Your statement is out of logic

You can invest and receive dividend. But you can not be hired and paid in anyway even you can invest your time into it. The working hour is a legal gray area here. Because taking off the working hours, how many hours are left for you to be a full time F1? INS is not looking into it if you don't document your working hours just like you clean your house without payment from your spouse. Who cares that! If you want to make money just find a partner with privileges.