The maker of Cadbury chocolate and Oreo cookies issued a statement saying it welcomed Pershing as an investor.
Another large hedge fund, Nelson Peltz's Trian Fund, also has a stake in the company.
In 2012, the Illinois-based global food maker spun off its grocery business into Kraft Foods Group, which merged with ketchup maker H.J. Heinz earlier this year to form Kraft Heinz. Kraft Heinz is backed by Warren Buffett's Berkshire Hathaway and 3G
While many activists are gobbling up Mondelez, hedge fund manager Charles Trafton told CNBC's "Power Lunch" why he is steering clear of the stock.
"It's too expensive. We don't own it and are not planning to buy any shares at this steep price. Most of the valuation has already come and gone."
But Trafton still likes the food sector overall, as a defensive move towards staple stocks. "We call it the pop-tart trade," said Trafton. "These stocks perform like internet stocks but at really cheap prices."