Mark Calabria, the new head of the Federal Housing Finance Agency, testifies on Capitol Hill in 2013 when he was with the Cato Institute. (J. Scott Applewhite/AP)

For years, the chief executives of two giant government-controlled companies, Fannie Mae and Freddie Mac, have operated under a strict constraint: They can’t be paid more than $600,000 a year.

The housing companies may have found a way around that congressionally mandated pay cap. Fannie Mae and Freddie Mac created a new job — president — transferring some of the work traditionally done by the CEOs to the new positions, according to government investigators. The presidents will be paid more than $3 million each.

That arrangement has been challenged by federal investigators and lawmakers. The companies’ new government regulator, Mark Calabria, said he is “reviewing” the matter. It has raised a thorny question for the Trump administration: How much should executives at government-controlled companies supported by taxpayers be paid?

The Treasury Department was alerted to the new plan late last year but did not raise significant concerns. Executive compensation “is a matter that requires careful consideration given the taxpayers’ ongoing support of both companies,” Craig Phillips, counselor to Treasury Secretary Steven Mnuchin, said in an October letter sent to the company’s regulator, the Federal Housing Finance Agency, and obtained by The Washington Post.

“Treasury believes that compensation packages for . . . executives should reflect fiscal discipline in light of their conservatorship,” the letter said.

At Fannie Mae, five executives earned more than $2 million each last year, while four executives at Freddie Mac earned more than $3 million, according to data compiled by Equilar, a research firm. The total amount spent on salaries for the top executives increased 31 percent at Fannie Mae and 4 percent at Freddie Mac last year, according to the data.

Fannie Mae declined to comment for this report. Freddie Mac challenged the conclusions of an Office of Inspector General report questioning the arrangement. “Simply put, the facts do not support the report’s conclusions,” company spokesman Christopher Spina said.

The companies’ regulator had also defended the arrangements, telling the FHFA inspector general’s office: “Many corporations have a president who reports to the CEO and is second-in-command for the organization. Some corporations have more than one president."

But Calabria, who took over as director of FHFA earlier this month after the CEO positions were split, said in a statement to The Post, “We take both our Congressional mandate and our responsibility to protect taxpayer resources very seriously and are currently reviewing the issue.”

The debate comes as the Trump administration has prioritized finding a way to release the companies from a decade of government custody and amid a growing debate around CEO salaries. For critics of the new pay deals, it is also a reminder that regulators tasked with coming up with rules to rein in Wall Street pay after the global financial crisis have failed.

Fannie Mae and Freddie Mac stand as part of the last unfinished business from the crisis. The companies have been under government conservatorship since 2008 and received more than $100 billion in taxpayer bailouts.

Lawmakers have been slow to develop a plan for their futures, concerned that tinkering with their structure could threaten the availability of 30-year mortgages. The companies buy mortgages from lenders, then package them into securities to sell to investors. More than half of the country’s mortgages are backed by Fannie Mae or Freddie Mac.

In the meantime, the housing giants have continued to grapple with how much to pay their top executives. To be sure, their pay is dwarfed by those at other large financial institutions such as JPMorgan Chase, whose CEO made $33 million last year, and Bank of America, whose chief made $26.5 million. And Fannie Mae and Freddie Mac executives still earn less than their predecessors before the financial crisis, when the CEOs each made more than $10 million a year.

In the midst of the crisis, the companies’ regulator cut CEO salaries by more than half to about $4 million but then struggled to find executives to fill the top jobs, said Jim Lockhart, the former head of FHFA.

Lawmakers also considered requiring that Fannie Mae and Freddie Mac executives be paid in line with federal workers, but that was abandoned in favor of just capping the salary of the CEO at $600,000 — nearly twice the top government salary.

“Six hundred thousand is too low, and maybe the $4- or $5 million we were doing is too high. Maybe there is something in between that,” said Lockhart, a senior fellow at the Bipartisan Policy Center and vice chairman of WL Ross, a private equity company.

Running companies of Fannie and Freddie’s size and complexity would typically be a career highlight for an ambitious executive. Fannie Mae has $3 trillion in assets, and Freddie Mac’s assets total $2 trillion. But the relatively low salary and the lack of rich stock options, or even the hope for a bonus, make it a tough sell, executive recruiters say. The companies’ CEOs also have little control over the ultimate fates of the housing giants, which is being debated by Congress and regulators, they say.

At $600,000, many qualified CEO candidates would consider the job a “public service,” said Alan Johnson, a compensation expert who consulted with Fannie Mae on pay issues before the crisis. “The job itself, that doesn’t feel like a lot of fun,” he said. “If something goes wrong, you are going to get blamed.”

That argument has been unconvincing to lawmakers and consumer advocates who say the companies are still benefiting from the backing of U.S. taxpayers. If they run into financial trouble, taxpayers are still on the hook for bailing them out. Sens. Elizabeth Warren (D-Mass.) and Thom Tillis (R-N.C.) have introduced legislation to block the new pay arrangements.

The issue became pressing as both companies faced major turnover last year. Fannie Mae’s longtime chief executive, Tim Mayopoulos, announced he would be stepping down before the end of the year.

While deciding how to replace Mayopoulos, now president of a digital lending company, Fannie’s board came up with a plan: The CEO’s pay would remain $600,000, but it would create a new position, president, and that person would earn more than $3 million a year.

The company’s CEO salary is “more than 90% below” the median for executives at comparable companies, Fannie Mae said in a report to shareholders earlier this year. “Our current level of chief executive officer compensation puts pressure on our ability to attract and retain executive talent,” Fannie said.

Both positions were filled by company insiders. Hugh Frater, who had served on Fannie Mae’s board since 2016 and is also the nonexecutive chairman of Vereit, a real estate investment company, was picked to be CEO. David Benson, their chief financial officer, was promoted to president. Less than two months after Benson was appointed, Fannie Mae proposed increasing his salary 11 percent to $3.6 million, the Office of Inspector General noted.

Fannie Mae is now spending $4.2 million for work that used to be done for $600,000 when it had only a CEO, the inspector general’s report concluded.

At about the same time, Freddie Mac’s longtime chief executive, Donald Layton, announced he would be stepping down this summer. Freddie also created a new position, promoting the head one of its largest business units, David Brickman, to the president’s job, earning $3.25 million. But unlike its sister housing company, Freddie Mac says that when Brickman becomes chief executive in July, his pay will fall to $600,000 and the president’s job will disappear.

“Freddie Mac created the position of president to ensure a seamless transition to the role of CEO,” Spina, the Freddie spokesman, said in a statement.

Still, the inspector general’s office has challenged the arrangement. Freddie Mac now spends $3.85 million to pay two people for work that used to be done by one person for $600,000, according to the report. Both companies are involved in “financial engineering” meant to allow them to “circumvent” the salary cap put in place by Congress, the report said.

correction: An earlier version of this report understated Freddie Mac's assets.