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 past 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.