Randomly pick a (long only) portfolio from all possible portfolios over the S&P 500. The expected performance of this portfolio should equal the actual performance of the S&P 500.
In contrast, consider investing in the S&P 500 as a zero sum game, where a zero outcome means that a portfolio provides the return of the S&P 500. In this game players compete for the highest return on investment. As success in the stock market game is not random, players can be more and less skillful. Professional players such as portfolio managers, professional day traders or insiders in average should outperform a naïve investor.
So as the average naïve investor underperforms an average professional investor, he or she also underperforms the S&P500 (otherwise the game wouldn't be zero-sum). Is this conclusion correct?
To me it seems counter-intuitive. A naïve investor following basic investment rules such as "buy the dip" or "sell in may and go away", picking stocks based on value metrics and whatever recommendations there are for beginners would underperform. Where in contrast an investor ignoring all recommendations and behaving not goal-oriented at all, which leads to a random portfolio, could expect an average return.
However, modeling a stock market as zero sum game deviates from reality. Not all investors play for the highest ROI: they might also be in the game for the fun of gambling, or (as a company) buying stocks in the context of a merger. Or they might be forced to sell when receiving a margin call. But still I would assume that the vast majority of stock transactions are performed rationally towards the goal of maximizing the ROI, leaving little room for naïve players to outperform the market.
Is there any literature discussing such ideas?