Inverse Index Funds

Just thinking. Jack Bogle revolutionized investing for small investors in the USA by making market cap weighted index funds mainstream. What would happen if someone structured a security such that its percentage ownership of the underlying index say the S & P 500 would be inverse of  its market cap? The hypothesis I am exploring is that the smaller companies have more room to grow over longer periods of time.

The way this would work is that the fund starts out as  inverse market cap weighted  and at the end of x years based on growth it returns capital and dissolves itself. The fund can then be re-established from scratch.

An alternative of course is that the smaller companies shrink drastically and move out of the index. Homework for me to run a simulation and publish those results.