Economic Modelling · Measures of investment risk

Tracking Error and Relative Risk Measures Explained

Updated 11 October 2026 · Fact-checked

Tracking error is the standard deviation of the difference between a portfolio's return and its benchmark's return. It measures relative risk. To solve questions, compute the active return each period, find its standard deviation, and then use the information ratio, which is mean active return divided by tracking error.

Understand Tracking Error and Relative Risk Measures

Absolute risk measures how much a portfolio's return varies on its own. Standard deviation of the portfolio return is the usual measure. Relative risk measures how much the portfolio's return varies compared with a reference point, such as an index or a set of liabilities.

Many investors are judged against a benchmark, not against zero. A fund manager who loses 5% when the index loses 8% has done well in relative terms. So the risk that matters is the risk of straying from the benchmark. The gap each period is the active return: portfolio return minus benchmark return.

Tracking error is the standard deviation of the active return. A small tracking error means the portfolio behaves like the benchmark. A large one means it can differ a lot, in either direction. The information ratio divides the mean active return by the tracking error. It tells you how much extra return you earn for each unit of relative risk taken.

For a pension fund or insurer, the reference point is the liabilities. Matching risk (or mismatch risk) is the risk that assets and liabilities do not move together, for example because of different interest rate or inflation sensitivity. You can measure it as the variance or standard deviation of the difference between asset and liability values or returns. Here the liabilities act as the benchmark.

Tracking error can be worked out from past data (ex-post) or from a model of weights and covariances (ex-ante). Both give the same idea: the volatility of the difference.

Key rules to remember

Active return: a_t = R_P,t − R_B,t; Portfolio return minus benchmark return in period t.
Mean active return: ā = (1/n) Σ a_t; Average of the active returns over n periods.
Tracking error (sample, from data): TE = √[ Σ (a_t − ā)² ÷ (n − 1) ]; Use n − 1 for a sample unless the question says to use n. State your choice.
Tracking error from variances: TE² = σ_P² + σ_B² − 2 ρ σ_P σ_B; ρ is the correlation between portfolio and benchmark returns.
Tracking error from active weights: TE² = Σ Σ (w_i − b_i)(w_j − b_j) σ_ij; w_i is the portfolio weight and b_i the benchmark weight. The difference is the active weight.
Information ratio: IR = ā ÷ TE; Mean active return per unit of tracking error. Use the same time period for both.
Matching (mismatch) risk: Var(A − L) = σ_A² + σ_L² − 2 ρ σ_A σ_L; A and L are asset and liability values or returns on a consistent basis.
Annualising: TE_annual = TE_monthly × √12; Valid when active returns are independent across periods.

How to solve Tracking Error and Relative Risk Measures questions

Use this method for any question on tracking error, information ratio or matching risk.

1Identify the reference point: a benchmark index or the liabilities.
2Write down the active return (or the asset-minus-liability difference) for each period, or its variance formula if data is not given.
3Compute the mean of the active returns.
4Compute the standard deviation of the differences. Use n − 1 for a sample and say so.
5If only variances and correlation are given, use TE² = σ_P² + σ_B² − 2ρσ_Pσ_B and take the square root.
6Compute the information ratio as mean active return divided by tracking error, using the same time basis.
7Annualise if asked, scaling the mean by the number of periods and the standard deviation by its square root.
8Interpret the result in one sentence: how much relative risk, and whether the extra return justifies it.

Quickest way: Shortcut with active weights or variances

When to use it: Use this when the question gives variances, correlation or active weights and not a full return series.

If the portfolio and benchmark have equal volatility σ, then TE² = 2σ²(1 − ρ). This saves time.
With two assets, active weights sum to zero, so the active weight on asset 2 is minus that on asset 1. TE² = x² (σ_1² + σ_2² − 2σ_12) where x is the active weight.
Take the square root only at the end.
Compute IR last as mean active return divided by TE.

