A schematic for different types of active management

This graph is depiction of Antti Petajisto's work from the July/August 2013 FAJ. The author tries to contrast a manager's  active share and tracking error versus a benchmark. The active share is half the absolute difference between the actual weight in the portfolio to a set of stocks versus the weight of the stocks in the index. It could be any allocation versus a benchmark weight. For example, it could be the weight in different commodities versus the DJUBS commodity index. 

The active share is the percentage of a fund's portfolio that differs from a benchmark index. The tracking error is the standard deviation of the difference in return between a fund and its index. 

You can contrast the active share versus a benchmark and the tracking error of the fund versus the benchmark. If you are an index investor, the active share and tracking error will both be zero. If you are a closet indexer, the active share will be low and tracking error will also be low. A concentrated stock picker will have a high active share and high tracking error. The exposures will be significantly different from the benchmark and returns will also be very different. A diversified stock picker will have a high active share but may not have high tracking error because the diversification may match the index itself. Similarly, a manager who has a high factor bet may have lower active share but high tracking error based on the factor differences versus the benchmark index.

Note that this framework can be used for almost any asset class to show how bets are taken versus some benchmark. It can easily be used to compare hedge funds versus a benchmark to determine whether they may be closet indexers. This is a very useful framework.