The big question among asset managers is how the Federal Reserve will go about the daunting task of trimming its massive bond-buying stimulus, the implications of which will greatly affect the health of the global economy, OppenheimerFunds CEO Bill Glavin told CNBC on Wednesday.
"We're all counting on the Fed threading the needle. I mean, it's not just for bond investors, frankly. It's for the world economy," Glavin said on "Squawk on the Street." "If they're clumsy in their unwinding, that will spike rates and that will have very negative impacts on the global economy."
But Glavin, whose firm boasts $237 billion in assets under management across 11 million accounts, said he doesn't think the Fed has been clumsy so far about winding down quantitative easing.
Glavin acknowledged that the markets, not Fed Chair Janet Yellen, control interest rates. The key for the Fed, though, is how the central bank communicates its plans to investors, he said.
"Generally I think they're on the right track and I think we have a long way to go," he said.
Looking forward, Glavin thinks rates will stay "relatively low for quite a while." At some point, though, he thinks the unwinding will cause rates to rise—but not as high as during the '70s and '80s.
—By CNBC's Drew Sandholm.