Tracking Error Calculator

A tracking error calculator measures how closely a fund or portfolio follows its benchmark index. It is used by passive investors evaluating index funds, ETFs, and tracker funds, as well as by institutional investors assessing active managers. A lower tracking error indicates the portfolio closely mirrors the benchmark; a higher tracking error suggests the manager is making significant active bets away from the index.

How to Use the Tracking Error Calculator

1. Enter the fund's periodic returns (monthly or annual) over the measurement period.
2. Enter the benchmark's returns for the same periods.
3. The calculator computes the difference in return (active return) for each period.
4. It then calculates the standard deviation of those active returns.
5. The result is the annualised tracking error, expressed as a percentage.

The Formula

Active Return (each period) = Portfolio Return minus Benchmark Return

Tracking Error = Standard Deviation of Active Returns, annualised

To annualise tracking error calculated from monthly data:

Annualised Tracking Error = Monthly Tracking Error multiplied by the square root of 12

Where Monthly Tracking Error is the standard deviation of monthly active returns.

For annual data, no annualisation is needed as the standard deviation is already in annual terms.

A tracking error of zero means the portfolio perfectly replicates the benchmark. A tracking error of 1% to 2% is typical for a well-run physical index fund. Active managers often have tracking errors of 4% to 8% or higher.

Real-World Example

A global equity fund has the following monthly returns compared to its MSCI World benchmark over 6 months:

Month 1: Fund 2.1%, Benchmark 2.0%, Active Return +0.1% Month 2: Fund minus 1.5%, Benchmark minus 1.2%, Active Return minus 0.3% Month 3: Fund 3.0%, Benchmark 2.8%, Active Return +0.2% Month 4: Fund minus 0.5%, Benchmark minus 0.3%, Active Return minus 0.2% Month 5: Fund 1.8%, Benchmark 2.1%, Active Return minus 0.3% Month 6: Fund 2.4%, Benchmark 2.2%, Active Return +0.2%

Active returns: 0.1%, minus 0.3%, 0.2%, minus 0.2%, minus 0.3%, 0.2%

Mean active return = (0.1 minus 0.3 plus 0.2 minus 0.2 minus 0.3 plus 0.2) divided by 6 = minus 0.3 divided by 6 = minus 0.05%

Deviations from mean: 0.15, minus 0.25, 0.25, minus 0.15, minus 0.25, 0.25

Squared deviations: 0.0225, 0.0625, 0.0625, 0.0225, 0.0625, 0.0625

Variance = (0.0225 plus 0.0625 plus 0.0625 plus 0.0225 plus 0.0625 plus 0.0625) divided by 6 = 0.295 divided by 6 = 0.0492

Monthly standard deviation = square root of 0.0492 = 0.222%

Annualised Tracking Error = 0.222% multiplied by square root of 12 = 0.222% multiplied by 3.464 = 0.77%

An annualised tracking error of 0.77% suggests this fund tracks its benchmark fairly closely, consistent with a passive or enhanced index fund.

Interpreting Tracking Error in Practice

For passive index funds and ETFs, tracking error is a key quality metric. Low-cost physical replication index funds from major providers typically achieve tracking errors below 0.2% for large-cap indices. Funds tracking less liquid or niche indices may have higher tracking errors due to sampling or liquidity constraints.

For active funds, tracking error is interpreted as a measure of how active the manager really is. A high active share (another related metric) combined with a high tracking error suggests genuine active management. Low tracking error in an "active" fund may indicate "closet indexing", where the fund charges active fees but closely replicates the index.

The information ratio (active return divided by tracking error) combines both measures to assess whether active bets are adding value relative to the risk taken. A positive information ratio above 0.5 is generally considered good for an active manager.

Frequently Asked Questions

Is a higher or lower tracking error better? It depends on the fund's objective. For a passive index fund, a lower tracking error is better because the goal is to replicate the benchmark as accurately as possible. For an active fund, tracking error is not inherently good or bad; what matters is whether the active bets (captured by the tracking error) are generating sufficient excess return to justify the additional risk and fees.

