Lesson 8.1: Performance Attribution

Introduction

In this lesson, students will learn about performance attribution, a critical concept in investment management that allows analysts and investors to assess how portfolio results are measured, attributed, and judged. We will explore the decomposition of returns into allocation and selection effects, differentiate between macro and micro attribution, and look closely at fixed-income attribution. By the end of this lesson, students will be able to interpret attribution results to explain portfolio performance and apply appropriate attribution methods to both equity and fixed-income investments.

Objectives

• Understand return attribution and how to decompose it into allocation and selection effects.
• Differentiate between macro versus micro attribution and understand fixed-income attribution.
• Learn how to interpret attribution results to explain performance.
• Practice decomposing returns into allocation and selection effects.
• Apply appropriate attribution methods to equity and fixed income.

Performance Attribution

Performance attribution is a methodology that describes how the returns of an investment portfolio can be explained through the actions of the manager and the chosen asset allocations. It involves analyzing the performance of a portfolio in-depth, breaking the performance down into two main types:

1. Allocation Effects - This reflects the contribution to performance based on the decision of how much to invest in different assets or asset classes.
2. Selection Effects - This denotes the impact of the investment choices made within those allocated assets or asset classes.

Decomposing Returns

At the most fundamental level, the total return of a portfolio can be expressed as:

$$ R_p = R_a + R_s $$

Where:

• $R_p$ is the total return of the portfolio,
• $R_a$ is the allocation effect,
• $R_s$ is the selection effect.

Allocation Effect

The allocation effect can be measured by assessing how much the portfolio's return would have differed if the weights in asset classes had been adjusted. Mathematically, this can be expressed as:

$$ R_a = \sum_{i=1}^{n} (w_i - w_{i, benchmark}) \times (R_{i, benchmark}) $$

Where:

• $w_i$ is the weight of asset class $i$ in the portfolio,
• $w_{i, benchmark}$ is the weight of asset class $i$ in the benchmark,
• $R_{i, benchmark}$ is the return of asset class $i$ in the benchmark.

Example 1: Allocation Effect Calculation

Consider a portfolio invested in two asset classes: Equities (40% weight) and Bonds (60% weight). The benchmark weights are 50% in Equities and 50% in Bonds. The returns during the period were 10% for Equities and 5% for Bonds. Applying the formula:

1. The allocation effect for Equities:

$$ R_a^{Equities} = (0.4 - 0.5) \times 0.1 = -0.01 $$

1. The allocation effect for Bonds:

$$ R_a^{Bonds} = (0.6 - 0.5) \times 0.05 = 0.005 $$

1. Thus, the total allocation effect:

$$ R_a = -0.01 + 0.005 = -0.005 $$

Selection Effect

Now, let's discuss the selection effect, which assesses the actual investment decisions made within those asset classes from their set allocations. This can be captured with the formula:

$$ R_s = \sum_{i=1}^{n} w_i \times (R_i - R_{i, benchmark}) $$

Where:

• $R_i$ is the return achieved in asset class $i$ in the portfolio, and\ n- $R_{i, benchmark}$ is the return of asset class $i$ in the benchmark.

Example 2: Selection Effect Calculation

Suppose the Equities in the portfolio returned 12%, while the Bonds returned 3%. The calculations will be as follows:

1. The selection effect for Equities:

$$ R_s^{Equities} = 0.4 \times (0.12 - 0.1) = 0.008 $$

1. The selection effect for Bonds:

$$ R_s^{Bonds} = 0.6 \times (0.03 - 0.05) = -0.012 $$

1. Thus, the total selection effect:

$$ R_s = 0.008 - 0.012 = -0.004 $$

Total Performance Attribution

By combining the allocation and selection effects, we can assess the total performance impact. Therefore, the total return can be expressed as:

$$ R_p = R_a + R_s $$

In our examples:

• Allocation effect: $R_a = -0.005$
• Selection effect: $R_s = -0.004$

Thus, the total effect would be:

$$ R_p = -0.005 - 0.004 = -0.009 $$

This means the portfolio underperformed the benchmark by 0.9%.

Macro vs. Micro Attribution

Attribution analysis can be broadly categorized into macro and micro attribution.

Macro Attribution

Macro attribution looks at the performance of broad asset classes. It evaluates how an investor's overall portfolio strategy, in terms of asset allocation, affected returns relative to a benchmark. As such, it emphasizes broad movements and decisions affecting the wider market landscape.

Micro Attribution

In contrast, micro attribution focuses on specific securities within asset classes. It assesses the performance influenced by individual stock selection within the broader asset class. This type of attribution allows for drilling down into portfolio specifics and is often used to identify successful and unsuccessful investments at a granular level.

Example 3: Macro and Micro Attribution

For instance, consider the following:

Assuming a portfolio has a total return of 7%, with a benchmark return of 6%. The macro attribution might reveal that the asset allocation (e.g., a higher weight in equities) contributed positively to performance. At a micro level, we might assess that a specific equity stock performed exceptionally well, contributing significantly to the total return, or conversely, a poorly performing bond reduced the overall performance.

Fixed-Income Attribution

Fixed-income attribution presents distinct challenges due to the complexity of bonds and interest rates. Here, performance is influenced by interest rate movements, credit spread changes, duration risk, and convexity.

Key Concepts to Understand

• Interest Rate Risk: This is the risk that an investment's value will change due to a change in interest rates. For bonds, this often results in a decrease in price as interest rates rise.
• Credit Spread: This is the difference in yield between bonds of different credit qualities. A significant change in the credit spread can greatly affect the return of a fixed-income portfolio.
• Duration: Duration measures a bond's sensitivity to changes in interest rates, with higher duration indicating greater sensitivity.

Calculating Fixed-Income Attribution

Fixed-income attribution can be assessed through bond yield modifications or changes in total return, presented as:

$$ R = \sum_{i=1}^{n} w_i \times (R_i - R_{i, benchmark}) $$

Where:

• $R_i$ represents yields or returns on fixed-income securities and\ n- $R_{i, benchmark}$ represents benchmark yields.

Example 4: Fixed-Income Attribution Calculation

Consider a portfolio invested in two bonds:

• Bond A (5% yield) - 70% weight
• Bond B (3% yield) - 30% weight

With a benchmark yield of 4% for both bonds. Given that the actual returns are calculated as:

1. Yield contribution for Bond A:

$$ R_A = 0.7 \times (0.05 - 0.04) = 0.007 $$

1. Yield contribution for Bond B:

$$ R_B = 0.3 \times (0.03 - 0.04) = -0.003 $$

Combining yields:

$$ R_{total} = R_A + R_B = 0.007 - 0.003 = 0.004 $$

This shows that the fixed-income portion of the portfolio outperformed the benchmark by 0.4%.

Conclusion

In summary, performance attribution is a critical tool to assess the skill and effectiveness of portfolio management. By breaking down performance into allocation and selection effects, portfolio managers can better understand where value is being added or lost relative to a benchmark. Knowing how to interpret and apply this attribution analysis to both equity and fixed income is essential for effective investment management.

Study Notes

• Performance attribution reports how a portfolio's return is composed of allocation and selection effects.
• Allocation effects assess the impact of being in certain asset classes, while selection effects evaluate specific investments in those classes.
• Macro attribution focuses on broad asset classes; micro attribution drills down into individual securities.
• Fixed-income attribution takes into account yield changes, interest rate risk, and credit spreads.
• A proper understanding of these concepts assists in diagnosing and potentially improving portfolio performance.