Tracking Error Calculator
The formula
What the tracking error tells you
The volatility of the difference between portfolio and benchmark — the risk you take when you claim to be "active relative to the S&P." Index funds report near-zero; enhanced index funds live between 0.5 and 2%; institutional active managers commonly 3–8%.
Calculation: TE = √(σp² + σb² − 2ρσpσb). Enter your inputs and every substitution is shown below the result.
Reading the result
Combine it with the information ratio to judge whether the active risk buys return. A 6% TE with 0.3% average shortfall is the worst combination: big risk budget, negative pay.
Rules of thumb: < 1% closet indexing · 1–4% conventional active · 4–8% high-conviction · > 10% "new portfolio, call it anything"
Limitations and best practice
Computed from monthly data it understates daily dispersion; from annual data it hides the path. And with a leveraged or short portfolio TE can look small while losses loom large — relative risk only.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is tracking error the same as volatility?
Can tracking error be too low?
Source & methodology
Standard definition in Grinold & Kahn, Active Portfolio Management; CFA Institute performance standards.
Tracking Error: the number, the method and the caveats
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Searchers land on a Tracking Error page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Tracking Error is on the table, the argument can stop being about impressions.
People rarely disagree about arithmetic; they disagree about assumptions that were never written down. Printing the substitution and the sensitivity ranking removes that category of disagreement for Tracking Error.
Nothing below is stock text pasted around a number: the worked example computes tracking error = 5.25 % from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Correlation with benchmark first, at ≈53.4 % of the headline for a ten-percent understatement of that input — which is the thread the rest of this guide pulls on.
The Tracking Error formula, explained
One formula, published in full: TE = √(σp² + σb² − 2ρσpσb). Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Portfolio volatility (%) (example value 16) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Benchmark volatility (%) (example value 12) is a measured number in the unit named by the label; the formula does not convert for you. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Correlation with benchmark (example value 1) is a quantity rather than a category — precision here is cheap and worth having. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
The default Tracking Error calculation, written out in full
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Portfolio volatility (%), Benchmark volatility (%), Correlation with benchmark. The computed tracking error comes out at 5.25 %, which the interpretation band labels “High active risk — a different portfolio wearing an index's clothes”.
- TE² = 16² + 12² − 2 × 0.97 × 16 × 12 = 27.520
- TE = √ that = 5.25% annualized
TE if correlation were 0.90 — 7.38 %. If your inputs change, this is usually the first companion figure to move.
Active share proxy sense — 43.7 %. Compare it against the main result of 5.25 % before drawing conclusions.
1-sigma relative range — 5.25 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
2-sigma relative range — 10.49 %. If your inputs change, this is usually the first companion figure to move.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
How far Tracking Error can reasonably move
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent? Settings beyond this model’s valid range were dropped rather than guessed at, which is why the table is shorter on one side.
| Correlation with benchmark setting | Tracking error |
|---|---|
| 80 % of the example value | 10.10 % |
| 90 % of the example value | 8.05 % |
| example inputs | 5.25 % |
That spread — 5.25 % at the low end, 10.10 % at the high — is what a careful read of Tracking Error looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Correlation with benchmark alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Tracking Error the most
This list was computed for this engine just now: ten percent on one input at a time, everything else on its example value. Some fields can only be tested in one direction here, and those rows say so instead of inventing a second figure. It is the fastest honest answer to “what matters most in Tracking Error?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Only one side of Correlation with benchmark can be probed here — −10 % gives 8.05 % versus 5.25 %, a ≈53.4 % response on the tracking error
- Portfolio volatility +10 % → Tracking Error = 6.64 % · −10 % → 4.02 % (the tracking error shifts ≈26.5 %)
- Nudge Benchmark volatility by ±10 % and Tracking Error lands between 4.53 % and 6.12 % (sensitivity ≈16.6 %)
Correlation with benchmark is the dominant lever here: a ten-percent decrease moves the result by about 53.4 %, from 5.25 % down to 8.05 % at the example value. That is where a careless figure does the most damage, so check it against a source, and treat Portfolio volatility as the second priority (≈26.5 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Is your Tracking Error good — reading the result bands
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “High active risk — a different portfolio wearing an index's clothes” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Correlation with benchmark alone a ten-percent decrease covers 5.25 % down to 8.05 % at the example value — the opposite direction leaves this model’s valid range, so only the upper probe is reported. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Placing this figure in context: calculators of this kind differ less in arithmetic than in what they choose to ignore. This one keeps Portfolio volatility (%) explicit so that the omissions are visible rather than hidden in a preset.
