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The trillion-dollar question: Allianz Global CEO

A 3 to 4 percent growth trajectory for the U.S. economy is a challenge right now, Allianz Global Investors CEO Elizabeth Corley said Thursday.

"That is why you see the Fed being accommodative," she told "Squawk Box" on CNBC. But pinning down what the U.S. economy is capable of in the long term is "literally the trillion-dollar question."

Corley, who oversees an investment giant with $488 billion assets under management, said Federal Reserve Chair Janet Yellen walked the tightrope beautifully Wednesday, trying to telegraph policymakers' views on when interest rates might start rising. "'Patient' out but not impatient in—I think it was a master class." Corley said.

This is a "very delicate balancing act" for not only the Fed but central banks around the world at time when global growth is "still pretty fragile and not well distributed," she said.

Growth in the U.S. is patchy; the euro zone is challenged; the U.K. faces headwinds; emerging markets are struggling; and China is trying to balance its economy, Corley said. "We are in a massive reset around the world. And it's going to be very difficult to move away and slowly normalize from where we are now."

As for opportunities, she likes European stocks better than U.S. equities. "If you look the DAX [in Germany] ... the Euro Stoxx ... at even the U.K., their returns are all stronger than the S&P and the valuations are much better. And you get a good dividend yield."

Corley added, "We've had investors in the last 12 months to 18 months dipping their toe into the water of Japan again. And they've seen great returns."

Allianz Global Investors is owned by Allianz SE, the German financial services giant.

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