Tracking error

What Is Tracking Error?

Tracking error is a quantitative measure of the divergence between the price movement of an investment portfolio and its chosen benchmark. Often expressed as a standard deviation percentage, it quantifies how closely a fund's investment performance tracks the performance of the index or benchmark it aims to replicate. A lower tracking error indicates that the portfolio's returns closely mirror those of its benchmark, while a higher tracking error suggests greater deviation. This metric is a crucial component within Investment Performance Measurement, especially for passively managed funds.

Tracking error is primarily used to assess the effectiveness of passive management strategies, such as those employed by index funds and exchange-traded funds (ETFs). These funds aim to deliver returns that are as close as possible to their underlying index. Any difference in performance, whether positive or negative, contributes to the tracking error. It is also relevant for active management strategies, where managers might seek to outperform a benchmark but still need to control how far their portfolio deviates.

History and Origin

The concept of tracking error evolved alongside the rise of modern portfolio management and the increasing popularity of index-based investing. While specific dates for its "invention" are elusive, its prominence grew significantly with the academic development of concepts like the Efficient Market Hypothesis and Modern Portfolio Theory in the mid-20th century, which provided frameworks for understanding market benchmarks and the performance of investments relative to them.

The widespread adoption of index funds, pioneered in the 1970s, made tracking efficiency a critical performance metric for investment products. As more investors sought low-cost exposure to broad markets, the ability of an index fund or ETF to accurately replicate its underlying benchmark became a key differentiator. The shift towards passive investing has been significant, with assets in U.S. passive mutual funds and ETFs surpassing active ones for the first time in 2024, driven by a continuous influx of capital into passive strategies over the past decade.⁵,⁴

Regulatory bodies and investment professionals increasingly utilize tracking error as a standard measure of a fund's adherence to its stated investment objective, particularly for passively managed vehicles.

Key Takeaways

Tracking error quantifies how much a portfolio's returns deviate from its benchmark's returns.
It is calculated as the standard deviation of the differences between the portfolio's and the benchmark's returns.
A low tracking error is desirable for index funds and ETFs, indicating effective replication of the benchmark.
Factors such as management fees, transaction costs, and differences in portfolio construction can contribute to tracking error.
Understanding tracking error is essential for evaluating the efficiency of both passive and, to some extent, active investment strategies.

Formula and Calculation

Tracking error is typically calculated as the standard deviation of the difference between the portfolio's returns and the benchmark's returns over a specified period. The formula is:

\text{Tracking Error} = \sqrt{\frac{\sum_{i=1}^{n} (R_{p,i} - R_{b,i} - \text{Average}(R_p - R_b))^2}{n-1}} \times \sqrt{k}

Where:

(R_{p,i}) = Portfolio return for period (i)
(R_{b,i}) = Benchmark return for period (i)
(\text{Average}(R_p - R_b)) = The average difference between portfolio and benchmark returns
(n) = Number of periods
(k) = Annualization factor (e.g., 252 for daily data, 12 for monthly data, 1 for annual data)

This formula effectively measures the volatility of the difference in returns, providing a single number to represent the degree of deviation.

Interpreting the Tracking Error

Interpreting tracking error involves understanding its context and magnitude. A low tracking error implies that a portfolio is closely mirroring its benchmark, which is the primary goal for passive investment vehicles. For example, an ETF designed to track the S&P 500 should ideally have a very low tracking error, indicating that its returns align closely with the S&P 500's returns.

Conversely, a higher tracking error suggests a greater divergence from the benchmark. For actively managed funds, a manager might intentionally take positions different from the benchmark in an attempt to generate alpha. In such cases, a higher tracking error may be acceptable if it is accompanied by superior relative return. However, for passive funds, a high tracking error signals inefficiency or issues in the fund's replication strategy. Investment professionals often use attribution analysis to break down the sources of tracking error, determining whether it stems from sector bets, stock selection, or other factors.

