Tracking Error: A Complete Guide for Investors
Tracking error is an important concept in investing that helps investors understand how closely an investment fund follows its benchmark index. It is especially useful when evaluating index funds, exchange-traded funds (ETFs), and other portfolios designed to match the performance of a specific market index.
For example, if an S&P 500 index fund aims to follow the S&P 500 Index, investors generally expect the fund to perform similarly to that benchmark. However, differences in expenses, trading costs, portfolio holdings, and fund management can cause its returns to vary from the index. Tracking error measures the variability of these differences over time.
Understanding tracking error can help investors compare funds, evaluate portfolio management, and make better-informed investment decisions. However, a lower tracking error does not automatically mean that a fund is better in every situation. Investors should also consider fees, risk, liquidity, investment objectives, and long-term performance.
In this guide, we will explain what tracking error means, how to calculate it, why it matters, and how investors can use it when evaluating investment funds.
What Is Tracking Error?
Tracking error is a statistical measure that shows how much an investment’s returns fluctuate relative to the returns of its benchmark index over a specific period.
A benchmark is a standard used to evaluate an investment’s performance. For example, a fund investing in large US companies might use the S&P 500 Index as its benchmark, while a fund investing in international stocks might track a global or regional stock market index.
Tracking error focuses on the differences between the investment’s returns and its benchmark returns. These differences are commonly called active returns.
If a fund consistently follows its benchmark closely, it will generally have a low tracking error. If its returns frequently differ from the benchmark, it will generally have a higher tracking error.
Tracking error is particularly relevant to passive investment strategies because these funds are designed to replicate an index rather than consistently outperform it.
However, actively managed funds can also have tracking error. In their case, a higher tracking error may reflect deliberate investment decisions intended to outperform the benchmark.
How Tracking Error Works
Suppose an index earns a return of 8% over a particular period, while an index fund earns 7.8%. The difference between their returns is negative 0.2 percentage points.
This difference is one observation of the fund’s relative performance. Tracking error examines how these differences vary across multiple periods, rather than measuring only one return difference.
For example, consider a fund whose monthly returns differ from its benchmark by 0.1%, -0.2%, 0.15%, and -0.1%. Tracking error measures the variability of those differences using a statistical calculation called standard deviation.
A single month of underperformance does not necessarily indicate high tracking error. What matters is how consistently the fund’s relative returns vary over the entire measurement period.
Tracking Error Formula
The standard formula for tracking error is the standard deviation of the differences between an investment’s periodic returns and its benchmark’s periodic returns.
\[ TE=\operatorname{SD}(R_p-R_b) \]
Where:
- \(TE\) = tracking error
- \(R_p\) = investment portfolio return for each period
- \(R_b\) = benchmark return for each period
- \(\operatorname{SD}\) = standard deviation
The formula calculates the active return for each period and then measures how much those active returns fluctuate around their average.
For historical monthly observations, a sample standard deviation is commonly calculated as:
\[ TE_m=\sqrt{\frac{\sum_{t=1}^{n}(A_t-\bar A)^2}{n-1}} \]
In this formula, \(A_t\) represents the portfolio’s active return in each month, \(\bar A\) is the average active return, and \(n\) is the number of observations.
When using monthly data, investors often annualize tracking error by multiplying the monthly figure by the square root of 12:
\[ TE_a=TE_m\times\sqrt{12} \]
This annualization convention assumes that monthly active returns are sufficiently comparable and that the usual statistical assumptions behind the calculation are appropriate. Actual results can differ when returns exhibit serial correlation or other unusual patterns.
Why the Formula Matters
The formula shows that tracking error is not simply the difference between a fund’s annual return and its benchmark’s annual return.
Instead, it measures the variability of relative returns across multiple observations. A fund can underperform its benchmark by a relatively consistent amount and still have a low tracking error.
This distinction is important because investors need to understand both the size of the performance gap and the consistency of that gap.
