What is attribution analysis
– Attribution analysis (also called performance or return attribution) is a method that breaks down why a portfolio produced the returns it did versus a chosen benchmark. It isolates the effects of an investor’s asset-allocation choices, security selections, investment style, and market-timing decisions to show where excess return (alpha) came from.
Key definitions (first use)
– Benchmark: a market index or combination of indices used as the yardstick for measuring performance (e.g., S&P 500, Nasdaq Composite).
– Asset class: a category of investments (for example, equities, fixed income, real estate); can be narrowed to geography or sector (e.g., U.S. technology stocks, European corporate bonds).
– Investment style: a manager’s consistent approach, such as large-cap vs. small-cap or value vs. growth.
– Alpha: the portion of return above what would be expected from the benchmark; commonly interpreted as “excess return.”
– Returns-based style analysis (RBSA): a technique that infers a fund’s style by finding a weighted mix of indices whose historical returns best match the fund’s returns. Bill Sharpe developed an RBSA approach that uses quadratic optimization to solve for the best-fitting index weights.
Step-by-step mechanics (how an attribution analysis is typically done)
1. Define the asset universe and classify holdings. Decide which asset classes, geographic markets, and sectors are relevant for the manager’s strategy.
2. Select or construct appropriate benchmarks. Use single indices or a custom blend that reflects the identified asset mix. RBSA can be used to derive a blended benchmark from multiple indices.
3. Measure portfolio and benchmark returns over the same period. Use total return (including dividends/interest) and the same timing conventions.
4. Decompose the active return (portfolio return minus benchmark return) into components, typically:
– Allocation effect (over/underweighting asset classes or sectors),
– Selection effect (picking securities within a sector), and
– Timing effect (benefits/costs from changing weights through time).
Some frameworks also include an “interaction” term that arises when allocation and selection effects occur together.
5. Attribute alpha. Quantify how much of the excess return is explained by each component (allocation, selection, timing). If desired, build sub-benchmarks to isolate sector vs. stock-selection contributions.
6. Interpret results and note uncertainty. Pay attention to whether timing results are statistically significant or plausibly due to luck.
Short checklist for running a basic attribution analysis
– [ ] Define universe and time horizon.
– [ ] Choose relevant indices for potential benchmarks.
– [ ] Calculate portfolio and index returns (same frequency and total return convention).
– [ ] Apply RBSA or construct a custom blended benchmark if manager style is mixed.
– [ ] Decompose active return into allocation, selection, and timing (and interaction if used).
– [ ] Review statistical significance and consider randomness, especially for timing effects.
– [ ] Document assumptions (currency, rebalancing rules, reconstitution dates).
Worked numeric example (simple, illustrative)
Assumptions:
– Portfolio total return over year: 18%
– Custom blended benchmark return for same period: 5%
– Active return (alpha) = 18% − 5% = 13%
Suppose attribution analysis assigns the 13% active return to:
– Sector allocation effect: +4%
– Market timing effect: +2%
– Stock selection effect: remainder
Calculation:
– Stock selection alpha = Active return − (Sector allocation + Timing)
– Stock selection alpha = 13% − (4% + 2%) = 7%
Interpretation: In this simple breakdown, the manager’s sector weightings added 4 percentage points, timing decisions added 2 points, and individual stock choices contributed 7 points toward the 13-point outperformance over the benchmark.
Practical notes and limitations
– Constructing the “right” benchmark is critical. A mis-specified benchmark will misattribute sources of return. RBSA helps when style is mixed or unclear.
– Market timing is the hardest component to measure reliably; some timing gains can be due to luck rather than skill. As a result, many practitioners place more