Two Sigma, one of the world’s largest hedge funds, has long prided itself on two things: the sophisticated, in-house algorithms that power its trading, and its commitment to secrecy. But recent internal troubles have forced Two Sigma to air its dirty laundry.

In March, the New York firm, with $60 billion in assets, took the unusual step of telling its investors in a filing that the relationship between David M. Siegel and John A. Overdeck, the billionaire co-founders and owners who run the firm, had turned so toxic that it could hurt Two Sigma’s future. In October, it had more bad news: An employee had altered some trading models without the firm’s knowledge, affecting its returns and drawing regulatory scrutiny.

And in late October, Mr. Overdeck’s personal life was dragged into the open after his wife alleged in a lawsuit related to their impending divorce that unbeknown to her, he and the couple’s lawyers had moved billions of dollars of their joint assets into trusts that would shield them from her, their three children and the Internal Revenue Service.

It’s the kind of mess that any investment firm wants to avoid for fear of losing clients and talent, especially one that has avoided the spotlight for much of its 22 years of existence. In a 2015 profile of Two Sigma, Forbes magazine said the two founders were “obsessive about avoiding publicity and keeping the firm’s secrets under wraps.”