Speaking from the SALT Conference in Las Vegas, Nevada, Cooperman said that he favored undervalued names such as Citigroup and outperformers like AIG.
"So, I think things that are depressed, like a Citicorp, which has got a great franchise, you're buying it below tangible book value, I think ultimately will work," he said. "We think AIG over the next three years gets to a 10 percent ROE, and that gets you into the mid-$60s stock price."
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And he exited General Motors at $39 per share, admitting that he owned three Lexus cars.
"I was always uncomfortable with it," he said. "And I just can't find American-made cars in my parking lot at my country club or (among) friends."
Calling GM a "fine company," he added, "I found other things that make more sense to me."
Apple, which Cooperman bought and sold a few times at a profit, was among his holdings again, he said.
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Cooperman said he had exited Apple around $650 per share and bought chipmaker Qualcomm. But he got back into Apple in the "low $500s."
"We think it's worth in the mid-$600s again, and we're going to ride that horse," Cooperman said. "We think it's attractively priced, good free cash flow, more intelligent use of their capital than they had a few years ago in terms of returning money to shareholders."
For the overall market, Cooperman said that he expected modest returns."I think we could have a high single-digit return for the year," he said. "Very strongly believe the conditions that lead to a bear market are not present."
Cooperman also said he didn't see signs of a bubble in the overall market.
"We don't have much cash," he said. "We're reasonably fully invested, but we have a lot of borrowing capacity because we have no leverage."
Cooperman invoked legendary investor Sir John Templeton's famous quote, "Bull markets are born on pessimism, grown on skepticism, mature on optimism and die on euphoria."
"I don't see any signs of euphoria in the market," Cooperman said. "Multiples are reasonably valued. Twenty-five percent of all stocks are yielding more than bonds, which is an attractive condition. Recessions cause bear markets because bear markets discount recession. There's no sign of recession. Economic data is looking a little bit better."
Cooperman argued that there were few options better than stocks at the moment.
"What are you alternatives in financial assets today? You could keep your money in cash, and that's somewhere between zero and 50 basis points. You could put your money in U.S. government bonds. That's 2.45, 2.50. I think two, three years from now you're going to be looking at 10-year government bond, 4 or 5 percent," he said.
"I think stocks are your best bet in financial assets."