Adjusted tracking error

What Is Adjusted Tracking Error?

Adjusted tracking error refers to the standard measure of tracking error with specific qualitative or quantitative considerations applied, aiming to provide a more nuanced understanding of a portfolio's deviation from its benchmark. While the core calculation of tracking error quantifies the volatility of the difference between a portfolio's return and its benchmark's return, "adjusted" implies a focus on how this metric is interpreted, managed, or modified in practice to account for factors beyond simple return divergence. This concept falls under the broader category of portfolio management and performance measurement, emphasizing the blend of quantitative analysis with real-world investment objectives and constraints. It is a critical component for both active management and passive management strategies in assessing risk and performance relative to a defined target.

History and Origin

The concept of tracking error emerged as portfolio managers increasingly sought to measure how closely their portfolios mirrored a specific index or benchmark. Its roots are intertwined with the rise of modern portfolio theory and the proliferation of index funds in the latter half of the 20th century. Early applications focused on quantifying the efficiency of index replication strategies, where minimal tracking error was the primary goal. Over time, as active management evolved, tracking error also became a measure of "active risk," reflecting the intentional deviations a manager makes to outperform a benchmark³², ³³.

Academics and practitioners, such as Roll (1992), further developed the framework for describing efficient frontiers constrained by tracking error, expanding its use beyond pure index replication to active portfolio optimization³¹. This evolution underscored that while a low tracking error is desirable for passive funds, active managers might strategically accept a higher tracking error to pursue greater excess return. The term "adjusted tracking error" itself doesn't refer to a new formula but rather reflects the ongoing refinement in how this fundamental metric is applied and interpreted, taking into account various influencing factors like transaction costs, taxes, and liquidity constraints that cause actual performance to diverge from theoretical perfect tracking²⁹, ³⁰.

Key Takeaways

• Adjusted tracking error considers standard tracking error in the context of specific real-world factors, offering a more comprehensive performance assessment.
• It highlights how deviations from a benchmark are interpreted, whether they are intentional "active risk" or unintentional "error."
• This concept is crucial for both index funds, which aim to minimize it, and actively managed portfolios, where it's a measure of controlled deviation.
• Factors like fees, taxes, and liquidity can naturally influence tracking error, leading to the need for "adjustment" in interpretation.
• A deeper understanding of adjusted tracking error aids investors in evaluating fund manager skill and aligning portfolio risk with investment objectives.

Formula and Calculation

Adjusted tracking error typically refers to the interpretation and contextualization of the standard tracking error calculation, rather than a fundamentally different mathematical formula. The underlying calculation for historical, or "ex-post," tracking error remains the standard deviation of the difference between the portfolio's returns and the benchmark's returns over a specified period.

The formula for tracking error ((TE)) is:

Where:

• (R_p) = Portfolio's return
• (R_b) = Benchmark's return
• (\sigma) = Standard deviation

To calculate this, one would typically:

1. Determine the periodic (e.g., daily, weekly, monthly) returns for both the portfolio and its benchmark over a chosen time horizon.
2. Calculate the difference between the portfolio return and the benchmark return for each period. This is the excess return.
3. Compute the standard deviation of these periodic excess returns.
4. Annualize the result by multiplying by the square root of the number of periods in a year (e.g., (\sqrt{252}) for daily data, (\sqrt{12}) for monthly data).

The "adjustment" comes in understanding the causes of this calculated tracking error and interpreting whether it's attributable to intended active bets, or unintended inefficiencies and costs. For instance, an index fund's tracking error might be "adjusted" for known expense ratios, trading costs, or rebalancing frequency, as these are inherent operational aspects that prevent perfect tracking²⁸.

Interpreting the Adjusted Tracking Error

Interpreting adjusted tracking error goes beyond simply looking at the numerical value; it requires understanding the context and the reasons behind the deviation from the benchmark. For a passive fund, a lower tracking error generally indicates better replication of the benchmark, suggesting efficiency in managing costs and rebalancing²⁶, ²⁷. However, even for Exchange-Traded Funds (ETFs) designed to track an index perfectly, factors like expense ratios, trading costs, and cash drag can lead to a non-zero tracking error, which is then understood as an "adjusted" or expected component of the deviation.

