Bannister noted that the 7 percent gain for stocks year-to-date is "exactly in the middle in August-to-date changes for the S&P in the last 100 years. It's a pretty ordinary market."
Low interest rates and a long cycle, he added, "don't really create value. What they do is they reallocate price. And so, what you're doing is front-loading the market return."
Bannister said that he was pleased to see that loan growth had picked up and added that he was "encouraged" by comments Federal Reserve Chair Janet Yellen made Friday.
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"I thought her paper was more of a wonkish, collaborative, conference-type paper—I've been to a lot of conferences," he said. "It's sort of, 'here's both sides. What do you guys think?' But I would watch inflation and wages from here on out."
Bannister also said that he thought a "zero percent real Fed funds, which is 2½ nominal" by Dec. 16 was too aggressive. "We're not going to get there."
Achieving his new price target won't necessarily be easy for the stock market, he added.
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"Remember, the easy money is a cycle is made in the first two-thirds of a cycle. After that, you really do have to get the earnings and the economy right. And you have to get out before there's any sort of recession signs," he said. "So, we're in that last one-third of the economic cycle, but we are about 5½ years into bull market, and it could become a secular bull market that crosses the six-year mark next March.
"I wouldn't look for a lot of growth from here. It'll definitely be a case of margins starting to peak, but top lines starting to pick up, particularly exports."
—By CNBC's Bruno J. Navarro