The Shawnee neighborhood in Louisville, Ky., is a paradox: The houses are affordable, but they can be difficult to buy. The prices are so low that most banks and lenders will not bother writing mortgages for them.

That was the problem facing Christopher T. Smith when he moved back to Shawnee, a historically Black neighborhood along the Ohio River, where his mother still lives in the house where he grew up.

He and his wife, Gloria, did not expect to buy in an area where houses are more often scooped up by speculators who can pay in cash. “We were just looking to rent,” said Mr. Smith, who works as a hospital housekeeper and a part-time gardener.

But then the broker who was showing them rentals mentioned that

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