Burnham and the 174 fund managers like him who hold large stakes of their diversified portfolios in Apple are pulled in two directions: hoping to prevent an unforeseen drop in Apple shares from upending their portfolios, while also benefiting from a company whose shares are up 12 percent this year so far.
"Your positioning in Apple may hold a big sway in how your fund does overall, particularly in categories like large blend where every basis point counts," said Laura Lutton, who oversees equity fund research at fund tracker Morningstar.
In 2014, for instance, funds that underweighed Apple compared to broad market indexes were the most likely to underperform their peers, she said.
Holding a concentrated position in one company is one way for stockpickers to stand out as investors move money to passive index funds. Yet it is unusual for diversified funds like Burnham's to hold more than 10 percent of their portfolios in one company, said Todd Rosenbluth, director of mutual fund research at S&P Capital IQ.
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"Investors may not realize that their fund manager is taking on a higher amount of risk," he said.
Most fund managers are inclined to take profits when a stock hits 7 percent of a portfolio, yet there are few set mandates set down by fund firms, Rosenbluth said. He said that he can't think of any fund families that have to sell if holdings exceed guidelines as a result of appreciation.
Diversified mutual funds are allowed by law to add shares of a company as long as its total weight is below 24.9 percent of their portfolios overall, but do not have to sell shares if they appreciate above that level, said Jay Baris, an attorney at Morrison & Foerster in New York.
Burham didn't set out to have such a big stake in Apple, he said. He began buying shares in 2005 when they traded at a split-adjusted level of less than $7 each. Those shares have now appreciated over 2,000 percent.
"It's the world's greatest company. I just don't see any reason to sell it," Burnham said, adding that he thinks that the stock should trade above $200 a share. Shares of the company closed at $123.59 on Friday.