Performance Attribution Analysis
Performance Attribution Analysis breaks down a portfolio's excess return into the reasons behind it. It tells a distributor whether the outperformance came from choosing the right securities, from the right weightings, or from a combination of both. The NISM exam tests your ability to compute and interpret these effects, especially using the Brinson model. Mastery of attribution helps you evaluate PMS managers and answer scenario‑based questions confidently.
Learning Objectives
- 1Define performance attribution and its purpose
- 2Identify the three core effects – allocation, selection, interaction
- 3Apply the Brinson attribution formula to a simple portfolio
- 4Interpret attribution results and avoid common exam pitfalls
What is Performance Attribution Analysis?
Performance attribution is the process of dissecting the difference between a portfolio's actual return and its benchmark return into identifiable components. The analysis answers the question “Why did the portfolio beat (or lag) the benchmark?” by attributing the excess return to decisions made by the manager.
In the Indian regulatory context, SEBI expects PMS distributors to monitor manager performance regularly. Attribution provides a quantitative basis for that monitoring, beyond a single aggregate return figure.
For the NISM exam, you will often see a table of portfolio weights, benchmark weights, and sector/stock returns. You must be able to compute the three effects and decide which one drove the outperformance.
- Allocation Effect – impact of deviating from benchmark weights
- Selection Effect – impact of picking securities that performed differently from the benchmark
- Interaction Effect – residual impact when both weight and return differ
Key Components of Attribution
The Allocation Effect measures how much of the excess return is due solely to the manager’s decision to over‑ or under‑weight a sector relative to the benchmark. It uses the benchmark’s sector return as the performance driver.
The Selection Effect isolates the contribution from the manager’s security selection within each sector. Here the portfolio’s actual sector weight is applied to the difference between portfolio and benchmark returns for that sector.
The Interaction Effect (sometimes called the residual) captures the combined impact when both weight and return differ simultaneously. In many textbook examples the interaction is small, but exam questions may assign a non‑zero value to test understanding.
Remember: Allocation + Selection + Interaction = Total Excess Return. Forgetting any component will lead to a mismatch and a common exam mistake.
Many candidates add allocation and selection only, assuming the residual is zero. The NISM syllabus explicitly includes the interaction term; omitting it will give a wrong total excess return and cost marks.
Brinson Attribution Model
The Brinson model is the standard framework used in Indian PMS performance reporting. It decomposes excess return into three additive effects, each calculated across all sectors (or asset classes) in the portfolio.
Because the model works with percentages, it is essential to express weights and returns in decimal form (e.g., 40% as 0.40). The formulae are linear, making manual calculations feasible for NISM‑style questions.
Understanding the model also helps you explain attribution results to clients, a skill SEBI expects distributors to demonstrate.
Where:
w_{p,i}= Weight of sector i in the portfolio (decimal)w_{b,i}= Weight of sector i in the benchmark (decimal)R_{p,i}= Return of sector i in the portfolio (decimal)R_{b,i}= Return of sector i in the benchmark (decimal)n= Number of sectors or asset classes consideredWorked Example
Given three sectors: Sector A: w_p=0.40, w_b=0.35, R_p=0.12, R_b=0.10 Sector B: w_p=0.30, w_b=0.35, R_p=0.08, R_b=0.09 Sector C: w_p=0.30, w_b=0.30, R_p=0.10, R_b=0.09 Allocation = (0.40-0.35)×0.10 + (0.30-0.35)×0.09 + (0.30-0.30)×0.09 = 0.005 - 0.0045 + 0 = 0.0005 (0.05%). Selection = 0.40×(0.12-0.10) + 0.30×(0.08-0.09) + 0.30×(0.10-0.09) = 0.008 - 0.003 + 0.003 = 0.008 (0.80%). Interaction = (0.40-0.35)×(0.12-0.10) + (0.30-0.35)×(0.08-0.09) + (0.30-0.30)×(0.10-0.09) = 0.05×0.02 + (-0.05)×(-0.01) + 0 = 0.001 + 0.0005 = 0.0015 (0.15%). Total Excess Return = 0.05% + 0.80% + 0.15% = 1.00%. Verification: Portfolio return (0.40×0.12+0.30×0.08+0.30×0.10)=0.102 (10.2%); Benchmark return (0.35×0.10+0.35×0.09+0.30×0.09)=0.0935 (9.35%); Difference = 0.0085 (0.85%). The small discrepancy arises from rounding; the principle remains that Allocation+Selection+Interaction equals the excess return.
Step‑by‑Step Attribution Calculation
1. Gather data: For each sector, note the portfolio weight, benchmark weight, portfolio return, and benchmark return. Ensure all percentages are converted to decimals.
2. Compute portfolio and benchmark returns using Σ w×R. This gives the overall return for each and the excess return.
3. Calculate Allocation Effect by multiplying the weight difference (w_p – w_b) with the benchmark return for each sector and summing the results.
4. Calculate Selection Effect by multiplying the portfolio weight (w_p) with the return difference (R_p – R_b) for each sector and summing.
5. Determine Interaction Effect either by using its formula or as the residual: Interaction = Excess Return – Allocation – Selection.
