Tracking Error Calculator
Calculate the tracking error between a portfolio and its benchmark in Excel format
How to Calculate Tracking Error in Excel: Complete Guide
Tracking error is a critical measure for evaluating how closely a portfolio follows its benchmark index. This comprehensive guide will walk you through the exact steps to calculate tracking error in Excel, including the mathematical formulas, practical examples, and interpretation of results.
What is Tracking Error?
Tracking error measures the standard deviation of the difference between a portfolio’s returns and its benchmark’s returns. It quantifies how much the portfolio’s performance deviates from the benchmark over time.
- Low tracking error (typically < 1%): Indicates the portfolio closely follows the benchmark
- High tracking error (typically > 2%): Suggests significant active management or different risk exposure
The Tracking Error Formula
The mathematical formula for tracking error (TE) is:
TE = σ(Rp – Rb)
Where:
- σ = standard deviation
- Rp = portfolio returns
- Rb = benchmark returns
Step-by-Step Calculation in Excel
1. Prepare Your Data
Organize your data in two columns:
| Period | Portfolio Return (%) | Benchmark Return (%) |
|---|---|---|
| Jan 2023 | 5.2 | 4.8 |
| Feb 2023 | 3.8 | 4.1 |
| Mar 2023 | -1.5 | -0.9 |
| Apr 2023 | 7.1 | 6.7 |
2. Calculate the Return Differences
In a new column, calculate the difference between portfolio and benchmark returns:
=Portfolio_Return – Benchmark_Return
3. Compute the Standard Deviation
Use Excel’s STDEV.P function to calculate the standard deviation of these differences:
=STDEV.P(difference_range)
4. Annualize the Tracking Error
For monthly data, multiply by √12 to annualize:
=Monthly_TE * SQRT(12)
Practical Example with Excel Formulas
Let’s calculate tracking error for the sample data above:
| Period | Portfolio | Benchmark | Difference |
|---|---|---|---|
| Jan 2023 | 5.2 | 4.8 | =B2-C2 → 0.4 |
| Feb 2023 | 3.8 | 4.1 | =B3-C3 → -0.3 |
| Mar 2023 | -1.5 | -0.9 | =B4-C4 → -0.6 |
| Apr 2023 | 7.1 | 6.7 | =B5-C5 → 0.4 |
Monthly tracking error = STDEV.P(D2:D5) = 0.47%
Annualized tracking error = 0.47% * SQRT(12) = 1.62%
Interpreting Tracking Error Results
| Tracking Error Range | Interpretation | Typical Portfolio Type |
|---|---|---|
| < 0.5% | Excellent tracking | Index funds, ETFs |
| 0.5% – 1.0% | Good tracking | Enhanced index funds |
| 1.0% – 2.0% | Moderate tracking | Actively managed funds |
| > 2.0% | Poor tracking | Highly active strategies |
Common Mistakes to Avoid
- Using arithmetic mean instead of standard deviation: Tracking error requires standard deviation of differences, not average differences.
- Incorrect annualization: Forgetting to multiply by √N (where N is periods per year) for annualized figures.
- Mismatched time periods: Comparing monthly portfolio returns with quarterly benchmark returns.
- Ignoring compounding: For multi-period calculations, use geometric returns rather than arithmetic.
Advanced Applications
Information Ratio
The information ratio (IR) builds on tracking error by incorporating excess return:
IR = (Rp – Rb) / TE
Where (Rp – Rb) is the average excess return.
Tracking Error vs. Tracking Difference
| Metric | Calculation | Interpretation |
|---|---|---|
| Tracking Error | Standard deviation of return differences | Measures consistency of tracking |
| Tracking Difference | Average of return differences | Measures directional bias |
Academic Research on Tracking Error
Several academic studies have examined tracking error’s predictive power:
- Federal Reserve study (2017) found that funds with tracking errors >1.5% tend to underperform their benchmarks net of fees
- Research from Columbia Business School shows that tracking error explains 40% of the variation in fund alpha
- The SEC’s 2020 report on index fund disclosure highlights tracking error as a key metric for investor protection
Excel Template for Tracking Error
To create a reusable template:
- Set up columns for dates, portfolio returns, benchmark returns
- Add a column for return differences with formula =Portfolio-Benchmark
- Create a summary section with:
- =STDEV.P(difference_range) for tracking error
- =AVERAGE(difference_range) for tracking difference
- =AVERAGE(portfolio_range)-AVERAGE(benchmark_range) for excess return
- Add data validation to ensure proper number formatting
Alternative Calculation Methods
Using Covariance Approach
Tracking error can also be calculated using:
TE = √(σ2p + σ2b – 2ρσpσb)
Where ρ is the correlation between portfolio and benchmark returns.
Rolling Tracking Error
For time-varying analysis, calculate tracking error over rolling windows (e.g., 12-month periods) to identify when tracking deviated most.
Industry Standards and Benchmarks
| Fund Type | Typical Tracking Error | Source |
|---|---|---|
| S&P 500 Index Funds | 0.02% – 0.15% | Morningstar 2023 |
| International Equity ETFs | 0.20% – 0.40% | Bloomberg 2023 |
| Small-Cap Funds | 0.50% – 1.20% | Lipper 2023 |
| Actively Managed Large Cap | 1.50% – 3.00% | CRSP 2023 |
Frequently Asked Questions
Can tracking error be negative?
No, tracking error is always non-negative because it’s a standard deviation (a measure of dispersion).
How does tracking error relate to alpha?
Tracking error is a component of the information ratio (alpha divided by tracking error), which measures risk-adjusted excess return.
What’s a good tracking error for an index fund?
For large-cap index funds, tracking error should typically be below 0.20%. Small-cap or international funds may have slightly higher tracking errors (0.20%-0.50%) due to less liquid markets.
How often should tracking error be calculated?
Most professional managers calculate tracking error monthly and report annualized figures. Quarterly calculations may be appropriate for less liquid strategies.
Conclusion
Calculating tracking error in Excel provides valuable insights into how closely your portfolio follows its benchmark. By following the step-by-step methods outlined in this guide, you can:
- Accurately measure your portfolio’s tracking efficiency
- Identify periods of significant deviation
- Compare your results against industry standards
- Make informed decisions about active vs. passive management
Remember that while low tracking error indicates close benchmark replication, some active strategies intentionally accept higher tracking error to pursue alpha generation. Always consider tracking error in the context of your investment objectives and risk tolerance.