Tracking error
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Many portfolios are managed to a benchmark, such as an index. Some portfolios are expected to replicate the returns of an index exactly (an index fund), while others are expected to deviate slightly from the index in order to generate excess returns or to lower transaction costs. Tracking error is a measure of how closely the portfolio follows the index, and is measured as the standard deviation of the difference between the portfolio and index returns.
If tracking error is measured historically, it is called 'realised' or 'ex post' tracking error. If a model is used to predict tracking error, it is called 'ex ante' tracking error. The former is more useful for reporting or analysis purposes, whereas ex ante is generally used by portfolio managers to control risk to satisfy client guidelines.
Tracking error is mathematically the same as Active Risk, and has historically been used in the context of index portfolio or fund management, but, especially in Europe, is now typically used to describe the standard deviation of returns, either active or passive. The active return is the difference in the return of a portfolio and its benchmark. An index manager aiming to match the return of a benchmark index seeks to minimize realised tracking error, i.e., the standard deviation of returns about the benchmark. An active portfolio manager, on the other hand, aims to achieve a positive active return with a low active risk.
It is important to distinguish between observed, or realised, tracking error and predicted tracking error. For active portfolios ex ante tracking error measures are necessarily lower than ex post. This is because future portfolio weights are randomly, but normally distributed around a mean (‘ex post stochastic’). Some studies have suggested a factor of as high as two (see Tracking error : ex ante versus ex post measures, Satchell and Hwang, Journal of Asset Management, Vol 2. No 3, December 2001).
Tracking Error = stdev(RETURN(portfolio) - beta * RETURN(index))
