# Tracking Error

## 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.

Tracking error is reported as a standard deviation percentage difference, which reports the difference between the return an investor receives and that of the benchmark he was attempting to imitate.

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## 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.

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