Tracking error is the annualised standard deviation of the return differences between an ETF and its benchmark. Formula: TE = √Var(RETF − Rbenchmark) × √12. For UK Tax Drag, we use 3 years of monthly returns (36 observations). Low tracking error (under 0.5%) is the target for index trackers. Higher tracking error (>1%) suggests sampling differences, optimisation, or replication issues. Critical distinction: tracking error is different from tracking difference — tracking error measures consistency; tracking difference measures the average gap (essentially OCF + drag).
The formula
TE = √[Σ(Di − D̄)² / (n − 1)] × √12 where: Di = RETF,i − Rbenchmark,i (return difference for month i) D̄ = sample mean of return differences n = number of observations (36 for 3-year monthly) √12 = annualisation factor Equivalently: TE = annualised standard deviation of (ETF return − benchmark return)
Conceptual: at each month, calculate how much the ETF gained or lost relative to its benchmark. The standard deviation of those differences, annualised, is the tracking error.
Tracking ERROR vs tracking DIFFERENCE — the key distinction
Two related but separate concepts:
| Tracking error | Tracking difference | |
|---|---|---|
| What it measures | Consistency of the gap (volatility) | Size of the gap on average (mean) |
| Formula | Standard deviation of (RETF − Rbenchmark) | Mean of (RETF − Rbenchmark) |
| Annualised by | √12 (volatility scaling) | ×12 or geometric (mean scaling) |
| Always negative? | Always positive | Usually negative (OCF drag) |
| Good ETF result | Low (close to 0) | Slightly negative (~ −OCF) |
Example: a perfectly tracking 0.07% OCF ETF would show tracking difference of about −0.07%/year (consistent fee drag) and tracking error close to zero (very little month-to-month variation in the gap). A sampling-based ETF might show tracking difference of −0.20% (OCF + sampling drag) and tracking error of 0.40% (variable gap due to sampling). Both matter.
Inputs we use
| Input | Source | Notes |
|---|---|---|
| ETF monthly returns | Issuer + LSE | Total return, GBP |
| Benchmark monthly returns | Stated benchmark from issuer factsheet | Total return, GBP, same currency conversion as ETF |
| Return differences | Calculated: RETF − Rbenchmark | Sign matters — positive = ETF outperformed |
| Annualisation | √12 multiplier | Standard volatility scaling |
Ex-post vs ex-ante tracking error
Two flavours of tracking error:
- Ex-post tracking error: calculated from observed historical return differences. This is what UK Tax Drag publishes — it tells you what actually happened.
- Ex-ante tracking error: forecast tracking error based on portfolio risk-model decomposition (factor exposures, security weights vs benchmark). Used by professional fund managers for risk budgeting.
Retail-facing tracking error is essentially always ex-post (historical). Don't confuse with the higher figures professional managers sometimes publish on their internal targets.
Typical tracking error ranges
| ETF type | Expected TE range |
|---|---|
| Full-replication large-cap index (S&P 500, FTSE 100) | 0.05–0.20% |
| Sampled broad index (FTSE All-World, MSCI ACWI) | 0.15–0.40% |
| Synthetic index ETF | 0.05–0.25% |
| Smart-beta / factor ETF | 0.30–1.00% (vs parent index) |
| Bond aggregate ETF | 0.15–0.50% |
| Emerging market ETF (often sampled) | 0.30–0.80% |
| Frontier market / niche EM ETF | 0.50–1.50% |
| Currency-hedged ETF | +0.10–0.30% above unhedged equivalent |
Worked example — VUSA tracking error
Vanguard S&P 500 UCITS ETF (VUSA) tracking the S&P 500 Total Return Index in GBP, 3 years ending April 2026.
| Month | VUSA return | S&P 500 GBP TR | Difference (Di) |
|---|---|---|---|
| May 2023 | +1.42% | +1.40% | +0.02% |
| Jun 2023 | +5.85% | +5.92% | −0.07% |
| Jul 2023 | +2.95% | +2.99% | −0.04% |
| ... (33 more rows) | ... | ... | ... |
| Mean D̄ | −0.0058% | ||
| Sample std dev of Di | ~0.018% | ||
| Annualised: 0.018% × √12 | ~0.063% | ||
VUSA's 3-year tracking error of approximately 0.06%/year is excellent — well within the expected range for a full-replication large-cap tracker. Its tracking difference of about −0.07%/year matches the published OCF, indicating clean operation with minimal sampling drag.
What tracking error tells you
- Quality of replication: for passive index trackers, lower TE = better fund management.
- Surprise factor: high TE means your ETF can deviate significantly from index returns month-to-month — a problem if you bought it specifically for index exposure.
- Sampling vs full replication: sampling-based ETFs (cheaper for very broad indices) typically have 2-3× higher TE than full-replication versions.
- Currency hedging cost: hedged ETFs typically have higher TE than unhedged because the hedging adjustments introduce additional return variation.
What tracking error does NOT tell you
- Direction of the gap. A TE of 0.5% doesn't say whether the ETF outperforms or underperforms — use tracking difference for that.
- Persistent underperformance. An ETF that always underperforms by 0.5% has tracking difference −0.5% and tracking error close to 0 (consistent gap).
- Causes of the gap. Could be OCF, sampling, optimisation, securities lending revenue, currency timing — all show up the same way in TE.
- Future tracking quality. ETFs that change replication methodology or restructure can have different TE going forward than historically.
The "low tracking error" obsession trap
For most retail investors, obsessing over 0.05% differences in tracking error is wasted effort. Comparison:
- Two S&P 500 trackers: TE 0.08% vs TE 0.12%.
- Difference over 30 years on £30,000: about £15-£25 per year in tracking noise.
- OCF difference of even 0.05% (over the same period): about £20-30 per year average + compounds.
Pick based on OCF first, total cost of ownership second (OCF + bid-ask spread + platform fees), tracking error third. Material TE differences (>0.30%) on broad trackers should raise eyebrows — small differences shouldn't.
How to reproduce this yourself
- Get monthly returns for the ETF (36 months, GBP TR).
- Get monthly returns for the stated benchmark (same window, same currency).
- Calculate return differences for each month.
- Apply STDEV.S to the differences column.
- Multiply by SQRT(12).
Issue: benchmark data is sometimes hard to access free for index providers. Yahoo Finance or Stooq sometimes have ticker proxies. Or use a similar ETF tracking the same index as a benchmark proxy (introduces small error).
Sources and methodology
Tracking error follows standard fund management practice (Roll, 1992; standard institutional risk-budgeting literature). The ETF Data Methodology documents all data sources. The site methodology documents the broader review process.
Related metric pages
How UK Tax Drag holds itself to account
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