"Anadarko takes advantage of the fact that most of the oil companies, especially the [exploration and production] shale companies in the United States, isn't very profitable if oil stays between $40 and $50 a barrel," the manager of the Oakmark Select Fund told CNBC's "Fast Money: Halftime Report."
Nygren added he expects the price of oil to rise back to about $70 per barrel, thus making the company even more profitable. U.S. crude has fallen over 40 percent in the last year and about 20 percent in 2015.
WTI crude in the last year
Regarding Cummins, Nygren said, "It's pretty easy to live with a stock like Cummins, which sells at about 10 times expected next year's earnings.
"Yes, there's a little risk if emerging markets go into a recession that they'll miss that number, but you get a 3.5 percent dividend yield and a company that will benefit from global growth," he said.
Anadarko's stock was up more than 1 percent midafternoon Wednesday, while Cummins was slightly lower.
Nygren also discussed the fall of Wal-Mart's stock, saying: "As the price keeps coming down and starts to be valued more like a structurally disadvantaged company, we get very interested in it, but it's not something we own right now."
"Structurally, when we look at the industry, we consider bricks-and-mortar stores to be at a disadvantage relative to online retail," he said.
Disclosure: Oakmark Funds holds at least 1 percent in both Anadarko's and Cummins' stocks as of Sept. 30, but does not own any Wal-Mart stock.