AP Images
Janet Yellen
The Republican presidential nominee said Yellen is keeping interest rates artificially low for political reasons - to support President Barack Obama through the end of his term.
The Fed has raised its benchmark interest rate just once since the financial crisis, arguing that low inflation warrants patience. And, although Obama appointed Yellen and she was confirmed by the Senate, the Fed is mandated to act without political interference.
"There's probably a good chance that she may just step down and allow him [Trump] to appoint somebody more in line with his thinking as opposed to try to work with the administration," said Bob Landry, a portfolio manager at USAA investments.
"He's been very critical of the Fed at times and she may not want to deal with his criticism going forward as president. Maybe she would just decide to turn it over to somebody that he can work more closely with."
Landry added that some of Trump's choices for advisors including Larry Kudlow and Judy Shelton provide some clues on how he would approach monetary policy, and who he would appoint as Fed chair. In a column for the Financial Times on Wednesday, Shelton wrote that "something has clearly gone wrong with the Fed's model; even when its own metrics have been."
We're at a point where speculation about a 25-basis-point rate hike "carries the threat of igniting the world's next financial crisis," she wrote.
Alternatively, Yellen could ride out her term of office until it expires on February 3, 2018, just over one year after the next president's inauguration.
The term of Fed Vice Chair Stanley Fischer will end on June 12, 2018, creating another important vacancy.
"While we expect Clinton to opt for continuity at the central bank as presidents have historically done, Trump's rhetoric suggests that he would try to change the composition of the Fed," wrote Lisa Berlin and Michelle Meyer, US economists at Bank of America Merrill Lynch, in a note on Thursday.
The duo said Trump's call to audit Fed policy decisions despite existing checks could damage the central bank's independence, and have further-reaching consequences for the economy.
"In our view, curbing Fed independence could damage confidence in the dollar and hurt the special status of the US as the center of global capital markets," they wrote. "We believe there is a risk of similar legislation gaining support under a Republican sweep."