For an actively managed portfolio, a higher adjusted tracking error implies a greater deviation from the benchmark, reflecting the manager's conviction in their investment decisions. This "active risk" is intentional and aims to generate alpha. Investors often assess this alongside the information ratio, which relates the excess return to the tracking error, providing a measure of risk-adjusted performance. The interpretation adjusts based on whether the tracking error is a result of purposeful security selection, sector tilts, or market volatility, as opposed to operational inefficiencies or poor execution²⁵.

Hypothetical Example

Consider two hypothetical index funds, Fund P (Passive) and Fund A (Active-ish). Both aim to track the S&P 500 Index over a year.

Scenario:

• S&P 500 Index Return: 10.0%
• Fund P Returns:
  • Q1: 2.4% (Index: 2.5%)
  • Q2: 3.1% (Index: 3.0%)
  • Q3: 1.9% (Index: 2.0%)
  • Q4: 2.5% (Index: 2.5%)
• Fund A Returns:
  • Q1: 2.0% (Index: 2.5%)
  • Q2: 4.0% (Index: 3.0%)
  • Q3: 1.5% (Index: 2.0%)
  • Q4: 3.0% (Index: 2.5%)

Calculating Excess Returns:

Calculating Tracking Error (Annualized Standard Deviation of Excess Returns):

• Fund P Excess Returns: (-0.1%, 0.1%, -0.1%, 0.0%)

  • Standard Deviation (\approx 0.0866%)
  • Annualized Tracking Error (= 0.0866% \times \sqrt{4} \approx 0.17%)

• Fund A Excess Returns: (-0.5%, 1.0%, -0.5%, 0.5%)

  • Standard Deviation (\approx 0.6455%)
  • Annualized Tracking Error (= 0.6455% \times \sqrt{4} \approx 1.29%)

Adjusted Interpretation:

• Fund P (0.17% Tracking Error): The low tracking error suggests Fund P is doing a good job of replicating the index. The "adjustment" here might be understanding that this small deviation is likely due to unavoidable factors like its expense ratio or the slight lag in rebalancing to match index changes. This is considered acceptable for a passive strategy.
• Fund A (1.29% Tracking Error): Fund A has a significantly higher tracking error. An "adjusted" interpretation would then ask: Is this intentional? If Fund A is an actively managed fund, this higher tracking error might represent the manager's "active bets" designed to outperform. For example, the manager might have overweighted certain sectors, leading to the larger deviations. If the overall return of Fund A (e.g., 11.0% total for the year) truly outperformed the S&P 500 (10.0%), then this higher tracking error, leading to a positive excess return, would be viewed as successful active management. If Fund A also ended up with an overall return of 9.0%, then the high tracking error would indicate significant underperformance due to poor active decisions. The "adjustment" is the qualitative assessment of the source and intent of the deviation.

Practical Applications

Adjusted tracking error is a versatile metric used across various facets of financial analysis and risk management:

• Fund Selection and Evaluation: Investors and consultants use tracking error to evaluate how consistently an investment policy statement aligns with its benchmark. For index funds and ETFs, minimal tracking error is highly desired, as it indicates efficient replication of the underlying index²⁴. For actively managed funds, tracking error helps assess the degree of active risk taken. A manager with a high tracking error is taking significant active bets, while one with a low tracking error is more closely hugging the benchmark.
• Portfolio Construction and Optimization: Portfolio managers use ex-ante (forward-looking) tracking error models to construct portfolios that aim for specific return objectives while staying within predefined risk tolerance levels relative to a benchmark. This helps in balancing desired diversification with active positions²², ²³.
• Risk Budgeting: Institutional investors often allocate "risk budgets" to different fund managers. Tracking error serves as a key measure within these budgets, ensuring that the cumulative active risk taken across various mandates remains within acceptable bounds for the overall portfolio²⁰, ²¹. The Federal Reserve, for instance, emphasizes comprehensive risk management for financial institutions, highlighting the importance of identifying, assessing, and mitigating various types of financial risk¹⁹.
• Regulatory Compliance and Disclosure: Regulatory bodies, such as the Securities and Exchange Commission (SEC), require funds to disclose their principal risks to investors¹⁸. While not explicitly "adjusted tracking error," the considerations that lead to its "adjustment" (e.g., liquidity risk, operational risk) are often part of these disclosures. The SEC provides guidance to funds on improving principal risk disclosures to be more clear and concise for investors¹⁷.

