The operative word is subordinate. If the person is in your managerial sphere then there is no way that you should have a personal relationship with this person. Even if you believe that you can be fair and even in all your decisions... do you want to look over your shoulder on every decision? Do you need the ever present possibility that someone may question your motives? Finally, your superiors will judge you by your actions and they will question your judgment as a manager that crossed the managerial/subordinate line.
Beware of workplace romances... they are career killers.