Hypothetical Example

Consider an Exchange-Traded Fund (ETF) that aims to replicate the performance of a hypothetical "Diversified.com U.S. Equity Index" (DCEI).

Over three months, the returns are as follows:

Month	DCEI Benchmark Return	ETF Return	Difference (ETF - DCEI)
1	2.0%	1.9%	-0.1%
2	1.5%	1.7%	0.2%
3	1.0%	0.9%	-0.1%

First, calculate the average difference in returns:
Average difference = $\frac{(-0.1\% + 0.2\% - 0.1\%)}{3} = \frac{0\%}{3} = 0\%$

Next, calculate the squared difference from the average difference:

Month 1: $(-0.1\% - 0\%)^2 = (-0.1\%)^2 = 0.0001\%^2$
Month 2: $(0.2\% - 0\%)^2 = (0.2\%)^2 = 0.0004\%^2$
Month 3: $(-0.1\% - 0\%)^2 = (-0.1\%)^2 = 0.0001\%^2$

Sum of squared differences = $0.0001\%^2 + 0.0004\%^2 + 0.0001\%^2 = 0.0006\%^2$

Now, apply the tracking error formula (assuming this is monthly data and we want annualized tracking error, so (k=12), but for simplicity, let's keep it monthly first to show the calculation, then consider annualization):

Monthly Tracking Error = $\sqrt{\frac{0.0006\%^2}{3-1}} = \sqrt{\frac{0.0006\%^2}{2}} = \sqrt{0.0003\%^2} \approx 0.01732\%$

To annualize (assuming 12 months for consistency):
Annualized Tracking Error = (0.01732% \times \sqrt{12} \approx 0.0600% \text{ or } 0.06% )

In this example, the ETF has an annualized tracking error of approximately 0.06%, which is considered very low, indicating it effectively tracks the DCEI. This low figure suggests minimal deviation from the index, demonstrating the efficiency of the ETF's portfolio management in replicating the benchmark.

Practical Applications

Tracking error is widely used across various facets of finance and investment performance analysis.

Passive Fund Evaluation: For index funds and Exchange-Traded Funds (ETFs), tracking error is a primary metric. Investors and analysts use it to gauge how efficiently these funds replicate their chosen benchmarks. A consistently low tracking error suggests a well-managed passive fund that minimizes deviations from its target index. Regulatory filings and fund fact sheets often disclose a fund's tracking error.
Manager Selection: Institutional investors and consultants assess tracking error when selecting active management firms. While active managers aim to outperform, their tracking error provides insight into their risk management discipline and how closely they adhere to their stated investment style. For instance, a manager aiming for consistent, benchmark-relative returns might be expected to have a lower tracking error than one pursuing a more aggressive, unconstrained strategy.
Performance Attribution: Tracking error is a key input in attribution analysis, which breaks down a portfolio's performance relative to its benchmark into various components, such as asset allocation, sector selection, and security selection. This helps identify the sources of any tracking error.
Risk Budgeting: In advanced portfolio management, tracking error can be used as a measure of "active risk" or "relative risk." Portfolio managers may establish a "risk budget" for their active decisions, measured by a maximum allowable tracking error. This ensures that their deviations from the benchmark remain within acceptable limits.
Market Commentary: Financial news outlets frequently discuss tracking error, particularly in the context of ETF performance. For example, reports might highlight how certain ETFs successfully minimize their tracking error, or conversely, explain reasons for higher tracking error in specific market conditions. An example includes discussions about how BlackRock planned to fully replicate certain ETFs to avoid increased tracking error.³

Limitations and Criticisms

While a valuable metric, tracking error has several limitations and criticisms that investors should consider.

Firstly, tracking error is a historical measure. It reflects past deviations but does not guarantee future performance or future tracking accuracy. Market conditions can change, impacting a fund's ability to closely track its benchmark.

Secondly, a low tracking error alone does not necessarily indicate a "good" investment. A fund could have a low tracking error simply by holding a highly similar portfolio to the benchmark but might still underperform due to fees or other operational inefficiencies. Conversely, an actively managed fund with a higher tracking error might deliver significant alpha and superior absolute return, which a focus solely on tracking error might obscure.

