"I could keep [money] in cash and that's zero, and the Fed has told us that it's going to be zero for a couple of more years," Cooperman said.
Cooperman also dismissed investing in U.S. government bonds, calling the 1.8 percent yield "ridiculous" on the 10-year note. "Adjusted for taxes and inflation you're getting a negative return."
As for bonds over the next three or four years, he said he believes there will be significant negative returns. "They make no sense."
Omega Advisors has $6.6 billion under management. It's up 30 percent year-to-date, while the hedge fund industry as a whole is only up about 5.7 percent.
Stocks Cheap Compared to 'Rich' Bonds Says Appaloosa's Tepper
Asked whether he's a bull or a bear, he said he's like a "buffalo," saying the stock market could go up 10 percent or down 10 percent. "More likely up than down because of the economy and because of the Fed," he said.
"Half the stocks in the market are now yielding more than fixed income. You have to go back to 1958 to see that kind of condition." But he warned that returns in stocks will be less than historical averages.
Cooperman remains bullish on stocks, despite the fiscal cliff next year of automatic tax increases and spending cuts hanging over the market. He said, he thinks the U.S. debt crisis is solvable. "We need to give up a little bit — a little pain, a little suffering. Some of the old-time virtues."
President Barack Obama and House Speaker John Boehner Press On
Cooperman said he hopes for leadership in the country before our debt crisis reaches a tipping point. "One of these days we're going to wake up and the market is going to turn on us. Not like it turned on Greece. But we face that risk."
—By Matthew J. Belvedere at @Matt_SquawkCNBC and Maneet Ahuja at @WallStManeet.