After being kidnapped seven years ago, Juerg Degenmann decided to move his family from Venezuela to Miami for increased security. Long a playground for Venezuelan elites, the Florida city seemed like a natural choice, especially since Mr. Degenmann already owned a vacation home there, and he had bought and sold several investment properties in the area.

He and his wife paid $1.85 million in 2013 for a waterfront townhome in Sunny Isles Beach with its own boat dock. He’d always done well with Miami investment properties, so...