1. That's overly restrictive. Why not let them own individual stocks in, say, a blind trust?
2. It's a free country. It's up to the voters to decide if they want to elect someone who profits from their position. What is needed is a law requiring public disclosure, not prohibition.
3. If you force people to divest their portfolios before taking public office you will reduce the pool of people willing to serve.
This is not to say that I disagree with the policy position, only that it's not the slam-dunk you seem to think it is.