Tracking Error Example
A simple example can make tracking error easier to understand. Imagine an index fund that follows a benchmark index and reports the following monthly returns.
| Month | Fund return | Benchmark return | Active return |
|---|---|---|---|
| January | 2.1% | 2.0% | +0.1% |
| February | -1.8% | -1.5% | -0.3% |
| March | 3.4% | 3.2% | +0.2% |
| April | 1.0% | 1.1% | -0.1% |
| May | -0.5% | -0.4% | -0.1% |
The active return is calculated by subtracting the benchmark return from the fund return.
For example, January’s active return is:
\[ 2.1\%-2.0\%=0.1\% \]
February’s active return is:
\[ -1.8\%-(-1.5\%)=-0.3\% \]
The same calculation is repeated for each month. The standard deviation of the resulting active returns gives the monthly tracking error.
Using the five observations above and the sample standard deviation formula, the monthly tracking error is approximately 0.193 percentage points. Annualizing it using the square root of 12 gives approximately 0.67 percentage points.
These figures are illustrative, not a prediction of future fund performance. Five months of data are also too limited to provide a reliable long-term assessment of a fund’s tracking behavior.
The example demonstrates that tracking error measures variation in active returns, rather than the fund’s total return or its overall investment risk.
Tracking Error vs. Tracking Difference
Tracking error and tracking difference are related concepts, but they measure different aspects of an investment fund’s performance.
Tracking difference measures the actual gap between a fund’s return and its benchmark return over a specified period. Tracking error measures the variability of that gap over multiple periods.
| Feature | Tracking error | Tracking difference |
|---|---|---|
| Main purpose | Measures variability in relative returns | Measures the return gap |
| Calculation | Standard deviation of active returns | Fund return minus benchmark return |
| Focus | Consistency of benchmark tracking | Actual relative performance |
| Low value means | Relative returns vary less | The return gap is small in absolute terms |
| Common use | Comparing tracking consistency | Evaluating underperformance or outperformance |
For example, suppose a fund underperforms its benchmark by 0.5 percentage points every year. Its tracking difference is negative 0.5 percentage points annually. If the gap remains nearly constant, its tracking error may be very low.
Another fund might outperform by 0.4 percentage points in one year and underperform by 0.6 percentage points the next. Its average return gap might look similar, but its tracking error could be higher because the differences fluctuate more.
The key takeaway: tracking difference tells you how much a fund lagged or exceeded its benchmark, while tracking error tells you how much its relative performance varied.
Why Is Tracking Error Important?
Tracking error helps investors evaluate whether a fund behaves as expected relative to its benchmark. It is particularly useful when selecting investments with specific performance objectives.
1. Evaluating Index Funds
Index funds aim to reproduce the performance of a particular market index. Tracking error helps investors determine how consistently a fund follows that index.
A lower tracking error may indicate that the fund’s returns have stayed closer to the benchmark’s relative performance pattern. This can be desirable for investors who want broad market exposure without significant deviations from the index.
2. Comparing Exchange-Traded Funds
Two ETFs may track the same index but produce different investment results. Differences in fees, trading activity, portfolio construction, and cash balances can affect their returns.
Comparing tracking error alongside tracking difference can help investors identify which ETF has followed its benchmark more consistently and which has delivered returns closer to the index.
3. Assessing Portfolio Management
Active portfolio managers often make investment decisions that differ from their benchmarks. Tracking error provides information about how much those decisions influence relative performance.
A higher tracking error can reflect meaningful departures from the benchmark. Investors can use this information to understand the manager’s approach and decide whether the strategy matches their investment goals.
4. Understanding Relative Risk
Tracking error is sometimes called active risk because it measures the variability of returns relative to a benchmark.
However, it is not a complete measure of investment risk. It does not directly measure the possibility of losing money, the size of potential market declines, or the volatility of the portfolio’s total returns.
Investors should evaluate it alongside other risk measures, including standard deviation, maximum drawdown, and downside risk.
5. Supporting Investment Decisions
Tracking error can help investors choose between passive funds, review an existing portfolio, and monitor whether an investment strategy is operating as intended.
