The rules for including a stock in indices such as S&P 500 are common knowledge, so everyone can know when e.g. company B is going to enter the index instead of company A. Since ETFs and mutual funds tracking the index have to buy shares of B and sell shares of A, this can potentially used by speculators who would try to quickly buy B and sell it to the ETFs in a high price, while buying A in a low price from the ETFs. Does such kind of speculation have any effect on the stock prices?
Specifically: Suppose someone invents a new index, X&Y 500, in which the identity of the companies is kept secret and revealed only to issuers of ETFs and mutual funds. All other things being equal (e.g. the companies in both indices are equally strong, have the same business potential, the volume of ETFs of both indices is the same, etc.), will the secret index X&Y 500 perform better than the revealed index S&P 500?
EDIT: To make the question even more focused, assume that there is no way to know in advance which stocks are going to enter/exit S&P 500 (e.g. these stocks are selected at random). So the difference between S&P 500 and X&Y 500 is that the stocks in the former are revealed to all traders at the same time, while the stocks in the latter are revealed only to ETF issuers.