A recent study of endowments by Tuo Chen of Columbia University shows there is a strong positive size effect between the size and returns. This is is consistent with the work of Piketty on inequality and wealth. There is a rising gap between the wealthy and not so wealthy because richer investors make higher returns. It is the reason for this success which may surprise many investors.
The poorer performance of smaller endowments is based on their caution. If you think the markets are not fair, caution may be warranted. Don't play a game that can work against the less sophisticated. There may be some value from an information channel, but the authors shows that risk-taking is a much greater driver. Perhaps it makes sense for investors to better understand their willingness to take risk over trying to get an information advantage in order to enhance performance.