What is the difference between tracking error and tracking difference? Tracking difference is the cumulative return gap between the fund and its benchmark over a period. Tracking error is the volatility of the active return. A fund with a consistent negative active return (always underperforming by 0.1% per month) would have a low tracking error but a negative tracking difference. Both should be examined when evaluating index funds.

How does fund size affect tracking error? Larger funds generally achieve lower tracking errors because they can afford to hold every constituent of the benchmark in the correct weights, achieving perfect or near-perfect replication. Smaller funds may use sampling, holding only a representative subset of stocks, which introduces additional tracking error. Very small ETFs may also struggle with liquidity in the underlying securities when making trades to rebalance.

What tracking error is acceptable for an ETF? For large, liquid ETFs tracking major indices such as the FTSE 100 or S&P 500, tracking errors below 0.15% annualised are typical and expected. For ETFs tracking emerging markets, small-cap indices, or thematic indices, tracking errors of 0.5% to 1.5% are more common due to higher trading costs and sampling requirements. Compare tracking error to the total expense ratio (TER) to understand the full cost of ownership.

Comparing Two Funds on the Same Benchmark

Take two funds tracking the same index over the same six months. Fund A produced the active returns already shown above: 0.1%, -0.3%, 0.2%, -0.2%, -0.3% and 0.2%, giving an annualised tracking error of 0.77%.

Fund B produced 0.3%, -0.3%, 0.35%, -0.35%, 0.3% and -0.3%. Its mean active return is 0.0%, so its deviations from the mean are the returns themselves. The squared deviations are 0.09, 0.09, 0.1225, 0.1225, 0.09 and 0.09, which sum to 0.615. Variance is 0.615 / 6 = 0.1025. The monthly standard deviation is the square root of 0.1025, which is 0.320%. Annualised, that is 0.320% x 3.464 = 1.11%.

Fund A has the lower tracking error and the worse outcome. Its tracking error is small because its active returns are small and cluster near a mean that is negative. Reading 0.77% against 1.11% as a straight contest misses the drift entirely.

One caution on the last row. Multiplying the mean monthly active return by 12 assumes the same average shortfall repeats every month. It is a rough figure, and the point of the pair is the contrast rather than the precision.

Daily Data and the Annualisation Factor

Tracking error is often quoted from daily returns, where the annualisation factor is the square root of 252 trading days rather than the square root of 12 months.

Notice that a monthly figure of 0.222% and a daily figure of 0.050% land on almost the same annual number, 0.77% against 0.79%. That agreement is a useful check on a data feed. If the two routes disagree by a wide margin, one of them is measured on a different basis or the return series has gaps.

The annualisation factor assumes returns are independent from one period to the next and have a constant variance. Serial correlation, which appears in illiquid holdings priced weekly or monthly, breaks both assumptions and understates the annual figure.

How Much Data Is Enough

A standard deviation estimated from six observations is not a precise number. The relative uncertainty of a sample standard deviation is roughly one divided by the square root of twice the sample size minus one.

Six months can support a rough ranking of two funds. It cannot support a claim that one fund beats another by a tenth of a percentage point, because the uncertainty around each estimate is wider than the gap. Twelve monthly observations narrow the uncertainty to about 21%, and thirty six narrow it to about 12%, which is why a three year figure carries more weight than a six month one.

Two further points matter when reading a published tracking error. Fund houses differ on whether they exclude the fund's own fee, and on whether they use monthly or daily returns, so two figures are only comparable when they were produced the same way.

Reading a Published Tracking Error

Fund documents rarely state the basis behind their tracking error figure, and the basis changes the number. Three questions settle it before you compare two funds.

Was the figure calculated from monthly or daily returns? The annualisation factors differ, 3.464 against 15.874.

Were the fund's own fees included in the return series? A fund measured after fees shows a lower tracking error than the same fund measured gross.

What period does it cover, three years, five years or since launch? A short period through a quiet market flatters almost any fund.

Ask for the basis, and state it whenever you pass the figure on. A tracking error quoted without its basis is a number that cannot be compared with anything.

Also try these free tools:

• Information Ratio Calculator
• Sharpe Ratio Calculator
• Beta Calculator