Stock picker Bill Mason still thinks the U.S. market is attractive, calling stocks fairly valued and cheap compared to bonds.

Specifically, he has his eye on names such as Amazon (NASDAQ: AMZN), Apple (NASDAQ: AAPL) and Alibaba (NYSE: BABA), as well as a health-care stock that has the potential of being the best stock to own for the decade.

Amazon had a bad year last year, but after the third-quarter report, Legg Mason Capital Management went heavily into the stock and made it their largest position, said Miller, the firm's chairman and chief investment officer.

That's because the company's chief financial officer referenced a focus on productivity and made the point again after the most recent quarter, he explained.

"You saw margins expand in the U.S. I think that's a sign that Amazon could be entering what [CEO] Jeff Bezos calls the 'check-in period' with Wall Street, which would be a year of margin expansion, and I think that would be good for the stock," he said in an interview with " Closing Bell ."

Apple, he said, has "incredible momentum" right now and he expects Apple Pay and Apple Watch to do well.

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However, while the company will continue to do well, he thinks the stock will face tough comparisons in 2016.

"Because it's the largest company in the history of the world and because it trades at below market multiple and because its current momentum is so strong, if Apple is struggling to reach new highs then the whole market is going to likely be struggling," Miller said.

"Apple over the next or so will probably do fine relative to the market, but next year, who knows."

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As for Alibaba, the Chinese ecommerce company is growing fast, Miller said. It also sold off from $120 earlier in the year to about $85.

"I think Alibaba can go back to $120 in the next 18 months, and that would be a nice return," he said.

Looking toward the health-care sector, Miller thinks synthetic biology company Intrexon has the possibility of being the best stock of the decade, although he noted it is "early days" for the company. The stock is a top 10 position for Legg Mason.

"Synthetic biology is kind of where software was when people first began to write software," Miller said. "Intrexon is a leader with great technology in that."

He also likes homebuilders (NYSE Arca: XHB) and financials (NYSE Arca: XLF).

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