Returns based attribution

Returns based attribution is a method of performance measurement used in investment performance analysis to explain the sources of a portfolio's returns, particularly when compared to a benchmark. This analytical technique attributes the difference between the portfolio's portfolio return and the benchmark's return (known as active return) to various factors, such as asset allocation and security selection decisions made by an investment manager. Returns based attribution models typically rely on statistical techniques, such as regression analysis, to decompose the portfolio's returns into components linked to different market factors or investment styles. This approach provides a high-level view of performance drivers, making it particularly useful when detailed underlying portfolio management holdings are unavailable or difficult to obtain.²⁸

History and Origin

The concept of performance attribution can be traced back to the 1960s, with early work by Peter O. Dietz and the Bank Administration Institute (BAI) on pension fund performance.²⁷ A significant development came with Eugene Fama's 1972 paper, "Components of Investment Performance," which proposed decomposing observed returns into components related to selectivity (stock picking ability) and timing (ability to predict market movements).²⁶, This laid foundational groundwork for subsequent models. In the mid-1980s, the Brinson models, notably by Gary Brinson, L. Randolph Hood, and Gilbert Beebower (1986), further formalized investment portfolio performance attribution. These models introduced the widely recognized breakdown of active returns into asset allocation and security selection effects, which continues to underpin many public performance attribution analyses. These early contributions paved the way for more sophisticated attribution analysis techniques, including returns based attribution, which uses statistical methods to infer performance drivers from return streams. A conceptual overview paper discussing the evolution and current methodologies of performance attribution provides further historical context and technical details.²⁵

Key Takeaways

Returns based attribution is a statistical method that analyzes a portfolio's returns against a benchmark to identify performance drivers.
It is particularly useful for analyzing portfolios where detailed, frequent holdings data might not be available, such as some hedge funds or private equity.²⁴
The method typically relies on regression analysis to determine a portfolio's sensitivity to various market factors or investment styles.²³
While offering a high-level overview, returns based attribution may be less precise than methods that use actual holdings data, and it can be susceptible to data manipulation if inappropriate benchmarks or time periods are chosen.²²,²¹
It helps asset owners and investment managers understand the broad influences on relative performance.

Formula and Calculation

Returns based attribution often employs multiple linear regression to model a portfolio's returns based on the returns of various market indexes or factor proxies. The general form of such a model can be expressed as:

R_P = \alpha + \beta_1 R_1 + \beta_2 R_2 + ... + \beta_n R_n + \epsilon

Where:

(R_P) = Portfolio's holding period return
(\alpha) = Alpha, representing the portfolio's excess return not explained by the systematic factors (often interpreted as manager skill)
(\beta_i) = Sensitivity (beta) of the portfolio to the (i^{th}) market factor or style index
(R_i) = Return of the (i^{th}) market factor or style index
(\epsilon) = Residual return, representing unexplained variance
(n) = Number of market factors or style indices included in the model

The coefficients ((\beta)) in this model indicate the implicit asset allocation or exposure to different factors that explain the portfolio's returns. For instance, a high (\beta) to a growth stock index suggests a significant allocation to growth stocks. While this formula provides a framework, the actual implementation involves selecting appropriate market factors and running the regression over a specified period.

Interpreting Returns based attribution

Interpreting the results of returns based attribution involves understanding what the regression coefficients and the alpha component signify. The (\beta) coefficients reveal the implicit exposures of the portfolio to different asset classes, market segments, or factor investing styles. For example, if a portfolio shows a high (\beta) to a small-cap value index, it suggests that a significant portion of its returns can be attributed to its exposure to small-cap value stocks, regardless of whether the investment manager explicitly intended this allocation.

The alpha ((\alpha)) generated by the model is often seen as the portion of the return that cannot be explained by these systematic exposures and is thus attributed to the manager's genuine skill, or "alpha." However, a significant residual term ((\epsilon)) indicates that the chosen factors do not fully explain the portfolio's returns, suggesting either unmodeled exposures or true idiosyncratic returns. It is crucial to select relevant and comprehensive factors for the attribution model to yield meaningful insights.

Hypothetical Example

Consider an investment manager running a diversified equity portfolio with a benchmark of 60% large-cap U.S. equities (S&P 500) and 40% U.S. aggregate bonds. The manager's investment style is growth-oriented, and they also invest in a small percentage of international equities.

To perform returns based attribution, a financial analyst might collect monthly portfolio return data for the manager's portfolio, the S&P 500 Index, a U.S. Aggregate Bond Index, a Russell 2000 Growth Index (as a proxy for growth factor), and an MSCI EAFE Index (for international exposure) over a 3-year period.

Using regression analysis, the analyst might find the following estimated model:

R_P = 0.001 + 0.70 R_{S\&P500} + 0.35 R_{US\_Agg\_Bond} + 0.10 R_{Russell2000Growth} - 0.05 R_{MSCI\_EAFE}

In this hypothetical outcome:

The constant (alpha) of 0.001 (or 0.1% per month) suggests a small positive active return not explained by the explicit factor exposures.
The 0.70 coefficient for S&P 500 indicates a higher-than-benchmark exposure to large-cap U.S. equities (benchmark was 60%).
The 0.35 coefficient for U.S. Aggregate Bond suggests a lower-than-benchmark exposure to bonds (benchmark was 40%).
The 0.10 coefficient for Russell 2000 Growth indicates an implicit positive exposure to small-cap growth stocks, explaining a portion of the portfolio's returns.
The -0.05 coefficient for MSCI EAFE suggests a slight negative exposure or an underweight to international equities that negatively contributed to returns, relative to the international market itself.

