There’s an old saying about the news business: If you want to make a small fortune, start with a large one.

As the prospects for news publishers waned in the last decade, billionaires swooped in to buy some of the country’s most fabled brands. Jeff Bezos, the founder of Amazon, bought The Washington Post in 2013 for about $250 million. Dr. Patrick Soon-Shiong, a biotechnology and start-up billionaire, purchased The Los Angeles Times in 2018 for $500 million. Marc Benioff, the founder of the software giant Salesforce, purchased Time magazine with his wife, Lynne, for $190 million in 2018.

All three newsrooms greeted their new owners with cautious optimism that their business acumen and tech know-how would help figure out the perplexing question of how to make money as a digital publication.

But it increasingly appears that the billionaires are struggling just like nearly everyone else. Time, The Washington Post and The Los Angeles Times all lost millions of dollars last year, people with knowledge of the companies’ finances have said, after considerable investment from their owners and intensive efforts to drum up new revenue streams.

“Wealth doesn’t insulate an owner from the serious challenges plaguing many media companies, and it turns out being a billionaire isn’t a predictor for solving those problems,” said Ann Marie Lipinski, the curator of the Nieman Foundation for Journalism at Harvard University. “We’ve seen a lot of naïve hope attached to these owners, often from employees.”

The losses may have the most immediate impact at The Los Angeles Times, where journalists are bracing for bad news. Kevin Merida, the newspaper’s widely respected editor, announced last week that he was resigning, a decision made after tension with Dr. Soon-Shiong over editorial and business priorities, according to two people familiar with the matter.