Tracking error: the return gap and its variability

Tracking asks how far, and how steadily, the holdings diverge from a reference you define. Excess return describes the gap between the two cumulative results; tracking error describes how much their return differences vary. The result describes that difference only. It does not judge whether the reference is appropriate for you or whether either portfolio's result meets a personal objective. These questions depend on information outside the calculation.

A reference contains 1 to 5 components from 23 cached ETFs plus cash in the display currency. Whole percentages add up to 100%, and each user has one saved reference. When none is saved, the card uses 60% SPY + 40% AGG, marked as an example. The available funds represent markets and styles; cash keeps a constant value in the display currency. The reference editor defines the comparison mixture without changing the holdings used in the replay.

The reference returns to its stated weights every day. Each day's return is the weighted sum of its components' returns, linked to the previous day's index value. The replay keeps quantities unchanged, so price movements change its weights. Even with identical ingredients and identical starting weights, these two rules create different paths. This comparison models those rules; it does not model trading costs or reconstruct transactions in an account.

The dashed horizontal line is zero: both sides have the same cumulative return there. Above it, the example's cumulative return is greater; below it, the reference's is greater. The curves end at +5.12 percentage points against the daily constant mix and -37.43 against SPY. The caption also states each curve's minimum and maximum with dates. A curve's level is a cumulative gap, not a daily return or the tracking-error figure.

Each table uses a fresh starting mix at the beginning of its own window. The one-year and five-year columns therefore answer separate historical comparisons, rather than cutting the last year from an already-drifted five-year portfolio. The tables repeat the card's cumulative and annualized rows and tracking error, with 247 overlapping samples for one year and 1,250 for five years. Amounts are percentages or percentage points, without a judgement label.

Against the daily constant stock-and-bond mix, the ingredients are the same. The example is not rebalanced, and SPY's share drifted from 60% to 74.6% over five years in a rising stock market. This explains its positive excess and its small but non-zero tracking error: 0.20% over one year and 0.97% over five years. The difference comes from the paths created by the two weight rules, even though both portfolios began with the same funds.

SPY alone has different ingredients from the example. Tracking error is 4.47% over one year and 5.44% over five years. Roughly, a 5% tracking error means the yearly gap typically varied by about 5 percentage points. It does not mean a fixed 5% loss, or specify which side finishes ahead. The final excess can be negative while tracking error remains positive, because a standard deviation measures variability without carrying the direction of the final gap.

Cumulative excess is the example's cumulative return minus the reference's cumulative return, expressed in percentage points. Annualized excess subtracts their two separately annualized returns. It is not the annualization of the gap itself. Calendar days determine the annualization period. Short spans magnify this conversion, so an annualized difference can look large even when the underlying cumulative difference covers only a brief interval.

Tracking error uses the sample standard deviation of overlapping 5-day return differences, multiplied by the square root of 252/5. Markets close at different times; daily returns can reflect that timing rather than a difference in exposure. On Hong Kong and A-share mixtures, daily tracking error was 1.6 to 1.8 times the five-day figure; for US-only mixtures it was about 0.9 to 1.05 times. At least 10 samples are required. Overlapping windows share days and are not independent samples.

The comparison follows the replay span, from 1M to 5Y, with a 1Y default, and follows its display currency. Components use historical exchange rates on each date. If a component lacks data needed for the comparison, the reference is unavailable; another fund is not substituted. The example's tables illustrate the one-year and five-year spans only. Different windows can contain different events and produce different comparisons.

The information ratio is not offered. It evaluates active management and can become unstable on short spans. This tool describes a gap and its variability without turning that comparison into a judgement about management or personal fit. Like the other Jade tools, it records historical movement of today's mixture, rather than predicting a future result.

Roll, R., A Mean/Variance Analysis of Tracking Error, Journal of Portfolio Management 18(4), 1992.