This analysis helps the client understand that the manager generated some active return, partly by overweighting U.S. large-cap equities, implicitly increasing exposure to small-cap growth, and potentially by underweighting or having negative security selection within international equities.

Practical Applications

Returns based attribution serves as a valuable tool across various facets of finance and investment strategy. Fund managers and asset owners utilize it to gain a high-level understanding of the drivers behind a portfolio's relative performance against its benchmark. It helps answer the fundamental question of "what factors contributed to the portfolio's returns?" without requiring detailed, daily transaction or holding period return data.

This approach is particularly useful in situations where granular portfolio holdings are either not accessible or change frequently, such as in the analysis of hedge funds, funds of funds, or certain private equity structures.²⁰ It provides insights into a manager's implicit asset allocation and style exposures. Furthermore, regulators and industry bodies, such as the CFA Institute, emphasize transparency and fair representation in investment performance reporting, often guided by standards like the Global Investment Performance Standards (GIPS).¹⁹,¹⁸,¹⁷,¹⁶ While not prescribing a specific attribution method, these standards promote clear and consistent reporting, for which returns based attribution can contribute a high-level overview. Recent reports highlight how asset managers are navigating challenges in attributing performance, especially with evolving investment mandates like ESG portfolios, underscoring the ongoing relevance and challenges of performance attribution.¹⁵

Limitations and Criticisms

While useful for a high-level overview, returns based attribution has several limitations. A primary criticism is its reliance on statistical inference rather than direct observation of portfolio holdings and transactions. This can make it less precise and potentially less accurate than holdings based attribution or transaction-based methods, especially if the portfolio's exposures change significantly over the measurement period due to active trading.¹⁴,¹³

The results of returns based attribution can be sensitive to the choice of factors included in the regression model. An incomplete or inappropriate set of factors may lead to misattribution of returns or a large unexplained residual. For instance, if a portfolio has significant exposure to a niche factor investing style not represented by the chosen indices, that contribution might be incorrectly absorbed into the alpha or residual.

Another drawback is the potential for data manipulation or misrepresentation. An investment manager could, for example, choose a benchmark or a measurement period that statistically flatters their performance.¹²,¹¹ Additionally, returns based attribution may not accurately reflect the impact of dynamic investment decisions, as it essentially attributes performance to an unchanging average portfolio over the period.¹⁰ For portfolios with illiquid securities or infrequent valuations, such as some alternative investments, outdated prices can distort the analysis.⁹ Research also highlights challenges in performance attribution when dealing with complex, multi-asset portfolios or those with ESG (Environmental, Social, and Governance) overlays, further demonstrating the need for careful application and interpretation of these models.⁸,⁷

Returns based attribution vs. Holdings based attribution

Returns based attribution and holdings based attribution are two distinct methodologies used in performance measurement, each with its own advantages and disadvantages.

Returns based attribution relies solely on the total portfolio return over a period, along with the returns of selected market indexes or factors, to statistically infer the drivers of performance. It is a "top-down" approach that doesn't require knowing the specific securities held in the portfolio or when transactions occurred. This makes it simpler to implement and particularly useful when detailed holdings data is unavailable, for example, when evaluating external managers like hedge funds. Its main drawback is that it is less precise and can be susceptible to misinterpretation or manipulation due to its inferential nature.⁶,⁵

Holdings based attribution, in contrast, is a "bottom-up" approach that uses the actual, beginning-of-period holdings of a portfolio (and sometimes changes throughout the period) to decompose performance. It provides a more granular and accurate breakdown of returns into components like asset allocation, security selection, and potentially currency effects. This method offers greater transparency and is preferred when detailed data is available. However, it is more computationally intensive and requires frequent, accurate holdings data. It may also struggle to fully reconcile to actual portfolio returns if there is high turnover or significant intra-period trading that isn't captured by the holding snapshots.⁴,³

The choice between the two often depends on data availability, the level of detail required, and the specific investment process being analyzed.

FAQs

What is the primary purpose of returns based attribution?

The primary purpose of returns based attribution is to explain why a portfolio's portfolio return differed from its benchmark by statistically identifying the broad factors or investment styles that contributed to its performance. It helps understand the general drivers of returns.

Is returns based attribution more accurate than holdings based attribution?

Generally, returns based attribution is considered less accurate and less precise than holdings based attribution because it relies on statistical inference from return streams rather than direct analysis of specific securities and transactions.² Holdings-based analysis, when data is complete and frequent, provides a more granular and direct explanation of performance.

Can returns based attribution be used for all types of portfolios?

Returns based attribution can be applied to many types of portfolios, but it is particularly useful for those where granular holdings data is difficult to obtain or analyze, such as hedge funds or funds of funds. However, its effectiveness depends heavily on the availability of appropriate market indexes or factors that adequately represent the portfolio's exposures.¹

What are the key outputs of a returns based attribution analysis?

The key outputs typically include alpha (the unexplained portion of the return, often seen as manager skill) and beta coefficients, which indicate the portfolio's sensitivity and implicit allocation to various market factors or investment styles (e.g., large-cap growth, small-cap value, international equity). These components help explain the portfolio's active return.

How does returns based attribution help an investment manager?

Returns based attribution helps an investment manager understand the broad stylistic or market exposures that have driven their portfolio's performance. It can provide insights into whether returns are primarily due to systematic market movements or potential manager skill, informing adjustments to their investment strategy and communication with clients.