The unease is the product of a little information and a lot of speculation. Mr. Summers, a Harvard University economist who served for two years as Mr. Obama's primary economic adviser, has said little about monetary policy in recent years. Investors are left parsing a handful of comments in which he has expressed some doubts on the benefits and concern about the consequences of the Fed's policies.
"People don't know what Larry might do," said Mohamed El-Erian, chief executive of Pimco, the giant bond fund manager. "There's a lack of a lot of information on Larry's views. We don't have enough information to make an assessment, just some second- and third-hand accounts."
Some doubts always attend the arrival of a new Fed chairman, but the consequences are particularly freighted at the moment because the Fed's effectiveness increasingly depends on its ability to reduce uncertainty among investors. The central bank floored its traditional gas pedal five years ago when it pushed short-term interest rates to zero. It has since focused on further reducing long-term interest rates—which determine the cost of most kinds of borrowing—largely by convincing investors that short-term rates will remain near zero.
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The sense of uncertainty is heightened by the fact that as many as five of the Fed's seven governors may be replaced in the next year.
One governor, Elizabeth A. Duke, stepped down at the end of August. A second governor, Sarah Bloom Raskin, has been nominated to serve as deputy Treasury secretary. Mr. Bernanke's term ends in January, as does the term of a fourth governor, Jerome H. Powell—although Mr. Obama could choose to reappoint Mr. Powell, a Republican who joined the Fed only in May last year and is said to be open to a longer stay. If Ms. Yellen is passed over by Mr. Obama, she, too, could choose to leave even before her term as vice chairwoman ends in October 2014.
Mr. Obama said last month that he would not announce his choice for the Fed's top spot until the fall, and that he was considering at least three candidates: Mr. Summers, Ms. Yellen and the former Fed vice chairman Donald L. Kohn. But the president's top economic advisers uniformly support the selection of Mr. Summers. They regard him as a creative thinker and an experienced crisis manager, qualities they value in particular because they expect the Fed may confront difficult choices as it begins to retreat from its six-year-old stimulus campaign.
They also insist that Mr. Summers supports the Fed's efforts to revive the economy and would continue those efforts.
But Mr. Summers has criticized the Fed's purchases of Treasury securities and mortgage-backed securities, warning that bond-buying on such a scale could distort financial markets. He said it was "less efficacious for the real economy than most people suppose." As a result, many investors suspect he would seek to end those purchases more quickly than Ms. Yellen.
(Read more: Larry Summers the next big risk for emerging markets?)
Julia Coronado, chief North America economist at BNP Paribas, said last week that the yield on the benchmark 10-year Treasury note already had started to rise as investors price in a Summers nomination. She added that the yield could eventually rise half a percentage point more than if the president nominated Ms. Yellen instead. Ms. Coronado estimated that this Summers effect would reduce domestic economic growth by 0.5 to 0.75 percentage point over the next two years, which could reduce job creation by 350,000 to 500,000 jobs.
A Summers nomination, she wrote, "would come at a cost of higher market volatility and interest rates, and a less buoyant economic recovery."
(Read more: Wall Street wants Yellen, not Summers, as next Fed chief)
Leadership changes at the Fed tend to unsettle financial markets more than changes in leadership at other major central banks, according to a 2007 study by Kenneth N. Kuttner, an economist at Williams College, and Adam S. Posen, president of the Peterson Institute for International Economics. That is partly because the Fed is the closest thing to a global central bank. But it also reflects the outsize role of the Fed chairman, who is less constrained than other central bankers in making policy.