Fannie Mae and Freddie Mac would require up to $157.3 billion in additional support from the U.S. Treasury in a severe economic downturn, according to the result of stress tests released on Thursday by the Federal Housing Finance Agency.

The tests, required by the Dodd-Frank financial-regulatory overhaul, are designed by the Federal Reserve to simulate a severe recession, in which the unemployment rate rises to 10% by mid-2016 and real gross-domestic product falls 4.5% by the end of 2015 before beginning to recover. The projections aren't meant to be "expected outcomes," the agency said.

Fannie and Freddie were put under government control in 2008, eventually requiring infusions totaling almost $188 billion from the U.S. Treasury, before the companies started turning a profit again. Under an agreement between the FHFA and the U.S. Treasury Department, the companies still have more than $258 billion in funding to draw from.

The same agreement requires that Fannie and Freddie send nearly all of their profits to the U.S. Treasury in the form of dividends and for the companies to reduce their capital reserves by $600 million a year, eventually reaching zero in 2018. In 2015, the companies each have a reserve of $1.8 billion.

According to the test results, even in a severe downturn the companies would have remaining funding to draw from the U.S. Treasury. Depending on how the companies are allowed to treat certain tax assets, the required draw could bet between $68.6 billion and $157.3 billion, according to the test.

Write to Joe Light at joe.light@wsj.com

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