Thirdly, the calculation of tracking error can be influenced by the frequency of data used (daily, weekly, monthly) and the specific period chosen. A short, volatile period might show a higher tracking error than a longer, more stable one, even for the same fund.

Moreover, some sources of tracking error are unavoidable, even for well-managed passive funds. These can include:

Fees and Expenses: Management fees, administrative costs, and trading commissions reduce a fund's net returns compared to its benchmark.
Sampling: Many large index funds and Exchange-Traded Funds (ETFs) do not hold every single security in their underlying index (full replication) but instead use a sampling approach. This involves holding a representative subset of the index securities, which can inherently lead to small deviations.²
Rebalancing and Corporate Actions: Indices are periodically rebalanced or adjusted due to corporate actions (e.g., mergers, stock splits). Funds tracking these indices must also adjust their holdings, which incurs transaction costs and may cause temporary deviations.
Cash Drag: Funds often hold a small portion of their assets in cash for liquidity purposes, which can cause a slight drag on performance if the benchmark is fully invested in equities.
Illiquidity: If an index includes illiquid or thinly traded securities, the fund may face challenges buying or selling them at favorable prices, leading to discrepancies.

Ultimately, investors should consider tracking error as one of several metrics in evaluating a fund's suitability for their portfolio. The Federal Reserve Bank of San Francisco has noted that managing tracking error is part of broader risk management within portfolio construction.¹

Tracking Error vs. Alpha

While both tracking error and alpha relate to a portfolio's performance relative to a benchmark, they measure distinct concepts.

Tracking Error quantifies the deviation or dispersion of a portfolio's returns from its benchmark's returns. It is a measure of relative volatility or "active risk." A high tracking error means the portfolio's returns are more inconsistent with the benchmark, regardless of whether it's outperforming or underperforming. It's about the variability of the difference. For funds aiming to replicate an index, the goal is to minimize tracking error.

Alpha (or Jensen's Alpha) measures the excess return of a portfolio compared to what would be expected given its beta (systematic risk) and the benchmark's return. It is a measure of a manager's skill or the value added by active decisions, independent of market movements. A positive alpha indicates outperformance, while a negative alpha suggests underperformance, after accounting for market risk. For active managers, the goal is to maximize alpha.

In essence, tracking error tells you how much a portfolio wanders from its benchmark, whereas alpha tells you how much better or worse it performs than what its risk profile (relative to the market) suggests. A fund can have a high tracking error and a high positive alpha (if it consistently deviates in a profitable way), or a high tracking error and a negative alpha (if its deviations are detrimental). Conversely, a passive fund aims for a low tracking error and an alpha close to zero, as its objective is simply to match the benchmark's return.

FAQs

What causes tracking error?

Tracking error can be caused by various factors, including fund management fees and expenses, transaction costs incurred when buying and selling securities, the use of sampling techniques instead of full replication, cash holdings for liquidity, and corporate actions that require adjustments to the portfolio. Differences in rebalancing schedules between the fund and its benchmark can also contribute.

Is a high tracking error always bad?

Not necessarily. For passive management strategies like index funds or ETFs, a high tracking error is generally undesirable because it means the fund is not effectively replicating its intended benchmark. However, for active management strategies, a higher tracking error might indicate that the manager is taking significant active positions in an attempt to generate alpha. In such cases, if the active risk leads to superior returns, the higher tracking error may be justified.

How can investors minimize tracking error?

Investors themselves cannot directly minimize a fund's tracking error, as this is the responsibility of the fund manager. However, investors can choose funds that have a history of low tracking error, particularly for passive investments. Examining the fund's expense ratio and its replication strategy (full replication vs. sampling) can also provide clues about potential tracking error. Diversification across multiple low-cost, broadly diversified index funds can help manage overall portfolio risk, though it doesn't directly reduce the tracking error of any single fund.