FRM Exam Part II · Portfolio Performance Evaluation

Tracking Error and Benchmark-Relative Risk Explained

Updated 11 October 2026 · Fact-checked

Active return is portfolio return minus benchmark return. Tracking error is the standard deviation of active return over time. It measures benchmark-relative risk. Divide mean active return by tracking error to get the information ratio. Annualise a periodic tracking error by multiplying by √ the number of periods per year.

Understand Tracking Error and Benchmark-Relative Risk

A portfolio manager with a benchmark is judged against it, not against zero. The benchmark could be the MSCI World index or a Bloomberg US aggregate bond index. The gap between your return and the benchmark return in a period is the active return.

Active return = portfolio return − benchmark return. It can be positive or negative. Its average over time tells you how much value the manager has added. Its variability tells you how much benchmark-relative risk was taken to get it.

Tracking error (also called active risk) is the standard deviation of active returns. A low tracking error means the portfolio hugs the benchmark. A high one means it deviates a lot. A fund with 0.5% tracking error is close to an index fund. A fund with 6% is a concentrated active bet.

Tracking error is not the same as active return. Active return is the size of the outperformance. Tracking error is the volatility of that outperformance. A manager can have a high average active return and a low tracking error, which is what you want. The information ratio combines the two: mean active return divided by tracking error.

You can also get tracking error from weights. Active weights are portfolio weight minus benchmark weight for each asset. Tracking error is then the volatility of the active-weight portfolio, using the covariance matrix. This is the ex-ante (forward-looking) measure. Tracking error computed from past active returns is ex-post.

Key formulas to remember

Active return: Rₐ = R_P − R_B; Portfolio return minus benchmark return for the same period.
Tracking error (ex-post): TE = √[ Σ(Rₐ,ₜ − R̄ₐ)² ÷ (n − 1) ]; Sample standard deviation of active returns. Use n − 1 unless the question says otherwise.
Information ratio: IR = R̄ₐ ÷ TE; Use mean active return and tracking error over the same horizon, annualised consistently.
Annualising: TE_annual = TE_periodic × √(periods per year); mean active return_annual = mean periodic × periods per year; Monthly: √12. Weekly: √52. The square-root rule assumes independent active returns.
Tracking error from two volatilities: TE² = σ_P² + σ_B² − 2ρσ_Pσ_B; Valid when the active return is exactly R_P − R_B. ρ is the correlation of portfolio and benchmark returns.
Ex-ante tracking error from active weights: TE = √(wₐᵀ Σ wₐ), where wₐ = w_P − w_B; Σ is the covariance matrix of asset returns.
Tracking error VaR: TEVaR = z × TE × portfolio value (over the horizon); Assumes normal active returns and zero mean active return. For 95% one-tailed, z = 1.645.

How to solve Tracking Error and Benchmark-Relative Risk questions

Use this order for any tracking error or benchmark-relative question.

1Identify the benchmark and the horizon. Check whether returns are monthly, quarterly or annual.
2Compute active return for each period as portfolio minus benchmark. Do not use raw portfolio returns.
3Find the mean active return, then the standard deviation of the active returns. That is the tracking error. Use n − 1 for a sample.
4If the question gives volatilities and correlation instead of a return series, use TE² = σ_P² + σ_B² − 2ρσ_Pσ_B.
5Annualise: multiply mean by periods per year and tracking error by the square root of periods per year.
6Compute the information ratio as mean active return ÷ tracking error, both on the same basis.
7Interpret. Say whether risk is low or high relative to the benchmark and whether return per unit of active risk is attractive. For VaR-style questions apply the z-value to tracking error.

Quickest way: Shortcut for time pressure

When to use it: Use when the question gives a small return series or gives volatilities and correlation and asks for one number.

Write the active returns down first. Many errors come from skipping this.
Take deviations from the mean active return. Square, add, divide by n − 1, square root.
Eliminate options by sign and size. Tracking error is never negative, and it is zero only if active return is constant.
If correlation is 1 and volatilities are equal, TE is zero. If correlation is 1 and volatilities differ, TE = |σ_P − σ_B|.
Annualise last, once, using √ for risk and × for return.

