I have written this before many months ago but I'll try again now.
The only entities that need to know I own a particular share are those entities that are capable of shipping me my share of the buildings or livestock or inventory or whatever that it is a share of, or of shipping me dividends.
To anyone else it is business intelligence they probably should not have and that maybe I would prefer they not have.
That's why this is a great complement to this idea:
All of this can be done in Open-Transactions; it does it out of the box.
Now sure, all of this can be done in Open-Transactions. However, using the bitcoin blockchain IN ADDITION to Open-Transactions allows you to directly trade stock for bitcoins and vis-versa over-the-counter without interference and dependence on a third-party server. You could even transfer stock directly to another OT server without the destination needing to trust the sender.
Basically, think about the current state of bitcoin exchanges, except pretend that they are OT servers. You can send USD to one server, buy bitcoins, and send them to any other server, including your own. If you want, you can later send those bitcoins to a completely different OT server and exchange them back to USD, which can be sent to you in a completely different way than you sent the USD initially. Sure, I'm oversimplifying OT servers and not stating how limited their abilities are in stealing something, but that is besides the point. It's still nice to know that you can provably show that you own something even if all of the backups for the server are lost, when you use the blockchain.