# Tracking error

Tracking error is a measurement of how much the return on a portfolio deviates from the return on its benchmark index. It is a very important metric for index trackers.

Tracking error is the standard deviation of the differences between the return on the portfolio and the return on the benchmark; the standard deviation of the excess returns:

σ2 = 1/(n - 1) Σ(xi - yi)2

Where σ is the tracking error
n is the number of periods over which it is measured
x is the percentage return on the portfolio in period i
y is the percentage return on the benchmark

Some sources claim that the average error should be subtracted from right side of the equations above. That would give us the standard deviation of the tracking error from the tracking error over time. The formula given here appears preferable as it is a measure of deviation from the benchmark itself.

In order to make the tracking error comparable it should be annualised. In order to do the right right of the equation should be multiplied by the number of periods in an year. Equivalents σ multiplied by the root of the number of periods in an year. So if the error is based on monthly returns, it should be multiplied by root 12 to annualise.

Tracking error may be calculated from historical data (as above) or estimated for future returns. The former is called ex-post tracking error, and the latter ex-ante (standard terminology for statistics).

## The causes of tracking error

For an actively managed fund tracking error is a measure of how actively managed it is. A closet tracker will have a low tracking error, a very actively managed fund a high tracking error.

An index tracker has two different causes of tracking error: