Formula, in Risk & Portfolio Construction
Tracking Error Formula
Tracking error is the standard deviation of the difference between a portfolio's returns and its benchmark's returns. A passive index fund aims for near-zero tracking error; an active manager accepts higher tracking error in pursuit of excess return. It is the denominator of the information ratio.
4 variables. Published May 26, 2026. By AI Fin Hub Research.
TE = stdev(R_p - R_b) = sqrt( (1/(n-1)) x sum_i ( (R_p,i - R_b,i) - mean_active )^2 )
Annualized: TE_annual = TE_period x sqrt(N) Variables
R_p,i - R_b,i
Active return in period i
Portfolio return minus benchmark return for each period. The series of these differences is what tracking error summarizes.
mean_active
Mean active return
Average of the active returns over the sample. Tracking error measures the dispersion of active returns around this mean, not around zero.
n
Number of observations
Count of return periods. The n-1 divisor gives the sample standard deviation, the standard convention for an estimate from data.
N
Periods per year
Annualization factor (252 daily, 52 weekly, 12 monthly). Tracking error scales by the square root of N like any volatility.
Step by step
- 1
Compute the active return for each period as portfolio minus benchmark return.
Active returns over four months: +0.5%, -0.2%, +0.8%, -0.1%.
- 2
Find the mean of the active returns.
Mean = (0.5 - 0.2 + 0.8 - 0.1)/4 = 1.0/4 = 0.25%.
- 3
Compute each active return's deviation from that mean, square it, and sum the squares.
Deviations: +0.25, -0.45, +0.55, -0.35 (in percent); squares 0.0625, 0.2025, 0.3025, 0.1225; sum = 0.69 (percent-squared).
- 4
Divide by n-1 and take the square root for the per-period tracking error, then annualize.
0.69 / 3 = 0.23; sqrt(0.23) = 0.4796% per month; annualized 0.4796% x sqrt(12) = 1.66%.
Worked example
Enhanced index fund, four monthly active returns
Active returns
+0.5%, -0.2%, +0.8%, -0.1%
Periods per year
12
Mean active = 0.25%. Deviations from mean (in %): 0.25, -0.45, 0.55, -0.35. Squared: 0.0625, 0.2025, 0.3025, 0.1225, summing to 0.69. Sample variance = 0.69 / (4-1) = 0.23 (percent-squared). Monthly TE = sqrt(0.23) = 0.4796%. Annualized = 0.4796% x sqrt(12) = 0.4796% x 3.464 = 1.66%.
Annualized tracking error of about 1.66%. This sits in the typical range for an enhanced-index strategy: tight enough to stay close to the benchmark, but loose enough to express modest active views. Pure passive funds usually report tracking error well under 0.5%.
Common variations
Run the numbers next
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Sources
- Active Portfolio Management , Richard C. Grinold and Ronald N. Kahn, McGraw-Hill (1999)
- Practical Portfolio Performance Measurement and Attribution , Carl R. Bacon, Wiley (2008)
Keep the topic connected
- Formula Information Ratio Formula
The information ratio formula: active return over a benchmark divided by tracking error. Measures the consistency of excess return, with an example.
- Formula Annualized Volatility Formula
The annualized volatility formula scales per-period return standard deviation by the square root of periods per year. Root-time scaling explained.
- Formula R-Squared Formula
The R-squared formula: the share of a portfolio's return variance explained by its benchmark. The squared correlation behind beta and alpha.
- Formula Beta Formula
The beta formula: covariance of asset and market returns over market variance. The CAPM regression slope measuring systematic risk, with an example.