Leon Cooperman: Apple stock 20% undervalued

Reacting to a new Apple letter from activist investor Carl Icahn, Apple shareholder Leon Cooperman told CNBC Thursday he believes the iPhone-maker's stock is 20 percent undervalued.

Icahn made good on a Tweet on Wednesday, and sent Apple a letter Thursday—asking the tech giant to accelerate share buybacks on the belief the stock is worth more than current levels.

Read MoreIcahn asks Apple tomake a tender offer for shares

While saying he respects Icahn, Cooperman, the billionaire founder of hedge fund Omega Advisors, said shortly after the letter's release that he'd leave it up to Apple management on share repurchases.

"There's nothing on the horizon nearly as profitable as the iPhone. I think they have to reinvest in the future to have new products," said Cooperman, who owns about 1.2 million Apple shares.

Scott Mlyn | CNBC

On stocks overall, Cooperman said they're fully valued and he's not surprised to see all the recent volatility—adding that while the market is not overvalued it's still not cheap.

Seventy-five percent of daily trading activity has nothing to do with fundamentals, he contended, advising individual investors to tune out the noise and keep focused on company earnings.

Read MoreWhy Cooperman likes stocks much better than bonds

"Bull markets don't die of old age," said Cooperman, arguing they run out of steam because of recessions. "There is no recession on the horizon."

But he wasn't ready to give the U.S. economy his stamp of approval.

"We have got what I call an economic stress list," Cooperman said. "Inflation is generally accelerating ... the yield curve is inverted, employment is declining [and] leading indicators are declining."

Omega Advisors CEO Leon G. Cooperman speaks at the CNBC Institutional Investor Delivering Alpha Conference in New York.
Heidi Gutman | CNBC
Omega Advisors CEO Leon G. Cooperman speaks at the CNBC Institutional Investor Delivering Alpha Conference in New York.

Cooperman's fair value assessment on stocks echoed comments he made to CNBC on July 16, ahead of his presentation at the Delivering Alpha conference presented by CNBC and Institutional Investor.

The Dow Jones industrial average is basically unchanged since then, despite a wild ride that saw a recent bottom in early August.

The Dow recovered through mid-September. Recently, it's been up by triple digits up and down by triple digits.

Year to date, the Dow was up 2.5 percent after Wednesday's strong rally on the back of well-received Fed minutes.

Read MoreInvestors turn to earnings after Fed stock boost

At Delivering Alpha, Coorperman gave 12 stock recommendations—some were new, such as Actavis and Citigroup while others were repeats of his previous recommendations made at the conference, such as SandRidge Energy and KKR & Co.

The Omega boss has an exceptional track record at the conference. In 2012, all 10 of his stock picks gained over the following 12 months. In 2013, eight out of 10 did.

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