See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
First of all in my view on passive investment where you are just putting in money and have no control over what happens to the investment it is ok to do that on H-1. So if you buy stock in IBM that’s OK because you don’t get to manage or run IBM just because you bought 200 dollars worth a stock. So passive investments were you don’t actually control the investment or the business activity they are ok for H-1.
But when you buy and rent out a house I think that would be objectionable. I think that could be considered to be a violation of your status. What if you invested money in a small company like say a two person company when you own 100 percent stock but you are not managing and somebody else is managing I think that would be ok (in fact closer to be ok). But the question, can you start your own IT company...well if you did in a partnership and if you were a passive investor and if you want to work for that company you would have to have a true employer-employee relationship with the company. That means somebody should be able to file you and then a H-1 concurrent, H-1 for your own company. So the decision tree is: Is my investment active or passive. If it is passive no problem I can invest even if I am on H-1. If it is active I would have to do an H-1B for my own company and make sure I have an employee employer relationship.
I am finding that government is very much more understanding or flexible when it comes to radical practices, dental practices, were you own your company but you have somebody who can fire you whether it is board of directors or president where you could be fired as long as that is there having a company on H-1 is possible.