The head of the world's largest asset management company said investors' appetite for those assets could move long-dated yields below those of shorter-term debt.

That condition, known as an inverted yield curve, is often considered a precursor to recession and could presage a decline for stocks.

"If there is a risk, it's that," Fink said in an interview. "I hope the Federal Reserve pays attention."

However, he said he did not see an inverted yield curve materializing within the next year as global economic growth accelerates.

U.S. President Donald Trump has promised to decide this month on a nominee for the Federal Reserve chair, who strongly influences interest rates.

"All of the publicized names are very qualified for that role," Fink said of the potential candidates. "I do believe whoever is the chair, whoever is added to the Federal Reserve, will have a giant task in front of them."

Potential Fed chair candidates are widely seen to include former Fed Governor Kevin Warsh, current Governor Jerome Powell and Stanford University economist John Taylor. Trump has suggested he may reappoint Fed Chair Janet Yellen to the post.

Despite nearly nine years of gains in U.S. stock markets, investors are flocking to bonds. Yields move inversely to prices, so demand pushes prices higher and yields lower.

U.S.-based bond funds have brought in more than $2 for every $1 gathered by equity funds this year, according to data from Thomson Reuters' Lipper research unit.

BlackRock alone reported nearly $60 billion in bond fund inflows and another $20 billion in "cash management" products that also invest in debt during the third quarter, compared to $12 billion for equity funds.

Longer-duration assets like 30-year U.S. Treasury bonds are purchased by individual savers, insurers, pension funds, governments and other investors to meet future spending needs. Economists and portfolio managers have argued that a shortage of safe assets like government bonds in developed markets has developed in the years since the 2007-2009 financial crisis.

Two Fed policies could affect the shape of the yield curve.

The central bank is on a path to raise the short-term rate it controls. And it is starting this month to reduce its approximately $4.2 trillion in debt holdings.

(Reporting by Trevor Hunnicutt; Editing by Jennifer Ablan and Richard Chang)

By Trevor Hunnicutt