How people get Tracking Error wrong
Computed from monthly data it understates daily dispersion; from annual data it hides the path. And with a leveraged or short portfolio TE can look small while losses loom large — relative risk only. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Feeding best-case scenarios and calling them plans. Run the number at least at expected and at pessimistic inputs; the gap between them is the actual risk you are accepting.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Correlation with benchmark dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Tracking Error to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Before you trust your Tracking Error: a short checklist
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Confirm the example values are plausible for your own situation before replacing them.
- Check Correlation with benchmark before anything else: it is the measured dominant input, ≈53.4 % of Tracking Error per ten percent.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Note the date and the inputs beside the number so the figure can be audited later.
- Confirm the answer against one independent method or published benchmark for Tracking Error.
How to use the Tracking Error tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — start from evidence. The inputs behind Tracking Error are portfolio volatility (%), benchmark volatility (%), correlation with benchmark. Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. One decimal place more than your data supports is one decimal place of fiction.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. Re-running a number costs seconds; retracting a decision costs considerably more.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. Estimates improve most when the worst case is written down in ink.
Step 5 — schedule the next run. In Investing & Markets the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
From calculation to decision: where Tracking Error earns its keep
Numbers earn their keep in conversations, and Tracking Error is no exception. In Investing & Markets discussions around Portfolio Management, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. A result worth acting on survives having its two shakiest inputs halved.
Used properly this is a five-minute filter that saves weeks. Compute Tracking Error, reject what fails, and only then bring in the expensive analysis for the survivors. Estimates improve most when the worst case is written down in ink.
There is a personal-administration use people overlook: periodic self-checking. Tracking Error quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Quick answers: what searchers ask about Tracking Error
What affects Tracking Error the most?
Tracking Error is driven above all by Correlation with benchmark. Perturbing only that field by a ten-percent decrease produced 8.05 % against the 5.25 % baseline — a ≈53.4 % response, while Portfolio volatility manages ≈26.5 %.
Which matters more: portfolio volatility or correlation with benchmark?
For Tracking Error, Correlation with benchmark wins the head-to-head (≈53.4 % against ≈26.5 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Tracking Error?
On the worked example above Tracking Error comes out at 5.25 %. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Tracking Error by hand?
TE = √(σp² + σb² − 2ρσpσb) is the entire method. Work the inputs in that order — TE² = 16² + 12² − 2 × 0.97 × 16 × 12 = 27.520 — and you will reach 5.25 % on the default figures, the same number this tool prints.
What happens to Tracking Error if correlation with benchmark changes by 10 %?
On these inputs a −10 % change in correlation with benchmark takes Tracking Error to 8.05 % against the 5.25 % example — around 53.4 % of the headline. The same test on every other field is in the sensitivity section.
Is the Tracking Error result of 5.25 % good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Tracking Error sit against the 5.25 % reference above, how far would a plausible input error move it (≈53.4 % per ten percent on Correlation with benchmark), and what does the alternative option compute to?
How do I calculate Tracking Error manually?
Write down the inputs, then follow the printed steps in order — TE = √(σp² + σb² − 2ρσpσb). A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
How often should I check Tracking Error?
Whenever an input changes by more than a few percent, and otherwise on the rhythm of your decisions — before a purchase, a review, a renewal. Tracking Error is a snapshot, not a subscription; stale snapshots are the most common silent error in Investing & Markets planning.
Is tracking error the same as volatility?
Only for the residual versus the benchmark. A fund can have lower absolute volatility than its index yet huge tracking error if it simply holds different things.
Can tracking error be too low?
Yes — under about 0.5% the fund is a closet indexer: you are paying active fees to hold benchmark noise. Fee audits start here.
Does this Tracking Error tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Investing & Markets figures and the reason you can re-run this page as often as you like.
Glossary for Tracking Error
- TE if correlation were 0.90
- 7.38 % for the Tracking Error worked case; it sits next to the main result because it carries context the headline leaves out.
- Active share proxy sense
- 43.7 % on the example inputs — a companion figure printed beside the headline of Tracking Error so that no result is read in isolation.
- 1-sigma relative range
- 5.25 % in the default Tracking Error calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Tracking error
- The primary output of this tool: 5.25 % for the default inputs, computed exactly from TE = √(σp² + σb² − 2ρσpσb).
- Worked example
- Every substitution in order, from the example inputs to 5.25 % — the audit trail for the headline figure.
- Verdict band
- The plain-language label — here “High active risk — a different portfolio wearing an index's clothes” — mapping the computed figure onto experience-based ranges for Investing & Markets.
- Sensitivity (−10 %)
- How far the Tracking Error moves when a single input is nudged ten percent, in whichever direction the model accepts; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: TE = √(σp² + σb² − 2ρσpσb). Source of record: Standard definition in Grinold & Kahn, Active Portfolio Management; CFA Institute performance standards. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.