Who this is for — Readers measuring how portfolio returns depart from a benchmark while distinguishing observed active risk, forecast active risk and a simple cumulative return difference.
Tracking error (TE), also called active risk, is the standard deviation of periodic active return:
ARₜ = Rₚ,ₜ − Rᵦ,ₜ; TE = sd(ARₜ)It measures variability, not direction. A portfolio that outperforms and one that underperforms can have the same TE if the dispersion of active returns is the same. Mean relative return enters the information ratio, not the TE denominator.
Ex post and ex ante
Ex-post tracking error is calculated on realised returns, with a sample or population convention and an annualisation rule. Ex-ante tracking error is a forecast built from active weights and a covariance or factor model.
For portfolio weights wₚ, benchmark weights wᵦ, active
weights a = wₚ−wᵦ and covariance matrix Σ:
TE_ex ante = √(aᵀΣa)The formula assumes weights, universe and matrix describe the relevant risk. Derivatives, options, currencies, off-benchmark securities, liquidity and nonlinearity may require additional models or scenarios. Ex ante and ex post need not agree: one is conditional on inputs, the other on the realised path.
The benchmark determines the measure
The same portfolio can have low TE to one index and high TE to another. Benchmark choice must be ex ante and economically consistent with mandate, asset universe, currency and hedge policy. Portfolio and reference must use compatible price/total-return variants, costs, close times and return frequency.
A poor benchmark creates misfit risk: the measure then captures structural differences between mandate and index alongside implementation choices. A low TE to an irrelevant index does not prove faithful execution of the mandate.
Tracking difference is not tracking error
Tracking difference commonly denotes average or cumulative return difference. Tracking error is dispersion of periodic differences. A fund can lag its index by a nearly constant fee and have negative tracking difference but very low TE. Another can average zero active return while moving widely above and below the index, giving high TE.
Compounding matters. Subtracting two cumulative returns is not generally the arithmetic sum of periodic active returns. The report should disclose whether it presents arithmetic active returns, geometric excess return or another linked measure.
Example
Suppose four monthly active returns are −0.4%, 0.2%, 0.6%, −0.4%.
Their mean is zero. Population TE is approximately:
√[((−0.4)² + 0.2² + 0.6² + (−0.4)²) / 4] ≈ 0.424%Using N−1 instead produces a different sample estimate. Annualising
with √12 requires the usual temporal-dependence assumptions. The
example does not establish whether that risk is suitable for any mandate.
Drivers of tracking error
TE can arise from active weights, off-benchmark holdings, sampling or partial replication, cash and flow timing, costs and fees, FX hedging, corporate actions and pricing methods, asynchronous rebalancing, securities lending, derivatives and basis, or data and reconciliation errors.
Performance attribution tries to connect active return with decisions. Risk attribution decomposes forecast or realised active risk. TE alone cannot identify which source dominates.
Annualisation and degenerate cases
The √m scale depends on assumptions about autocorrelation and
stability. Stale prices, overlapping returns and differently rebalanced
benchmarks may violate them. Observation count must be adequate for the chosen
frequency.
If active return is constant every period, TE is zero even when that constant
is nonzero. Information ratio is undefined for both 0/0 and nonzero
mean divided by zero; publishing infinity is misleading. Numerical precision
may instead create a tiny TE and a huge unstable ratio. Both cases require
explicit treatment.
Common error — Calling the difference between fund and index ending returns “tracking error”. TE is the standard deviation of periodic differences.
Sources
- CFA Institute, Investment Risk and Performance — active-risk definition and comparison with information ratio, alpha, beta and Sharpe.
- CFA Institute, Portfolio Performance Evaluation — 2026 refresher reading — benchmarks, relative risk, attribution and appraisal.
- Jeffery V. Bailey, Evaluating Benchmark Quality, Financial Analysts Journal (1992) — benchmark quality and its implications for active return and risk.
- GIPS Standards, Guidance Statement on Benchmarks, revised 2023 — benchmark choice, presentation and disclosure.
- Andrew W. Lo, The Statistics of Sharpe Ratios — autocorrelation and limitations of square-root-of-time annualisation.