Tracking error is used within the finance industry to determine how well one instrument tracks another. Often tracking error is incorrectly defined as the standard deviation of active returns rather, than the square root of the average squared active return. While these terms are similar in many cases, we discuss examples where the definition can significantly differ.

## Defining tracking error

Consider two financial instruments, where one is designed to track the other. The active return is the return difference between the two instruments and the tracking error should quantify the average size of the active returns; that is – how closely they mimic each other. If the tracking error, is zero then you expect them to be a carbon copy of each other.

As Figure 1 shows, tracking error can be modelled by two components – a drift term and a stochastic term. The drift term represents a constant deviation in tracking between two instruments. A real-world example of this might be the management fees charged by an ETF provider. The stochastic term adds noise to the tracking over the short term, but over long periods should average to zero.