(CNN) — The Trump administration has another idea to make housing more affordable: Let homeowners take their mortgage rate with them when they move.

On Wednesday, Federal Housing Finance Agency Director Bill Pulte said the administration is “actively evaluating” so-called portable mortgages. The proposal aims to address the housing market’s lack of supply.

The administration stepped up efforts to address housing affordability this past week. Pulte – who oversees Fannie Mae and Freddie Mac, the two government-backed entities that guarantee more than half of US mortgages – said officials are also weighing how to make mortgages assumable and whether to introduce a new 50-year mortgage option .

Just over half of homeowners with a mortgage have a rate below 4%, according to a Redfin a

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