Tracking Error

When a fund is measured against a benchmark, the number that says how much it dares to differ from that benchmark is the tracking error. Each period the fund earns some return and the benchmark earns some return; the difference is the active return. Tracking error is simply the Standard Deviation of those active returns — the volatility of the fund's out- and under-performance around the index.

$$\text{TE} = \operatorname{sd}\!\big(R_p - R_b\big).$$

$R_p$ is the portfolio's return in a period, $R_b$ is the benchmark's, and $R_p - R_b$ is the active return. Take the standard deviation of that gap across many periods and you have the tracking error. Like any volatility, you annualise it by multiplying by the square root of the number of periods per year: a quarterly tracking error scales up by $\sqrt{4} = 2$.

A pure index fund aims for a tracking error near zero (often under 0.1%): it's trying to be the index. A closet indexer might run 1–2%. A high-conviction active manager runs 4–8% or more. The number tells you, at a glance, how much of a bet the manager is really taking.

Worked example

A fund's active returns over six quarters (in %) were:

$$+1.0,\ -0.5,\ +0.8,\ -1.2,\ +0.3,\ +0.6.$$

• Step 1 — the average. $(1.0 - 0.5 + 0.8 - 1.2 + 0.3 + 0.6)/6 = 1.0/6 = 0.17\%$ per quarter.
• Step 2 — the deviations from that average, squared, then summed. They come to about $3.61$.
• Step 3 — sample variance (divide by $6-1=5$): $3.61/5 = 0.72$, so the quarterly tracking error is $\sqrt{0.72} = 0.85\%$.
• Step 4 — annualise: $0.85\% \times \sqrt{4} = 1.70\%$ per year.

So this fund runs an annual tracking error of about 1.7% — a modestly active portfolio. Pair it with the annualised active return ($0.17\% \times 4 = 0.67\%$) and you get an information ratio of $0.67/1.70 \approx 0.39$. Tracking error is the denominator that turns raw outperformance into a risk-adjusted verdict on active skill.

Where it misleads

• It ignores direction. A fund that underperforms by a steady, predictable amount every quarter can have a low tracking error and still be a bad fund. Tracking error measures wobble around the benchmark, not whether you're on the right side of it. Always read it alongside the average active return.
• Ex-ante understates ex-post. A risk model's forecast ("this portfolio has 3% tracking error") often turns out too low when correlations shift and previously offsetting bets start moving together. Realised tracking error in a crisis usually beats the model's estimate.
• It's benchmark-specific. Change the benchmark and the number changes. A portfolio with tiny tracking error to one index can look wildly active against another.