Where did the outperformance actually come from?
A portfolio beat its benchmark by +1.5 points. That single number is compatible with wildly different stories: a brilliant run of stock picking, one lucky sector bet, or good picks partly cancelled by bad positioning. Attribution takes the number apart.
Two sources, two formulas
Relative performance comes from being in different places than the benchmark, and from holding different things within those places.
Allocation effect (per sector) = (portfolio weight − benchmark weight) × (benchmark sector return − benchmark total return)
This asks: did overweighting this area help, given how the area performed relative to the whole index?
Selection effect (per sector) = portfolio weight × (portfolio sector return − benchmark sector return)
This asks: within this area, did the specific holdings beat the area's own index?
Sum both across all sectors and you have the relative performance, decomposed — exactly, with nothing left over. Note the weight in the selection term: it is the portfolio's. Some presentations use the benchmark weight instead and then need a third interaction term to make the columns add up; the two-effect version above folds that interaction into selection, sums exactly, and is what this lesson needs.
Worked example
Over one year:
- Benchmark total return: +10%
- Energy: 10% of the benchmark, returning +30%
- The portfolio held 20% in energy, and its energy holdings returned +25%
Allocation: (0.20 − 0.10) × (30% − 10%) = 0.10 × 20% = +2.00 points
Selection: 0.20 × (25% − 30%) = 0.20 × (−5%) = −1.00 point
Net contribution from energy: +1.00 point
Read what that says. Everything energy contributed came from being twice as heavy in the sector that happened to lead — and the stock picking inside that sector gave a full point back. A manager describing this year as evidence of stock-selection skill would be describing the one component that went the wrong way.
Why decomposition changes the conversation
A relative return is one claim. Attribution turns it into several testable ones, and each has a different repeatability profile.
- An allocation win is essentially one decision. It can be repeated only if the manager can repeatedly identify leading sectors — a much stronger claim than the return implies.
- A selection win spread evenly across many sectors is many small decisions, which is the breadth that the information-ratio lesson said matters.
Same +1.5, entirely different amount of evidence. This is also why attribution and the statistics of the next lesson belong together: decomposition tells you how many independent bets a record actually contains, and that number governs how much the record can prove.
Attribution describes history. It does not certify skill, does not predict the next year, and identifies nothing to buy.
In the data
The benchmark half of the grid is published: an S&P 500 fund reports its money by sector.
The portfolio half comes from each holding's own classification, and the two do not always speak the same language. Apple's record:
One scheme files Apple under Technology, the other under Information Technology, and elsewhere a fund's "Consumer Cyclicals" meets a single stock's "Consumer Cyclical". The names have to be matched by hand, one scheme throughout, before the two sides of the attribution will sum to anything.
Try it now
Pick two sectors and read the benchmark side of the grid from the fund's sector weights above. Check that each holding you assign to those sectors is classified under the same scheme as the fund's weights.
Invent plausible portfolio weights and sector returns, then compute the allocation and selection effect for each sector using the two formulas.
Sum the four numbers. Then write one sentence describing where the relative performance came from — and one more on how many separate decisions that implies.