Why can tracking difference be small while tracking error is noticeable?

Declare the window, sign and observation frequency

Choose the same return basis, currency, dates and cash-flow treatment for the portfolio and benchmark. Define active return in each period as portfolio return minus benchmark return. A positive number then means portfolio outperformance for that period; a different source may use the opposite sign.

CFA Institute describes active risk, also called tracking error, as the standard deviation of active returns. For clarity, the worksheet below reports an unannualized sample standard deviation. It separately defines the full-window cumulative tracking difference, because an arithmetic average of period gaps is not generally the same quantity.

An original four-period return-gap example

Stipulate four equal observation periods. The fictional benchmark returns 0% in each, and the fictional portfolio returns −1%, 0%, +1% and 0%. Assume no external cash flows, fees, taxes or other adjustments. These are invented returns, not measurements from a fund or an index.

The benchmark’s cumulative return is 0%. The portfolio’s cumulative growth factor is 0.99 × 1 × 1.01 × 1 = 0.9999, giving a cumulative return of −0.01%. Under the declared portfolio-minus-benchmark convention, full-window tracking difference is therefore −0.01 percentage points. The arithmetic mean of the four period active returns is instead zero.

Compute variability with the denominator visible

In percentage-point units, the four active returns are −1, 0, +1 and 0, with mean zero. Their squared deviations sum to 2 squared percentage points. Dividing by n − 1 = 3 and taking the square root gives a sample standard deviation of approximately 0.816497 percentage points per observation period.

If the same four observations are treated as the complete finite population for a descriptive calculation, dividing by n = 4 gives approximately 0.707107 percentage points. The difference comes from the denominator convention. Neither number is annualized, and neither is a confident estimate of future variability from only four invented observations.

Read level and variability together

The tiny cumulative gap does not mean the portfolio matched the benchmark every period. Its positive and negative active returns largely offset. Conversely, a constant nonzero period gap has zero standard deviation around its mean, even though it can accumulate a meaningful return difference. Standard deviation measures variability, not whether the average gap is desirable.

Before comparing published figures, check observation frequency, length of history, total-return treatment, fee basis, annualization method and whether a sample or population denominator is used. A daily tracking-error estimate and an annual return gap are not interchangeable. This worksheet makes no independence assumption or square-root-of-time annualization claim.

Method, sources, and limits

The four-period series and calculations are original hypothetical teaching inputs, checked on 26 October 2026. No product’s tracking quality was measured or ranked. Definitions and reporting conventions must be read from the actual methodology; the exercise is not a forecast, benchmark-selection recommendation or statement that a low tracking metric implies low investment risk.