Ken French talks about the effect of omission on diversification.
Key point - its not just all about correlations. Raw variances matter too.
The idea of bets by omission is a really important one and something I recently talked about with Ron Elmer who is the author of "The 401K Cook Book". Ron's point is that many portfolio managers who are benchmarked against the S&P 500 hold only a fraction of the 500 stocks in the index. Perhaps the stocks that they hold are the ones that they feel most strongly about. Or perhaps they just don't have the man power to examine all 500 stocks. Either way, the stocks that they don't hold actually represent a bet against those stocks. In effect they are underweight those stocks.
We should be very careful to think about what we are not including in our portfolios because these "omissions" actually represent unintended bets against those securities.