Do rich people on average have the vast majority of their wealth invested or they have lots of liquid cash/no productive properties? I often read about really rich people with billions of dollars, and I'd like to   know if they have, for example, just a big part of their wealth in shares of their company or they have lots of wealth in not productive activities?
The Federal Reserve has two statistical programs that I believe might address your question. The first is the Survey of Consumer Finances (SCF) and the second is the Flow of Funds (FoF). You should be able to find the data on the Fed's website.