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Hedge fund billionaire David Tepper said Thursday he's "not as bullish" as he could be—taking a more cautious view of the stock market almost five years to the day since his comments on CNBC sparked the "Tepper Rally" in the stock market.

"I have problems with earnings growth [and] problems with multiples," he said. "So I can't really call myself a bull [near-term]," said Tepper, founder and president of Appaloosa Management, which currently manages more than $20 billion.

Appearing on "Squawk Box" as investors look to next week's meeting of Federal Reserve policymakers, Tepper said it might be a good time to take money off the table, adding that he has lots of cash right now.

"We have some longs and shorts and we're hedged in, but we don't have a huge equity book right now," he said.

Tepper called the stock market environment "challenging" and questioned whether earnings estimates for next year are too high.

Acknowledging he was not as definitive as usual, he said he's "not loving it," but if stocks were to fall 20 percent or so he'd be a buyer. He added that he still believes the market will go higher in the long term.

As for all the recent wild swings in the U.S. stock market, he blamed global reserve drawdowns. Money flows are not going in one direction anymore, he continued—warning the market should remain volatile as investors adjust to the new realities.

He said world economic growth is looking lower at a time when the Fed appears to be ready to raise interest rates while most other central banks are easing.

"The United States is not held hostage by the global economy. The U.S. stock market … which is 50-50 U.S. and the rest of the world is not the U.S. [economy]," Tepper said.

Tepper sees this as stock picker's market

Growth and margins for corporations matter more than the Fed, Tepper said, adding that it's a moment to pick individual stocks.

During a memorable appearance on "Squawk Box" in September 2010, the Appaloosa boss sparked the so-called "The Tepper Rally" when he said the Fed's asset-purchase program virtually guaranteed strength in stocks.

Since then, the has gained more than 70 percent.

In the current market, he thinks Apple is a cheap stock, which he has a small position in, "about 0.75 percent of our book."

"It does have a lot of Chinese exposure for it's growth, which is a bit of a problem. But the multiple is low so I can deal with it," Tepper said.

"[But] it's always going to have a lower multiple," he argued, "because it is still a device company that, even though people think it can't be replaced, still something can come along."

'I lost money in the Chinese market'

While Apple's exposure in China may not be that troubling for Tepper, he's pretty down on the stock market there.

"We were involved in China. I was reading the situation there wrong. I thought they were easing when they were not easing, and I lost money in the Chinese market," Tepper said, adding that he sold his stake in Chinese e-commerce giant Alibaba in early July.

"[The Chinese] just keep making policy mistake, after policy mistake, after policy mistake over there," he said. "It's a learning curve to get onto a market economy. You could say that. And maybe one day they'll get it."

But Tepper said it's not good when that "learning curve" is playing out in real time in the world's second-largest economy. "It's kind of bad when they're a $10 trillion or $11 trillion economy and they influence more than a third of the world's economy."

Tough year for hedge funds, but not Tepper

It's been a tough year for hedge funds with most seeing gains erased for the year, after August's wild market rout on China concerns.

Appaloosa on the other hand, is reportedly up over 12 percent net for the year through August, according to a person familiar with the matter. By comparison, the HFRI hedge fund index fell 1.87 percent for August—paring year-to-date gains to just 0.2 percent.

Though 2014 was a relatively low-key year for Appaloosa, up a meager 2.2 percent net of fees, Tepper's track record is undoubtedly one of the best in the industry.

The fund returned a record 42 percent in 2013 and has had only three down years in its history: 1998 (down 29 percent), 2002 (down 25 percent), and 2008 (down 27 percent), according to the book "The Alpha Masters."

But the years after those declines, the fund had record net performance in 1999 (up 61 percent), 2003 (up 149 percent) and 2009 (up 132 percent).

Appaloosa returned 10 to 20 percent of investor assets at the end of last year, the fourth-straight year of returning money to clients.

Tepper's past stock market calls

In some other past calls, Tepper told "Squawk Box" that the Fed had to taper its bond-buying to keep the stock market advance on an even keel. The term "taper" become common parlance on Wall Street, and gave rise to the phrase "taper tantrum."

, Tepper told CNBC the Fed would not taper for "a long time now." The central bank started its gradual paring back of asset purchases in January 2014.

, Tepper was more cautious, when speaking at SkyBridge Capital's SALT 2014 conference in Las Vegas, saying "don't be too frickin' long right now."

By December 2014, Tepper said in an email to CNBC: "This year rhymes with 1998. Russia goes bad. Easing [is] coming from Europe. Sets up 1999 … [oops] I mean 2015." He said he wasn't calling a top for in the market for the year. "You [just] have to be aware of the possibility for some sort of overvaluation of the markets."