However, Tepper said, "At some point, the market will get to a level that I will slow down that horse and eventually get off." He did not specify when that might be.
While Tepper provided no further details on what may cause him to get out of the market, a source told CNBC's Scott Wapner that Tepper got more fully invested in December.
The source said Tepper started to believe last month that the market was going to continue higher as the Federal Reserve was putting more money into the system and as U.S.-China trade tensions were starting to ease.
Appaloosa outperformed in December and so far in January, the source told Wapner.
The S&P 500 gained nearly 2.9% in December, capping an almost 29% advance for all of 2019 in the best year since 2013. The index picked up where it left off in 2020, increasing nearly 2.8% this month.
Tepper is well-known for a 2010 market call he made on CNBC that super-low interest rates by the Federal Reserve, coupled with the central bank's massive bond-buying, would make most investment choices go up. The Fed-driven stock market rally that ensued at the time became known as the "Tepper rally." The market rally continued the entire decade.
Tepper started Appaloosa in 1993, and grew it into a powerhouse, returning 25% a year. In May, he said he was returning Appaloosa capital to investors and converting the fund into a family office. Tepper also owns the NFL's Carolina Panthers.
On Friday morning, Kernen also got an exclusive market commentary from Druckenmiller, the founder of Duquesne Capital. In an email to Kernen, Druckenmiller said he agreed with Tepper's characterization of the stock market. He also noted the Federal Reserve's three rate reductions in 2019 under Chairman Jerome Powell.
"I revealed a very bullish posture intermediate-term since October when Powell guaranteed he would not rescind the insurance [rate] cuts unless inflation was persistently above target," Druckenmiller recalled. "Since then, both have worked out, and the Fed is still whining about inflation being below target."
President Donald Trump's "election prospects have increased with two trade agreements and big win in Iran, which the Democrats have responded poorly to," Druckenmiller added. "So I am still 'riding the horse' and bullish immediate term," he added, giving a nod back to Tepper's analogy.
In the early 1990s, while heading investment strategy at Soros Fund Management, Druckenmiller oversaw a series of trades that sent the British pound tumbling and yielded a profit of about $1 billion. At Duquesne over the years, he returned an average of 30% annually to investors. Years before Tepper, Druckenmiller turned his hedge fund into a family office in 2010.