What is a 'Tracking Error'
Tracking error is the divergence between the price behavior of a position or a portfolio and the price behavior of a benchmark. This is often in the context of a hedge or mutual fund that did not work as effectively as intended, creating an unexpected profit or loss instead.
BREAKING DOWN 'Tracking Error'
Since portfolio risk is often measured against a benchmark, tracking error is a commonly used metric to gauge how well an investment is performing. Tracking error shows an investment's consistency versus a benchmark over a given period of time. Even portfolios that are perfectly indexed against a benchmark behave differently than the benchmark, even though this difference on a day-to-day, quarter-to-quarter or year-to-year basis may be ever so slight. Tracking error is used to quantify this difference.
Calculation of Tracking Error
Tracking error is the standard deviation of the difference between the returns of an investment and its benchmark. Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows:
Tracking Error = Standard Deviation of (P - B).
For example, assume that there is a large cap mutual fund that is benchmarked to the Standard and Poor's (S&P) 500 index. Next, assume that the mutual fund and the index realized the follow returns over a given five-year period:
Mutual Fund: 11%, 3%, 12%, 14% and 8%.
S&P 500 index: 12%, 5%, 13%, 9% and 7%.
Given this data, the series of differences is then (11% - 12%), (3% - 5%), (12% - 13%), (14% - 9%) and (8% - 7%). These differences equal -1%, -2%, -1%, 5%, and 1%. The standard deviation of this series of differences, the tracking error, is 2.79%.
Interpretation of Tracking Error
If you make the assumption that the sequence of return differences is normally distributed, you can interpret tracking error in a very meaningful way. In the above example, given this assumption, it can be expected that the mutual fund will return within 2.79%, plus or minus, of its benchmark approximately every two years out of three.
From an investor point of view, tracking error can be used to evaluate portfolio managers. If a manager is realizing low average returns and has a large tracking error, it is a sign that there is something significantly wrong with that investment and that the investor should most likely find a replacement.