For example, an investor seeking to replicate a broad stock index may prefer a fund with consistently low tracking error and reasonable expenses. An investor seeking active outperformance may accept higher tracking error if the strategy is appropriate and its additional risks are understood.
What Causes High Tracking Error?
Several factors can cause an investment fund’s returns to differ from those of its benchmark.
Management Fees and Operating Expenses
Investment funds charge management fees and may incur other operating expenses. These costs reduce the returns received by investors and can contribute to a negative tracking difference.
For index funds, expenses are a common reason that net returns fall below benchmark returns. However, a consistent fee-related return gap does not necessarily produce high tracking error if the gap remains stable over time.
Portfolio Sampling
Some indexes contain hundreds or thousands of securities. Buying every constituent in precisely the same proportion may be expensive or impractical.
A fund may therefore use representative sampling, holding a selection of securities intended to reproduce the benchmark’s overall characteristics.
Sampling can reduce transaction costs, but it can also cause returns to differ from the index, especially when the selected securities perform differently from those that are omitted.
Cash Holdings
Funds sometimes hold cash to meet redemption requests, pay expenses, or manage daily operations.
If the benchmark is fully invested in securities, holding cash can cause the fund to perform differently from the index during market movements. The impact depends on the amount of cash held and how the market behaves.
Trading Costs
Buying and selling securities creates costs, including bid-ask spreads, commissions where applicable, and market impact.
These costs can increase when the benchmark changes its constituents or when the fund needs to adjust its holdings. Higher trading costs may widen the fund’s return gap and contribute to variation in active returns.
Dividend and Income Timing
Differences in dividend treatment and reinvestment timing can affect tracking results. For example, a fund and benchmark may record dividend income at different times or use different assumptions about reinvestment.
For a fair comparison, investors should compare equivalent return series, such as total returns against total returns, rather than comparing a fund’s total return with an index’s price-only return.
Index Rebalancing
Market indexes periodically change their constituents and weightings. Funds tracking these indexes must adjust their holdings to reflect the changes.
The costs and timing of these adjustments can lead to short-term differences between fund and benchmark returns.
Taxes and Foreign Markets
Withholding taxes on dividends, differences in tax treatment, and variations in market closing times can also influence tracking performance. These issues are particularly relevant to international funds.
Investors should review the fund’s methodology and benchmark documentation to understand how such differences are handled.
What Is a Good Tracking Error?
There is no single tracking error value that is considered good for every investment fund. The appropriate level depends on the type of fund, its investment strategy, the benchmark it follows, and the measurement period.
For a passive fund designed to replicate a broad market index, investors generally expect tracking error to be relatively low. A higher figure may deserve further investigation, especially if the fund’s stated objective is to follow the benchmark closely.
An actively managed fund, on the other hand, may intentionally maintain higher tracking error because its manager selects investments that differ from the benchmark.
Investors can use the following general guide when evaluating tracking error.
| Tracking error level | Possible interpretation |
|---|---|
| Very low | Returns have followed the benchmark closely |
| Low | Limited variability in relative performance |
| Moderate | Noticeable differences from the benchmark |
| High | Significant variation in relative returns |
These categories are illustrative rather than universal industry standards. A value that is high for a large-cap index fund might be normal for a specialized investment strategy.
Investors should compare funds that follow the same benchmark, use similar reporting periods, and calculate tracking error consistently.
How to Reduce Tracking Error
Fund managers may use several methods to reduce tracking error when their objective is to replicate an index.
Choose appropriate portfolio holdings. Holding the benchmark’s securities in similar proportions can reduce differences between fund and index returns. When full replication is impractical, careful portfolio sampling can help.
Control investment expenses. Lower management fees and efficient operations can reduce performance gaps, although expenses primarily affect tracking difference unless their impact varies over time.
Manage cash balances. Maintaining appropriate cash levels helps a fund avoid unnecessary deviations from a fully invested benchmark.
Improve trading efficiency. Careful trade execution, effective rebalancing, and managing transaction costs can help reduce unwanted differences.
