Tracking error

investopedia says: A 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 errors are reported as a "standard deviation percentage" difference. This measure reports the difference between the return you received and that of the benchmark you were trying to imitate.

Alternatively, tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. See Evaluating fund managers for an example application.

Tracking error models
Tracking error is measured as the dispersion of a portfolio's returns relative to the returns of its benchmark, and is expressed as the standard deviation of the portfolio's active return (annualized).

A portfolio created to match the benchmark index (e.g. an index fund) that always matches its benchmark's actual return (zero active returns) would have a tracking error of zero.

There are two types of tracking error models: Backward looking tracking error is useful to analyze fund manager performance. This model has little predictive value and may be misleading if used in that fashion.
 * Based on historical performance: Also called backward-looking or ex post tracking error.
 * Predicted future performance: Also called predicted or ex ante tracking error.

A portfolio manager uses a forward-looking estimate of tracking error to accurately reflect the portfolio risk going forward.

This is done by using a multifactor risk model which contains the risks associated with the benchmark index. Statistical analysis of historical returns in the benchmark index are used to obtain the factors and quantify their risk (variances and correlations are involved). The portfolio's current exposure to the various factors are calculated and compared to the benchmark's exposures to the factors. A forward-looking tracking error is then calculated from the differential factor exposures and risks of the factors.

The forward-looking tracking error is useful in risk control and portfolio construction. "What-if" scenarios can be evaluated to optimize the portfolio within the desired level of risk. Although there are no guarantees that the forward-looking tracking error will match the backward-looking historical error over a period of time (for example, one year), the average of forward-looking tracking error estimates obtained at different times during the year will be reasonably close to the backward-looking tracking error estimate obtained at the end of the year.