“This company has to answer to shareholders, to our regulator and to Congress, and those groups often demand completely contradictory things,” Mr. Syron said in an interview.

Indeed, executives of both companies maintain that one of the reasons the firms hold so many bad loans is that Congress has leaned on them for years to buy mortgages from low-income borrowers to encourage affordable housing. In 2004, Freddie Mac warned regulators that affordable housing goals could force the company to buy riskier loans.

Others, however, dismiss that explanation. “Sure, it’s hard to deal with the pressures of Congress and shareholders and regulators,” said a former high-ranking Freddie Mac executive. “But that’s why executives get paid so much. It’s not acceptable to blame those pressures for making bad choices.”

In a statement, Freddie Mac said executives were unable to verify that Mr. Andrukonis’s memorandum existed, and that the company’s default and delinquency rates were substantially lower than other firms. “There is little to nothing that Freddie Mac could have done to prevent the losses that it is now incurring,” wrote company spokesman, David R. Palombi.

Mr. Mudd said the companies were victims of circumstance.

“You’ve got the worst housing crisis in U.S. recorded history, and we’re the largest housing finance company in the country, so when one goes down, the other goes with it,” he said. A Fannie Mae spokesman, Brian A. Faith, said that beginning in 2005, executives “sounded the alarm” about riskier loans and began limiting their purchases.

The depths of Freddie Mac’s problems are complicated by its long-planned, continuing search for a chief executive to replace Mr. Syron, who is expected to remain chairman. Two people who were approached  Kenneth I. Chenault of American Express and Laurence D. Fink of BlackRock  said they did not want to be considered for the position.

Image Richard F. Syron, the chief executive of Freddie Mac, says he had to balance the demands of shareholders and Congress. Credit... Mark Wilson/Getty Images

Some outsiders are surprised to learn that among the candidates the company is considering is Alan Schwartz, who headed Bear Stearns as it collapsed.