Steven Mnuchin, nominated to be the next Treasury secretary, stands to benefit as an investor from the revival of Fannie Mae and Freddie Mac under a policy change he outlined to privatize the mortgage giants, though he has pledged to quit the positions soon after his confirmation.

Financial disclosures made public Wednesday show Mr. Mnuchin owns investments in a hedge fund that has made a significant investment in Fannie and Freddie run by a Trump donor, John Paulson. The fund enjoyed a big gain after Mr. Mnuchin said just...