Monitor benchmark changes. Funds can review index announcements and adjust holdings efficiently when constituents or weightings change.
Use consistent performance data. Fund managers and investors should compare equivalent return periods and methodologies. Inconsistent data can make tracking error calculations misleading.
These practices can improve benchmark replication, but tracking error cannot always be eliminated. Market conditions, fund size, liquidity, and operational requirements may continue to create differences.
Tracking Error for Different Types of Investors
Tracking error has different implications depending on an investor’s objectives.
- Passive investors: May prioritize low tracking error because they want their fund to follow the selected index closely.
- ETF investors: Can use tracking error and tracking difference together when comparing funds that follow the same benchmark.
- Active investors: May accept higher tracking error when a manager deliberately departs from the benchmark in pursuit of better returns.
- Retirement investors: May use tracking error to assess whether a fund provides the intended market exposure, while also considering diversification, costs, and overall portfolio risk.
- Financial analysts: Can use tracking error to evaluate benchmark-relative performance and examine how a portfolio’s active positioning changes over time.
No single tracking error target is appropriate for everyone. Investors should begin with the purpose of the investment and then decide how closely its performance should match the benchmark.
Limitations of Tracking Error
Although tracking error is useful, it has several limitations.
First, it is a historical measure. A fund with low tracking error in the past may experience greater deviations in the future because of changing market conditions or portfolio decisions.
Second, tracking error does not show whether a fund has generated positive returns. A fund can have low tracking error while losing money alongside its benchmark during a market downturn.
Third, tracking error does not explain why performance differences occurred. Investors need to examine expenses, portfolio holdings, trading activity, and other factors to identify the causes.
Finally, the calculation depends on the selected benchmark, return frequency, and measurement period. Different methodologies can produce different results.
For these reasons, tracking error should be treated as one part of a broader investment analysis rather than a standalone measure of fund quality.
Frequently Asked Questions About Tracking Error
1. What does tracking error mean in simple terms?
Tracking error measures how much an investment’s returns vary relative to its benchmark over time. It helps investors understand whether a fund follows its target index consistently.
2. Is a lower tracking error better?
A lower tracking error is generally desirable for a passive fund that aims to replicate an index. However, it is not automatically better for an actively managed fund that intentionally takes positions different from its benchmark.
3. How is tracking error calculated?
Tracking error is calculated by finding the standard deviation of the differences between a portfolio’s periodic returns and its benchmark’s periodic returns. Monthly tracking error is often annualized by multiplying it by the square root of 12.
4. What is the difference between tracking error and tracking difference?
Tracking error measures the variability of relative returns over time. Tracking difference measures the actual return gap between an investment and its benchmark over a specified period.
5. Can tracking error be negative?
No. Standard deviation cannot be negative, so tracking error is zero or positive. However, tracking difference can be negative when a fund underperforms its benchmark.
6. Do ETFs have tracking error?
Yes. ETFs can experience tracking error because of management fees, trading costs, cash holdings, portfolio sampling, and differences in dividend treatment or index rebalancing.
7. Does high tracking error mean an investment is risky?
High tracking error indicates greater variability in returns relative to a benchmark. It does not necessarily mean the investment has greater overall volatility or a higher probability of losing money.
8. Why do index funds sometimes underperform their benchmarks?
Index funds may underperform because of management fees, transaction costs, cash holdings, taxes, and the timing of portfolio adjustments. These factors can create differences between the fund’s returns and the benchmark’s returns.
Conclusion
Tracking error is a valuable tool for understanding how closely an investment fund follows its benchmark. It measures the variability of relative returns and helps investors evaluate passive funds, compare ETFs, and assess active portfolio management.
The most important distinction is that tracking error measures consistency, while tracking difference measures the actual performance gap. Both metrics provide useful information, but neither should be used in isolation.
Before choosing a fund, investors should consider its tracking error alongside fees, historical performance, diversification, liquidity, and investment objectives. By evaluating these factors together, investors can make more informed decisions and select investments that better match their financial goals.
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