When you think about famous investors, Warren Buffett and Michael Burry are two that immediately come to mind.

Buffett and his company Berkshire Hathaway (NYSE: BRK.A)(NYSE: BRK.B) have been beating the market for decades, and Buffett is widely seen as one of the greatest investors of all time. Burry rose to fame for being one of the few investors to spot the housing bubble right before the Great Recession. His short bets on mortgage-backed securities yielded hundreds of millions in profits for his fund at the time.

Both Buffett and Burry are great investors in their own right, and both happen to own two of the same stocks heading into 2023.

1. Charter Communications

Burry's fund Scion Asset Management opened up a new stake in the broadband cable operator Charter Communications (CHTR 2.24%) in the third quarter of the year. You may know it better through its subsidiary brand Spectrum. Scion purchased 10,000 shares currently valued at a little more than $3.85 million. Considering it's one of just six stocks Scion owns, though, it's certainly notable.

Berkshire currently owns more than 3.8 million shares of Charter valued at $1.48 billion, amounting to a roughly 2.5% stake in the company. Berkshire has sold shares of Charter on 10 different occasions since 2017 but hasn't made any moves on the stock in 2022.

Charter offers mobile, broadband, and wifi services, and the company has also received grants to expand its broadband network into rural areas.In Q3, the company only grew its total customer relationships by less than 1%, but the big news was the better-than-expected growth in internet revenue, which was up nearly 4% year over year while both video and voice revenue fell year over year. There were also a net 75,000 internet customer additions in the quarter, which trumped voice and video as well.

While Charter's legacy businesses seem to be struggling, Charter still had about $1.5 billion of free cash flow in the quarter and generated a profit of close to $1.2 billion. Buffett and Burry must like what they are seeing out of the company's transition.

2. Liberty Latin America

Liberty Latin America (LILA 5.39%) is another position that Burry opened in the third quarter. It's a communications company that provides broadband internet, mobile, and video services in Latin America and the Caribbean under various brands. Burry purchased more than 155,700 shares in the third quarter, currently valued at $1.19 million.

Liberty Latin America also happens to be Berkshire's smallest position, and the conglomerate only owns about 1.28 million shares valued under $10 million. This probably tells us that both Buffett and Burry see Liberty as a high-risk, high-reward stock.

Liberty Latin America was spun out of Liberty Global a few years ago and has since acquired AT&T's wireless and wireline operations in Puerto Rico and the U.S. Virgin Islands for $1.95 billion.

In a presentation from August, management at Liberty Latin America told investors that it expects to create more than $180 million of run-rate synergies from the AT&T deal in its various markets. Liberty Latin also had $73 million of adjusted free cash flow in the second quarter of the year.

At a conference in September, CEO Balan Nair expressed lots of optimism about Liberty Latin's business in Puerto Rico, where it has spent a lot of time rebuilding infrastructure. Nair said the projected cash flows of its Puerto Rico division can generate $600 million of EBITDA (earnings before interest, taxes, depreciation, and amortization), which makes it worth more than the entire company right now.

"Essentially, you get Puerto Rico and left over you get the rest of my business for free, Panama... Chile, all the Caribbean islands. It's like insanity," Nair added. Apparently, Buffett and Burry are intrigued.