Tracking Error - The Volatility of the Gap to the Benchmark

By EC Assets Research Team, Performance Analytics · Published 29 October 2026

Tracking Error: Tracking error is the standard deviation of the difference between a portfolio's return and its benchmark's return, usually annualised from monthly data. It measures how far a portfolio can drift from its index, forms the denominator of the information ratio, and is the unit in which active risk budgets are set.

What Tracking Error Measures

Tracking error is the volatility of the difference between a portfolio's return and the return of its benchmark. Each period the portfolio either beats the index or trails it, and tracking error is the standard deviation of those differences, conventionally annualised. If active returns are roughly normal, a portfolio with 4 percent tracking error spends about two years in three within 4 percentage points of its expected active return.

It is the denominator of the information ratio and the unit in which active risk is budgeted. An index fund aims for a tracking error near zero; an active manager is hired to spend some, and the question an investor asks is how much active return each unit buys.

Tracking error and total risk are different targets. Roll (1992) showed that a manager who minimises tracking error for a target excess return ends up with a portfolio that usually is not mean-variance efficient in total-return terms and has a beta above one, and that constraining the beta can improve it.

How It Works

$$TE = \sigma(R_p - R_b) = \sqrt{\sigma_p^2 + \sigma_b^2 - 2\rho,\sigma_p\sigma_b}$$

Correlation dominates. Two portfolios with the same 15 percent volatility have a tracking error of 15 × √(2 × (1 - ρ)), so small departures from perfect correlation produce large active risk:

A correlation of 0.95 sounds like an index fund; it is the tracking error of a fairly active one.

Splitting the portfolio into a beta to the benchmark and a residual separates two sources of active risk:

$$TE^2 = (\beta - 1)^2\sigma_b^2 + \sigma_\varepsilon^2$$

The first term is market exposure above or below the index, from leverage, cash or timing; the second is stock selection and factor tilts. Usually only the second is what the investor is paying for.

Worked Example

A fund has 16 percent volatility, its benchmark 15 percent, and the correlation between them is 0.95. Its tracking error is √(16² + 15² - 2 × 0.95 × 16 × 15) = √(481 - 456) = 5.0 percent. The two return series look almost identical on a chart, yet in about one year in three the gap between them lands more than 5 points away from its average.

A second fund makes no selection decisions at all. It holds the index with 20 percent leverage, a beta of 1.2, and its tracking error is 0.2 × 15 = 3.0 percent, all of it from beta. In a year when the index beats the cost of borrowing by 10 percent, the fund outperforms by 2 percent, which looks like skill and is only leverage. Combine a smaller beta gap of 1.1 with 3 percent of residual risk and the tracking error is √(1.5² + 3²) = 3.4 percent, a fifth of its variance still coming from beta.

Tracking error also aggregates. Three managers with 4 percent tracking error each, equally weighted and with uncorrelated active returns, produce √(3 × (1/3)² × 4²) = 2.3 percent in total. If their active returns are correlated at 0.5, the total is 3.3 percent. Active risk diversifies only to the extent that managers make different bets.

When It Applies (and Limitations)

It is symmetric. Tracking error counts outperformance and underperformance alike. A manager who beats the index by a steady margin has low tracking error; one who beats it by a large but irregular margin has a high one, even without a single year behind the benchmark.

It assumes uncorrelated active returns. Annualising by √12 understates tracking error when monthly active returns are autocorrelated, as they are for portfolios holding stale-priced or illiquid assets; see return smoothing. Pope and Yadav (1994) showed that serial correlation in return differences biases tracking-error estimates scaled up from shorter intervals.

It depends on the benchmark. A benchmark that does not match the strategy inflates tracking error with exposures the manager never intended, and one built around a style can make a factor tilt look like low active risk. Neither is a property of the manager.

Forecasts and outcomes differ. A risk model forecasts tracking error from current holdings and estimated covariances; realised tracking error depends on what happened. Forecasts tend to fall short when correlations shift in stressed markets, which is when the budget matters most.

Why It Matters for Institutional Investors

It is how active risk is budgeted. Plans set a total tracking-error limit and divide it among managers. Because active risks diversify, the individual budgets can add up to more than the plan total, as the three-manager example shows, provided the bets are genuinely different. Jorion (2003) proposed adding a constraint on total volatility to a tracking-error target, which addresses the excess total risk that Roll identified.

It exposes closet indexing. A fund charging active fees with a tracking error close to an index fund's delivers mostly the index. Cremers and Petajisto (2009) combine tracking error with active share, the fraction of holdings that differ from the index, to separate concentrated stock pickers, factor bets and closet indexers.

It sets the pace of evidence. Active return divided by tracking error is the information ratio, and tracking error determines how noisy that ratio is. A high tracking error relative to the active return means many years pass before outperformance can be told apart from luck, which is why manager selection based on short records so often rewards chance.

References

1. Roll, R. (1992). A Mean/Variance Analysis of Tracking Error. Journal of Portfolio Management, 18(4), 13-22.
2. Pope, P. F., & Yadav, P. K. (1994). Discovering Errors in Tracking Error. Journal of Portfolio Management, 20(2), 27-32.
3. Jorion, P. (2003). Portfolio Optimization with Tracking-Error Constraints. Financial Analysts Journal, 59(5), 70-82.
4. Cremers, K. J. M., & Petajisto, A. (2009). How Active Is Your Fund Manager? A New Measure That Predicts Performance. Review of Financial Studies, 22(9), 3329-3365.
5. Grinold, R. C., & Kahn, R. N. (2000). Active Portfolio Management (2nd ed.). McGraw-Hill.