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Tracking difference tells you the gap between a fund's return and its benchmark's return over a stated period. Tracking error describes the variability of the periodic return gaps. A fund can finish a period with exactly the same return as its benchmark even though their paths differed along the way.
To see the distinction, follow one fictional fund and one benchmark across three monthly intervals. Their cumulative return difference is zero, but the monthly gaps have a positive sample standard deviation. We leave that dispersion unannualized and state the calculation explicitly.
Identify the two return series
Use a fund's NAV total return and a matching benchmark total return for this comparison. NAV means net asset value. A return based on NAV and a return based on the share's exchange-traded market price are different measurements. Neither should silently replace the other.
Mackenzie Investments' explanation of excess return and tracking error defines tracking difference as fund NAV total return minus index total return. We keep that fund-minus-index direction throughout this guide. Its description of tracking error uses annualized daily return differences; our worked example instead uses a declared, unannualized monthly sample.
Before comparing actual figures, identify the share class and benchmark version. Match the currency, valuation times, observation dates, distribution and reinvestment treatment, and any hedging convention. Keep the fund's cost basis and the benchmark's tax or gross-versus-net basis visible too. A total-return index and a price-only index do not supply the same return series merely because their names are similar.
The example fixes those choices rather than calculating a real fund's results. It does not explain which expenses or investment decisions caused a tracking gap.
Follow three matched monthly intervals
Assume a fictional USD-denominated fund share class and a fictional USD total-return benchmark. Normalize each total-return wealth index to 100 at M0. The fund then follows 100 → 101 → 100 → 100; the benchmark stays at 100 at every observation.
These levels are dimensionless reference values for the return paths. They are not dollar amounts, quoted share prices or a sequence of investor cash payments. M0, M1, M2 and M3 mark four successive fictional month ends, with matching valuation times for the fund and benchmark. That gives three nonoverlapping monthly return observations.
There are no external investor contributions or withdrawals, market purchases or sales, or terminal cash payments in this illustration. Distributions, fees, taxes, currency or hedging changes and other adjustments are assigned zero. The stipulated levels therefore describe the complete example; they are not observations of an actual fund or index.
For each month, calculate return as the ending normalized level divided by the starting level, minus one. Define that month's active return as the fund return minus the benchmark return. “Active” here names this return gap; it does not identify an active-management strategy.
| Interval | Fund normalized start → end | Fund NAV total return | Benchmark total return | Active return gap |
|---|---|---|---|---|
| M0 → M1 | 100 → 101 | +1% | 0% | +1 pp |
| M1 → M2 | 101 → 100 | −100/101% ≈ −0.990099% | 0% | −100/101 pp ≈ −0.990099 pp |
| M2 → M3 | 100 → 100 | 0% | 0% | 0 pp |
The second month's proportional return is 100/101 − 1 = −1/101. As a percentage, that is −100/101%, approximately −0.990099%. It is not −1%: the decline starts from 101, rather than 100. Keep the fraction for calculations and round only the displayed decimal.
Compound each path before taking tracking difference
First calculate each series' cumulative return from M0 to M3. Multiply its own monthly growth factors, then subtract one.
Fund cumulative return = (101/100) × (100/101) × 1 − 1 = 0%.
Benchmark cumulative return = 1 × 1 × 1 − 1 = 0%.
Under our fund-minus-index convention, the full-window tracking difference, or TD, is therefore 0% − 0% = 0 percentage points. Both normalized paths end where they started.
That result does not make the monthly gaps disappear. Adding them gives 1 − 100/101 + 0 = 1/101 percentage points, rather than zero. Averaging them gives 1/303 percentage points, approximately +0.003300 pp. Neither operation replaces separately compounding the two paths and then subtracting their cumulative returns.
A return difference also uses a different operation from dividing one series' growth factor by the other's. State the measurement and its sign before interpreting a reported tracking figure.
Measure how the monthly gaps vary
To illustrate the variability question, calculate a sample standard deviation of the three active returns. Use proportions in the formula:
a₁ = 1/100, a₂ = −1/101, a₃ = 0.
Their arithmetic mean is (1/100 − 1/101 + 0) ÷ 3 = 1/30300 as a proportion. Multiplying by 100 expresses that mean as 1/303 percentage points, approximately +0.003300 pp.
For this illustration, choose the sample standard deviation with N = 3 and denominator N − 1 = 2. Let ā denote that arithmetic mean:
s = √[((a₁ − ā)² + (a₂ − ā)² + (a₃ − ā)²) ÷ (3 − 1)].
