sigmaquant.performance.metrics.tracking_error#

sigmaquant.performance.metrics.tracking_error(returns, factor_returns)#

Compute tracking error as the sample standard deviation of active returns.

Parameters:

  • returns (Iterable[float]) – Time series of portfolio returns.

  • factor_returns (Iterable[float]) – Time series of factor or benchmark returns. Must be aligned in time with returns.

Returns:

Sample standard deviation of active returns (ddof=1).

Return type:

float

Notes

  • NaN values are ignored.

  • Tracking error is defined as the sample standard deviation of

active returns:

Let \(a_t = r_t - b_t\) denote the active returns.

The tracking error estimator is:

\[\widehat{\text{TE}} = \sqrt{ \frac{1}{T - 1} \sum_{t=1}^{T} (a_t - \bar{a})^2 }\]