, where he offered insights on the most important business stories of the day, and was a regular contributor to CNBC and other networks.

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