Limitations and Criticisms

While a valuable tool, tracking error, and thus adjusted tracking error, has several limitations and criticisms:

• Directionally Agnostic: Tracking error measures the volatility of the difference in returns, but it does not indicate whether the deviation was positive (outperformance) or negative (underperformance)¹⁵, ¹⁶. A fund that consistently underperforms its benchmark by a fixed margin could have a zero tracking error, which might mislead an investor if not "adjusted" by considering the actual return differential¹⁴.
• Context Dependency: Its interpretation heavily depends on the investment strategy. A high tracking error for a passive fund is a failure, but for an active fund, it might be a sign of significant active bets¹³. Critiques argue that holding tracking error constant for skilled active managers can be problematic, especially when market conditions change or index concentration increases, potentially limiting beneficial diversification¹².
• Backward-Looking (Ex-Post): When calculated historically (ex-post), tracking error is a measure of past performance. It doesn't guarantee future deviations. Predicting future tracking error (ex-ante) requires sophisticated models and assumptions that may not hold true in different market environments¹¹.
• Sensitivity to Data Frequency: The calculation can be sensitive to the frequency of data used (e.g., daily vs. monthly returns), which can impact the magnitude of the result.
• Behavioral Implications: Focusing too rigidly on tracking error can sometimes incentivize "benchmark hugging" in active managers, leading them to take less conviction in their best ideas to avoid large deviations, even if those deviations could lead to substantial outperformance⁹, ¹⁰. This can potentially stifle truly active management that aims to provide significant alpha for investors.

Some researchers even argue that for actively managed funds, those with low tracking error ironically exhibit lower alpha, higher beta, and lower average performance compared to funds with high tracking error, suggesting a complex relationship that necessitates careful adjustment in interpretation⁸. The CFA Institute, for example, explores how allowing some tracking error in index funds might even boost after-tax returns by avoiding frequent taxable events associated with strict benchmark replication⁷.

Adjusted Tracking Error vs. Tracking Error

The distinction between "Adjusted Tracking Error" and "Tracking Error" is primarily one of emphasis and interpretation rather than a fundamental difference in calculation.

In essence, "tracking error" is the raw numerical output, while "adjusted tracking error" refers to the insights gained after considering the various operational, strategic, and market-related factors that contribute to or influence that numerical result. It transforms a simple statistical measure into a more comprehensive risk management and performance assessment tool.

FAQs

What does it mean if a fund has a high adjusted tracking error?

A high adjusted tracking error means the fund's returns have significantly deviated from its benchmark's returns. For an active management strategy, this often implies the manager is taking substantial active bets to generate excess return. For a passive management fund like an index fund, a high tracking error is generally undesirable, indicating inefficiency or a failure to replicate the benchmark closely. The "adjustment" comes from understanding the intent behind the deviation.

Can adjusted tracking error be negative?

No, tracking error (and thus adjusted tracking error) is a measure of volatility, expressed as a standard deviation, which is always a non-negative value. It quantifies the magnitude of deviations, regardless of whether the portfolio outperformed or underperformed the benchmark¹, ². The underlying excess returns (portfolio return minus benchmark return) can be positive or negative, but the standard deviation of those differences will be a positive number, representing the dispersion of those differences.

How do fees and expenses relate to adjusted tracking error?

Fees and expenses, such as management fees or trading costs, are significant factors that naturally contribute to tracking error, especially for passive management funds. Even if an index fund perfectly replicates its benchmark's holdings, the deduction of these costs will cause its net returns to lag the benchmark, creating a consistent tracking error. When considering "adjusted" tracking error, these inherent costs are acknowledged as an expected component of the deviation, influencing the interpretation of the fund's efficiency.

Is a low adjusted tracking error always good?

Not always. For passive management (e.g., index funds), a low tracking error is desirable as it indicates efficient replication of the benchmark. However, for active management, an extremely low tracking error might suggest that the manager is "benchmark hugging" — meaning they are investing very similarly to the index to avoid large deviations. While this reduces active risk, it also limits the potential for significant outperformance or alpha, which is typically the goal of active management. The interpretation depends on the fund's stated objective.