Tracking Error

Tracking error is a measure of how consistently a portfolio's returns follow the returns of its benchmark. It is calculated as the standard deviation of the difference between the two sets of returns over time. A low tracking error means the portfolio moves almost in lockstep with its index; a high one means its returns wander away from the index, sometimes above it and sometimes below.

For index funds and exchange-traded funds (ETFs), tracking error is a test of how well the fund does its job. For active managers it is a deliberate choice: it shows how much "active risk" they take in trying to beat the benchmark. It is often confused with tracking difference, which measures how far a fund's total return ended up from the index over a period rather than how much the gap varied along the way.

Picture a learner driver following an instructor's car along a winding road. A good learner keeps roughly the same distance the whole way. A nervous one speeds up, falls back and swerves, even if both arrive at the destination at about the same time.

Tracking error measures that wobbling. It ignores whether the follower ends up slightly ahead or behind at the finish and focuses on how steady the gap was during the journey. An index fund wants a tiny wobble, because its promise is to copy the market. An active fund accepts a bigger wobble, because it is trying to take a different route and, it hopes, get there faster.

Tracking error is the standard deviation of active returns, the period-by-period difference between portfolio and benchmark:

• $d_t$ is the active return in period $t$: the portfolio's return minus the benchmark's return.
• $\bar{d}$ is the average active return across all periods.
• $N$ is the number of periods.

Suppose a fund's monthly active returns over five months are +1%, −1%, +2%, 0% and −2%. Their average is 0%. The squared deviations are 1, 1, 4, 0 and 4, which add to 10. Dividing by 4 gives 2.5, and the square root is about 1.58%. That is the monthly tracking error; multiplied by the square root of 12, it is about 5.5% a year.

The related information ratio divides the average active return by tracking error, showing how much outperformance a manager produced per unit of active risk:

A manager who beats the index by 2% a year with a 4% tracking error has an information ratio of 0.5.

The two measures answer different questions. Tracking difference is the gap between the fund's total return and the index's total return over a period, for example −0.10% over one year. For a well-run index fund it is usually close to the negative of the fund's costs, such as its expense ratio. Tracking error is how much that gap fluctuated. A fund can have a steady −0.20% tracking difference with almost no tracking error, or a tracking difference of zero with a large tracking error if big positive and negative gaps happened to cancel out.

Investors choosing between index funds generally look first at tracking difference, because that is what reaches their pocket, and then at tracking error as a sign of how reliable the replication is.

• Costs. Management fees, trading costs and taxes on dividends reduce the fund's return relative to an index that bears no costs.
• Sampling. Funds tracking broad bond or small-company indices often hold a representative sample rather than every security, which creates small mismatches.
• Cash drag. Holding cash for redemptions or awaiting investment causes the fund to lag in a rising market.
• Rebalancing and index changes. When the index adds or drops members, the fund must trade, often at prices slightly different from those the index assumes.
• Securities lending and derivatives. Income from lending securities can help; synthetic replication through swaps adds counterparty risk.
• Active decisions. For active managers, sector bets, stock selection and concentrated positions are the main source, by design.

Institutional investors set tracking error budgets when they hire managers. A pension fund might ask an "enhanced index" portfolio manager to stay within about 1% to 2% a year of the index, while a concentrated stock-picker may run 6% or more. Measured together with R-squared and alpha, tracking error helps reveal whether a manager is really active. In February 2016 the European Securities and Markets Authority (ESMA) used tracking error, active share and R² to flag possible closet index funds.

In the European Union, ESMA's Guidelines on ETFs and other UCITS issues (ESMA/2012/832) require index-tracking UCITS funds to state the anticipated level of tracking error in their prospectus and to report the realised tracking error, and explain any divergence, in their annual report. In the United States there is no specific tracking error rule, but an index fund's prospectus and shareholder reports show its returns next to its index under rules administered by the Securities and Exchange Commission (SEC), so investors can see the gap. A fund manager's fact sheet often reports tracking error alongside beta and the Sharpe ratio.

Tracking error has limits. It treats outperformance and underperformance alike, depends heavily on the period measured, and assumes the benchmark is the right one. A fund measured against a poorly matched index can show high tracking error even if it follows its true strategy faithfully.

• Guidelines on ETFs and other UCITS issues (European Securities and Markets Authority)