Closet-indexing is a term used to describe a portfolio that appears to be (and is advertised as) actively managed and non-indexed. It occurs when the investor or manager holds securities in such a quantity that he or she effectively earns beta (the market portfolio).
For example, take a small-cap mutual fund with assets under management of, let's say, five billion USD. The fund will select individual securities rather than arbitrarily buying them according to their (float-adjusted) weight in the index. They will be viewed by both regulators and most investors as an "active" fund. The fund may even have a great manager. However, it has a high chance of performing in line with the index simply because of how diversification works.
Once the number of individual equity securities reaches a certain threshold—typically between 15 and 30 in the case of equities—the benefit to diversification by adding additional equities decreases dramatically. The diversification, volatility, and return differences between owning 75 and 50 stocks with similar weights is negligible.
Small-cap stocks are those with market capitalizations between ~300 million and two billion USD. In the aforementioned small-cap fund example, the manager has to allocate the five billion to companies with market caps around one billion on average. Assume the fund company limits the stake the fund can take in any given equity to 5% of market cap. The fund must hold a minimum of 100 stocks ($1 billion avg mkt cap * .05 = $50 million; $5 billion fund / $50 million = 100 holdings). At this point, the fund will, for all practical purposes, produce beta returns with a margin of error (MOE).
Better performing funds tend to hold fewer positions with higher concentration. Paradoxically, as a fund becomes more popular and increases in size, they eventually have no choice but to move away from concentration and become "closet-indexers."
(As an aside, funds with fewer positions and greater concentration also tend to experience greater drawdowns.)
If you call a spade an ace is it an ace?
Annual active returns will often, for better or worse, deviate from the index by more than the MOE. Truly active investors must be ready to experience greater pain in volatile periods. But they’re also far more likely to hit grand slams from time to time. If an investor seeks active returns they should not buy an index. It makes sense then that they should also avoid that which is called "active" but delivers annual index performance within the MOE.