Common mistakes in Tracking Error and Benchmark-Relative Risk

Treating tracking error as the average active return.
Both are called 'active' measures and are quoted in percent.
Fix: Tracking error is a standard deviation. Average active return is a mean. Only the second tells you whether the manager outperformed.
Using the portfolio's own standard deviation as tracking error.
Students forget the benchmark must be subtracted before measuring volatility.
Fix: Compute active returns first, then their standard deviation.
Annualising tracking error by multiplying by the number of periods.
Mixing up the rule for returns with the rule for risk.
Fix: Returns scale with time. Standard deviations scale with the square root of time. Monthly TE × √12.
Using a high information ratio as proof of skill.
The ratio looks like a clean score.
Fix: It is an estimate from a limited sample. A short history gives noisy results, and it says nothing about whether the return came from luck or from hidden factor exposure.
Dropping the correlation term in TE² = σ_P² + σ_B² − 2ρσ_Pσ_B.
Students copy the portfolio variance formula with plus signs.
Fix: Active return is a difference, so the covariance term is subtracted.
Assuming ex-ante tracking error equals the realised ex-post figure.
Both carry the same name.
Fix: Ex-ante is a model forecast from current weights. Ex-post is measured from past returns. They can differ when risk or positions change.

Worked examples

Example 1

A fund's quarterly returns over four quarters are 3%, 5%, −1% and 4%. The benchmark returns are 2%, 4%, 1% and 3%. Compute the quarterly tracking error (sample standard deviation).

Show the solution

Active returns: 3 − 2 = 1%, 5 − 4 = 1%, −1 − 1 = −2%, 4 − 3 = 1%.
Mean active return = (1 + 1 − 2 + 1) ÷ 4 = 0.25%.
Deviations: 0.75, 0.75, −2.25, 0.75.
Squared deviations: 0.5625, 0.5625, 5.0625, 0.5625. Sum = 6.75.
Variance = 6.75 ÷ 3 = 2.25. Tracking error = √2.25 = 1.50%.

Answer: Quarterly tracking error = 1.50%.

Example 2

A portfolio has annual volatility 12% and its benchmark has annual volatility 10%. The correlation between them is 0.95. The portfolio's mean annual active return is 1.5%. Find the tracking error and information ratio.

Show the solution

TE² = 12² + 10² − 2 × 0.95 × 12 × 10 = 144 + 100 − 228 = 16.
TE = √16 = 4%.
IR = 1.5% ÷ 4% = 0.375.
Interpretation: the manager earns about 0.38% of active return per 1% of active risk.

Answer: Tracking error = 4%; information ratio = 0.375.

Exam tips

Check the units. Questions often give monthly data and ask for annualised answers.
If the stem gives volatilities and correlation, expect the TE² formula. If it gives return series, expect the standard deviation of differences.
Read whether the question wants ex-ante or ex-post tracking error, then pick the weights-based or return-based method.
In interpretation questions, link a high tracking error to high active risk and weak benchmark tracking, not to poor performance by itself.
For tracking error VaR, state the confidence level and z-value you use, and apply it to active returns, not total returns.

Practice questions from Portfolio Performance Evaluation

Tracking Error and Benchmark-Relative Risk in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Tracking Error and Benchmark-Relative Risk: frequently asked questions

What is the difference between active return and tracking error?

Active return is the portfolio return minus the benchmark return. Tracking error is the standard deviation of those active returns. One measures outperformance, the other measures how variable it is.

How do I calculate the information ratio?

Divide the mean active return by the tracking error, both on the same time basis. For example, 2% mean active return and 5% tracking error give an information ratio of 0.40.

Should I use n or n − 1 for tracking error?

Use n − 1 for a sample of returns, which is the normal case. Follow the question if it states a population calculation.

What is the difference between ex-ante and ex-post tracking error?

Ex-ante tracking error is a forecast based on current active weights and a covariance matrix. Ex-post tracking error is calculated from historical active returns.