What is tracking error?

Tracking error measures how closely a portfolio follows its benchmark. It is the standard deviation of the difference between the portfolio's return and the benchmark's return. A low tracking error means the portfolio moves almost exactly like its benchmark; a high one means its results can differ widely from it, in either direction.

It measures how much a portfolio deviates, not whether it does better or worse — that is the active return.

The formula

With the active return in each period $t$ defined as

a_t = R_{p,t} - R_{b,t}

the tracking error is its standard deviation, annualized in the same way as volatility:

\text{TE} = \sqrt{\frac{1}{n - 1} \sum_{t=1}^{n} (a_t - \bar{a})^2} \times \sqrt{m}

where $\bar{a}$ is the average active return and $m$ the number of periods in a year: 12 for monthly returns, 252 for daily ones.

A simple illustration

Over six months, a portfolio's monthly returns differ from its benchmark's by +0.5%, −0.3%, +0.8%, −0.6%, +0.1% and −0.5%. The average difference is zero, and the monthly standard deviation is about 0.57%:

\text{TE} \approx 0.57\% \times \sqrt{12} \approx 2.0\%

In a typical year, the portfolio's return can be expected to land within about two points of the benchmark's, above or below.

How to read it

Tracking error	Typical of
under 0.5%	index funds tracking the same index
1–3%	cautious active funds, broad factor tilts
4–8%	concentrated active funds, stock-picking portfolios
over 10%	portfolios with little in common with their benchmark

Low is not always better. An index fund should have a very low tracking error. An active fund with a very low one is mostly charging active fees for an index-like result.
High means the benchmark explains little. A portfolio with a tracking error of 10% can beat or trail its benchmark by ten points or more in any year, regardless of skill.

The information ratio

Tracking error is often combined with the average active return into the information ratio, which measures active return per unit of active risk:

\text{IR} = \frac{\bar{a}}{\text{TE}}

It plays the same role for outperformance that the Sharpe ratio plays for return. An information ratio above 0.5, sustained over many years, is considered very good.

A worked example

Worked through on a sample portfolio. The figures below are that portfolio’s, not yours.

How much tracking error do I have versus my benchmark?

I can report tracking error only if your portfolio return series and the benchmark returns are available. Your data shows month-by-month portfolio returns alongside the benchmark returns for the same periods. Using those snapshots, Floreo calculates tracking error as the standard deviation of the difference between your portfolio's periodic returns and the benchmark's returns.

Here are the inputs available from your return snapshots:

Monthly portfolio time-weighted returns are in the period list.
The benchmark is "HSBC MSCI World UCITS ETF" (IE00B4X9L533) with its monthly return_pct in each snapshot.

I don't see a pre-computed tracking error value in the data returned for this turn. If you want, I can calculate tracking error now from the monthly snapshots you have—do you want the result annualized (p.a.) or expressed as monthly standard deviation?

See these numbers for your own portfolio

Floreo works out every figure on this page from your own holdings — returns, risk, allocation, currencies — and the assistant explains them the way this page does. Import from your broker, or try it on the sample portfolio first.

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