“Operating with essentially zero capital is not sustainable,” the CEO said Thursday morning, just after his company reported a $1.14 billion profit in the first three months of the year, the 17th consecutive quarter of profitability.

Welcome to the upside-down world of Fannie Mae FNMA, +2.51% , the company in question, and its little brother, Freddie Mac FMCC, +1.84% .

The two mortgage companies have always straddled the worlds of government and business, but ever since the financial crisis of 2008, that in-between area has been increasingly uneasy.

“Conservatorship,” into which Fannie and Freddie were placed at the height of the crisis, was supposed to be a temporary fix of an emergency situation . But with Congress unable to agree on a permanent way forward, it’s become the way the enterprises must operate.

Further exacerbating the problem is a 2012 amendment to the 2008 bailout terms that says the two enterprises must remit all their quarterly profits to the Treasury Department. Those revamped rules have been challenged in court by equity shareholders.

“We try to run our business as prudently as possible,” Fannie CEO Tim Mayopoulos said on the earnings call Thursday, when asked how any executive can manage in such an environment. Fannie and Freddie have both been experimenting with selling portions of their credit risk to capital markets investors to hedge those risks, he noted.

They’ve also tightened underwriting standards to avoid credit risk in the first place. The average Fannie borrower’s FICO score was 746 in the first quarter. By way of comparison, the median credit score across the entire mortgage market in 2001, before the bubble era, was 701.

Fannie’s serious delinquency rate also shows cleaner credit quality. It fell for the 24th quarter in a row in the beginning of the year, to 1.44%. According to the company’s financial statement, that number would be even lower if foreclosures didn’t take so long in many states.

But many analysts believe mortgage lending is now tighter than it should be to nurture a healthy market. Fannie and Freddie were created to provide liquidity to the mortgage market, to absorb credit risk that individual banks could not.

And there are other potential strains on the enterprises’ finances. Both must deal with shifts in interest rates, for example. Fannie’s profits were down from $1.89 billion a year ago and $2.47 billion in the fourth quarter, largely because of derivative bets which cost them $2.81 billion during the quarter.

In addition, while reducing the size of their portfolios lays off some risk to capital markets, it also offers Fannie and Freddie less upside.

All this means that any given quarter, if there is a loss, could force Fannie or Freddie to tap taxpayer funds from the Treasury Department. That likelihood grows every quarter as the two shrink their capital reserves down to zero by 2018.

Mayopoulos isn’t the only housing official to call the current system unsustainable. In February, Mel Watt, director of the Federal Housing Finance Agency, which regulates the two enterprises, urged Congress to take action.

“Investor confidence is critical if we are to have, as we do today, a well-functioning and highly liquid housing finance market that makes it possible for families to lock in interest rates, obtain 30-year, fixed-rate mortgages, and prepay a mortgage if they want to refinance or need to move,” Watt said.

“We need policymakers to act,” Mayopoulos said Thursday, but he acknowledged that there’s scant chance that will happen and even less housing officials can do to nudge Congress in that direction. “We’ll just stay tuned and see what happens,” he added.