Common mistakes in Tracking Error and Relative Risk Measures

Using portfolio standard deviation instead of the standard deviation of active returns.
Students mix up absolute risk and relative risk.
Fix: Always form the difference series first. Tracking error is the standard deviation of that series.
Dividing by n instead of n − 1 without saying so.
Habit from population formulas.
Fix: Treat the data as a sample and use n − 1, unless the question says otherwise. Write down your choice.
Forgetting the correlation term and adding variances.
Students treat portfolio and benchmark as independent.
Fix: Use σ_P² + σ_B² − 2ρσ_Pσ_B. A high correlation gives a low tracking error.
Calculating the information ratio with mismatched time periods.
Mean is annual but tracking error is monthly.
Fix: Put both on the same basis before dividing.
Annualising by multiplying tracking error by 12.
Confusing the scaling of means with that of standard deviations.
Fix: Multiply the mean by 12 and the standard deviation by √12, assuming independent periods.
Thinking a low tracking error means low risk.
Relative risk is read as absolute risk.
Fix: A portfolio can track a volatile benchmark closely and still have high absolute risk.

Worked examples

Example 1

A fund and its benchmark had annual returns over four years. Fund: 10%, 6%, 12%, 8%. Benchmark: 8%, 5%, 9%, 6%. Calculate the mean active return, the tracking error (sample) and the information ratio.

Show the solution

Active returns: 10 − 8 = 2%, 6 − 5 = 1%, 12 − 9 = 3%, 8 − 6 = 2%.
Mean active return = (2 + 1 + 3 + 2) ÷ 4 = 2%.
Deviations from the mean: 0, −1, 1, 0.
Sum of squares = 0 + 1 + 1 + 0 = 2.
Sample variance = 2 ÷ 3 = 0.6667, so TE = √0.6667 = 0.8165%.
IR = 2 ÷ 0.8165 = 2.449.

Answer: Mean active return 2%, tracking error about 0.82%, information ratio about 2.45.

Example 2

A portfolio has annual return volatility 12% and its benchmark has 10%. The correlation between them is 0.9. Calculate the tracking error. The portfolio's mean active return is 1.5% a year. Find the information ratio.

Show the solution

TE² = σ_P² + σ_B² − 2ρσ_Pσ_B.
σ_P² = 0.0144 and σ_B² = 0.0100.
2ρσ_Pσ_B = 2 × 0.9 × 0.12 × 0.10 = 0.0216.
TE² = 0.0144 + 0.0100 − 0.0216 = 0.0028.
TE = √0.0028 = 0.05292, or 5.29%.
IR = 1.5 ÷ 5.29 = 0.283.

Answer: Tracking error about 5.29% a year and information ratio about 0.28.

Exam tips

Show the active return column first. Marks are given for the method even if the arithmetic slips.
State whether you use n or n − 1 and keep it consistent.
In matching risk questions, say what the liabilities are and why assets differ from them, such as duration or inflation link.
Be ready to compare absolute and relative risk in words. Short, clear definitions earn marks in MCQs and written parts.
In computer-based work, compute the difference series in a column or vector first, then apply the standard deviation function.

Practice questions from Measures of investment risk

Tracking Error and Relative Risk Measures 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 Relative Risk Measures: frequently asked questions

What is the difference between absolute and relative risk in investment?

Absolute risk is the variability of the portfolio's own return, usually its standard deviation. Relative risk is the variability of the return compared with a benchmark or liabilities. Tracking error is the main measure of relative risk.

How do I calculate tracking error?

Find the active return for each period, which is portfolio return minus benchmark return. Then take the standard deviation of those values, usually with n − 1 in the denominator. If given variances and correlation, use TE² = σ_P² + σ_B² − 2ρσ_Pσ_B.

What does the information ratio tell you?

It shows the mean active return earned per unit of tracking error. A higher value means the manager is rewarded better for the relative risk taken. It only has meaning if the mean and tracking error use the same time period.

What is matching risk?

Matching risk is the risk that the value of assets moves differently from the value of liabilities. You can measure it by the variance or standard deviation of the difference between the two. It is the relative risk measure when liabilities are the benchmark.