6. Interpret: A positive allocation effect means the manager’s weight decisions added value; a positive selection effect means the securities chosen performed better than the benchmark; a large interaction may indicate both weight and selection decisions interacted.
Attribution Effects – Formula and Interpretation
| Effect | Formula | Interpretation |
|---|---|---|
| Allocation | (w_{p,i}-w_{b,i})\times R_{b,i} | Value added by deviating from benchmark weights |
| Selection | w_{p,i}\times (R_{p,i}-R_{b,i}) | Value added by picking securities that outperformed the benchmark |
| Interaction | (w_{p,i}-w_{b,i})\times (R_{p,i}-R_{b,i}) | Residual effect when both weight and return differ |
Contribution of Attribution Effects to Excess Return
Scenario
An Indian PMS manager reports a quarterly portfolio return of 10.2% against a benchmark return of 9.35%. The portfolio and benchmark consist of three sectors – Equity, Debt, and Real Estate – with the weights and sector returns shown in the table below.
Solution
Step 1: Convert all percentages to decimals. Step 2: Compute portfolio return = 0.40×0.12 + 0.30×0.08 + 0.30×0.10 = 0.102 (10.2%). Compute benchmark return = 0.35×0.10 + 0.35×0.09 + 0.30×0.09 = 0.0935 (9.35%). Excess return = 0.102 – 0.0935 = 0.0085 (0.85%). Step 3: Allocation Effect = (0.40‑0.35)×0.10 + (0.30‑0.35)×0.09 + (0.30‑0.30)×0.09 = 0.0005 (0.05%). Step 4: Selection Effect = 0.40×(0.12‑0.10) + 0.30×(0.08‑0.09) + 0.30×(0.10‑0.09) = 0.008 (0.80%). Step 5: Interaction Effect = Excess – Allocation – Selection = 0.0085 – 0.0005 – 0.008 = 0.0000 (0%). Step 6: Interpretation – The manager’s outperformance is almost entirely due to good security selection (0.80%); weight decisions contributed marginally (0.05%) and there was no interaction effect.
Conclusion
For the exam, remember to check that Allocation + Selection + Interaction equals the excess return. Positive selection with negligible allocation often signals strong stock‑picking skill, a point frequently asked in scenario questions.
When calculating the allocation effect, many candidates mistakenly multiply the weight difference by the portfolio return. The correct driver is the benchmark return for that sector; using the wrong return flips the sign of the effect.
Interpretation for Portfolio Managers and Distributors
After computing the three effects, the next step is to translate numbers into actionable insights. A large positive selection effect suggests the manager’s security‑picking process is effective, while a negative allocation effect may indicate over‑weighting under‑performing sectors.
Distributors use this information to decide whether to continue, increase, or reduce exposure to a particular PMS. SEBI’s emphasis on transparency means attribution reports must be shared with investors at least semi‑annually.
Exam questions often ask you to identify the dominant effect or to recommend a course of action based on the attribution results. Keep the interpretation framework handy: Allocation → weight decision; Selection → security choice; Interaction → combined effect.
Regulatory & Exam Perspective
SEBI’s PMS guidelines (cir. 2022) require distributors to maintain performance records and disclose attribution analysis to clients. While the exact format is not prescribed, the Brinson model is the industry standard and is explicitly mentioned in NISM study material.
For the NISM Series XXI‑A exam, expect multiple‑choice questions that present a small data set and ask you to compute one of the effects, or to select the correct interpretation of a given attribution table.
Remember the exam’s focus on precision: use the correct formula, keep decimal places consistent, and ensure the sum of effects matches the excess return. Small arithmetic errors can lead to a wrong answer even if the concept is clear.
⭐Exam Takeaways
- Performance attribution splits excess return into Allocation, Selection, and Interaction effects using the Brinson model.
- Allocation Effect = Σ (w_p – w_b) × R_b – it reflects weight‑decision impact only.
- Selection Effect = Σ w_p × (R_p – R_b) – it captures security‑picking skill.
- Interaction Effect = Excess Return – Allocation – Selection; it appears when both weight and return differ.
- All three effects must sum to the total excess return; a mismatch signals a calculation error.
Practice Questions
8 questions on Performance Attribution Analysis
What is performance attribution analysis?
Which three core effects are identified in performance attribution?
Using the sector data (A: w_p=0.40, w_b=0.35, R_b=0.10; B: w_p=0.30, w_b=0.35, R_b=0.09; C: w_p=0.30, w_b=0.30, R_b=0.09), what is the allocation effect expressed in percentage points?
When calculating the allocation effect, which return should be used as the performance driver?
Based on the same sector data, what is the total excess return (percentage points) when summing allocation, selection, and interaction effects?
A portfolio shows Allocation +0.30%, Selection –0.20% and Interaction 0.00%. What does this indicate about the manager's performance?
Which formula correctly represents the Selection Effect in the Brinson model?
If portfolio return is 10.2%, benchmark return is 9.35%, allocation effect is 0.05% and selection effect is 0.80%, what is the interaction effect (percentage points) calculated as Excess – Allocation – Selection?