Methodology — Active-Risk (Tracking-Error) Decomposition
Transparency is a feature. This page explains what the active-risk decomposition does and why — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.
Active risk is the forward-looking (ex-ante) form of tracking error: the volatility of a portfolio's return relative to its benchmark, implied by a covariance matrix rather than read off realized history. It is the benchmark-relative twin of the risk-contribution view — the same idea applied to a portfolio's bets against its benchmark instead of its outright positions.
What drives it
The decomposition is built on active weights — each holding's portfolio weight minus its benchmark weight. This is the key property: an asset held at exactly its benchmark weight contributes nothing to active risk. Only the positions where the portfolio deliberately deviates from the benchmark — the over- and under-weights — drive the number.
The contribution split
Active risk splits exactly into per-holding contributions that add back up to the total, so you can see which active bet drives the tracking error. We report three standard views of that split — the marginal, component, and percent contributions to active risk (MCAR / CCAR / PCAR): how much a bet moves active risk at the margin, its share of the total, and that share as a percentage. The split is exact (it follows from active risk being a scale-consistent risk measure), and the contributions are signed — a bet that hedges the overall active position can reduce tracking error.
Ex-ante vs. ex-post
This is the forward-looking, covariance-based view. Its realized counterpart — the sample variability of an observed active-return series — is the tracking-error page. Both estimate the same quantity from different inputs: a covariance forecast versus realized history.
Honest limits
- The estimate is only as good as the covariance matrix it is built from — it is a forecast, not a measurement.
- Outputs are stated in the covariance's own return frequency; annualize the headline figure if a yearly number is wanted (the per-asset percentage shares are frequency-free).
- With no active position (portfolio equals benchmark) or a degenerate covariance there is no active risk to divide among holdings; rather than return a misleading zero-based split, the decomposition is reported as undefined.