Reuters/Kevin Lamarque
The four-year term of Federal Reserve Chair Janet Yellen, who was nominated by President Barack Obama, will end in February. Trump has said he has "a lot of respect" for Yellen, but whether he'll pick her for another term is still unknown.
It's a critical choice as the Fed slowly reverses the recession-era policies it put in place, particularly historically low interest rates and bond purchases that expanded the assets on its balance sheet to $4.5 trillion.
The Fed hasn't achieved all of its objectives, but its policies helped encourage the spending and investment that stabilized the economy after 2009 and catapulted the stock market. If the Fed's leadership gets too trigger happy in reversing these policies - speeding up Yellen's gradual pace - it could push the economy towards another recession.
Byron Wien, the vice chairman of Blackstone's private-wealth-solutions group, doesn't foresee a disruption because of who Trump chooses. But he notes that the wrong choice could be disruptive.
"I have no reason to be fearful," Wien, told Business Insider. "This is not something Donald Trump knows a whole lot about, and so I think he'll rely on advisers like Gary Cohn and Steven Mnuchin when he considers appointees. He's already said he's comfortable with Janet Yellen. Maybe he'll replace her, but I don't see him replacing her with anybody who's really a serious threat to the stability we're currently enjoying."
Trump doesn't face just one nomination. Yellen's vice chairman, Stanley Fischer, is stepping down next month for "personal reasons." He's a Yellen ally personally and on policy issues.
"I think Stanley Fischer was a positive force - a very knowledgeable guy, and very balanced," Wien said. "I just hope that the replacement is reasonable and understands that aggressive tightening would be deleterious to both the economy and the stock market."
'A great level of uncertainty'
If Trump is nominating someone else, it would be safest to announce his choice around October to allow time for the Senate confirmation proceedings to conclude before Yellen's term ends in February, Kristina Hooper, global markets strategist at Invesco, told Business Insider.
Trump is a unique president by Washington's standards. That means he could make the unusual choice of someone with a non-academic, corporate background, although ex-Fed Governor Kevin Warsh is considered the leading contender.
"For decades, we were accustomed to having someone form academia or someone from within the Federal Reserve structure appointed as chair," Hooper said.
She added that former Fed Chairman Ben Bernanke's post-recession policies reassured investors partly because of his expertise on the Great Depression. He had a body of work from which markets could glean his policy ideology.
"Now we could have a business leader, someone who's never articulated their monetary policy ideology, someone who may have never even formed an ideology around monetary policy," Hooper said. "That carries with it a great level of uncertainty."