Academic studies have shown that closet indexing is a big problem. Studies like the one described in the influential Cremers and Petajisto paper show both that many funds closet index and that funds that do closet index tend to underperform.
So how do you avoid these bad funds? Christine Benz at Morningstar recently wrote a post answering the question of whether an investor can look at the R-squared of the fund to determine if a fund is a closet indexer, specifically Selected American Shares. Benz references the Cremers and Petajisto study's active share measurement of holdings overlap to claim Selected American Shares is not an index tracker. However, R-squared is useful when detecting closet indexers as demonstrated in the recent Amihud and Goyenko paper. Are we to believe that Selected American's poor recent performance aligning with it's rising R-squared is a coincidence?
Still, Benz is right to point out that R-squared is not a perfect mechanism to use to detect closet indexing. (Neither is Active Share, but that's a point for a different blog post.) For one thing, R-squared is calculated based on past performance. Monthly returns are typically used, meaning you need a good chunk of data (several years) to get real significance. This means it will fail to find closet indexing that is more short-term. Studies such as the one done by Chevalier and Ellison suggest that mutual fund managers may closet index to "lock in" a good year. Such closet indexing may only last a quarter or so, and would therefore go essentially undetected by R-squared.