Subtract the mean before squaring each deviation. The resulting sample variance is 30301/306030000 in squared proportional-return units. Its square root is a proportional-return dispersion; multiplying by 100 converts it to percentage points:
Sample SD in percentage points = √(30301/30603) ≈ 0.995054 pp.
This is monthly-frequency active-return dispersion over three observations, with no annualization. N − 1 is our declared sample convention, not a claim about every fund provider's estimator. It is not the annualized daily tracking-error figure described in the Mackenzie note, and it should not be compared directly with one.
Because this particular benchmark is flat every month, the active returns happen to equal the fund's own monthly returns. Their sample standard deviations consequently coincide here. The definitions still differ: fund-return volatility uses the fund returns, while tracking dispersion uses fund-minus-benchmark returns. A changing benchmark would require the latter differences to be calculated separately.
Keep the five results attached to their questions
The fund and benchmark can have the same cumulative return while the active returns vary within the window. The table brings those measurements together without treating the mean gap as the cumulative TD.
| Measure | Exact calculation or basis | Result and unit |
|---|---|---|
| Fund cumulative NAV total return | (101/100) × (100/101) × 1 − 1 | 0% |
| Benchmark cumulative total return | 1 × 1 × 1 − 1 | 0% |
| Full-window tracking difference | Fund cumulative return minus benchmark cumulative return | 0 pp |
| Arithmetic mean monthly active return | (1 − 100/101 + 0) ÷ 3, in pp | 1/303 pp ≈ +0.003300 pp |
| Monthly active-return sample SD | Centered sample SD; N = 3, denominator N − 1 = 2 | √(30301/30603) pp ≈ 0.995054 pp; unannualized |
A standard deviation is nonnegative, while a fund-minus-index return difference can be positive, zero or negative. The zero TD here describes the matching endpoints. The positive sample SD describes the variation in the three monthly gaps. It is not evidence that the calculation went wrong.
For real comparisons, retain the observation frequency, window, estimator and annualization status alongside the return-series choices. A shorter sample or a different set of observations can answer a different question. Neither a small final gap nor a low tracking-error figure establishes safety, a maximum loss, a future tracking band or a better investment. This one-fund illustration does not rank funds or identify the cause of any deviation.
Frequently asked questions
Can tracking difference be zero while tracking error is positive?
Yes. In this example, both normalized paths start and end at 100, so the cumulative TD is 0 pp. The monthly active gaps are +1 pp, −100/101 pp and 0 pp. Their declared unannualized sample SD is approximately 0.995054 pp. The final return gap and the path's variability answer different questions.
What does a negative tracking difference mean?
Under the fund-minus-index convention used here, it means the fund's return was below the benchmark's return for the same window and measurement basis. That is not the same as saying the fund itself had a negative return. The sign does not forecast the next period or establish a fund-quality ranking.
Is tracking error the ETF market-price discount to NAV?
No. A discount compares a specified market price with a NAV reference at a stated time. Tracking error concerns the variability of periodic fund-minus-benchmark returns. Our example uses normalized NAV total-return levels, not exchange-traded prices, executable quotes or a premium/discount calculation.
Is the sample SD shown here an annual tracking-error figure?
No. It uses three monthly observations and the sample denominator N − 1, with no annualization. Mackenzie's note describes an annualized daily-return-difference measure. To compare actual reported figures, check their frequency, window, estimator, return basis and annualization convention rather than comparing the displayed numbers alone.
Why not add or average the monthly gaps to get cumulative tracking difference?
Monthly returns compound along each path. Compound the fund's growth factors and the benchmark's growth factors separately, then subtract the full-window returns. Here that TD is 0 pp, while the sum of monthly gaps is 1/101 pp and their arithmetic mean is 1/303 pp. Those sums and averages are valid descriptions of the monthly gaps, but they are not the cumulative return difference.
Explore HypaForecast
Browse market questions or visit the BTC 5-minute and 15-minute pages. These general navigation links are separate from the fictional fund and benchmark example.
Sources and scope
Mackenzie Investments: Excess return and tracking error supplies the NAV-total-return-minus-index-total-return definition and the distinction between a return gap and its variability. It describes annualized daily dispersion and warns about differences in fund and index calculation methods. It is a fund manager's explanatory note, not a universal reporting standard.
The saved explanatory text was read on 21 October 2026; its publication date and exact original retrieval time are not established here. The example's three-month paths, monthly sample estimator and exclusions are explicit teaching choices, not a reproduction of an issuer's full methodology. No current fund results, annualized values, causal explanations, investment recommendations or legal rules are supplied by this illustration.
HypaForecast publishes educational guides and operates a prediction market. This fictional benchmark-tracking explanation does not establish an ETF offering, an investment ranking, future performance or your eligibility to use a service.
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