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Performance attribution

A reconciled decomposition of absolute or active return into decisions represented by a model, distinct from measurement, appraisal and causal proof of skill.

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Who this is for — Readers reconciling return with decisions represented by the process—allocation, selection, factors, instruments, costs or operations—without automatically assigning causality or skill.

Performance attribution decomposes a result into components defined by a model. It starts from coherent returns, weights, classifications and a benchmark and ends with effects that must reconcile to the total within an explained residual.

It differs from performance measurement, which calculates return; attribution, which attempts to explain how it was earned; appraisal, which evaluates process quality and possible skill; and risk attribution, which decomposes risk rather than return. An accounting decomposition can be exact without proving that a decision caused the outcome or is repeatable.

Performance attribution: from benchmark to portfolio Allocation, selection and interaction depend on the chosen attribution model Performance attribution: from benchmark to portfolio Allocation, selection and interaction depend on the chosen attribution model Rₚ − R_b = allocation effect + selection effect + interaction benchmarkallocationselectioninteractionportfolio Classification Sectors, countries or factors must bedefined before calculation. Effects Each formula explicitly assigns weightsand returns to components. Multi-period linking Arithmetic effects require a linkingmethod through time. Cyclepedia · educational diagram: state conventions, period and data
Every bar belongs to a convention: model, classification and linking determine how active return is distributed.

Requirements before choosing a model

Attribution needs aligned portfolio and benchmark currency and period; compatible price or total returns; opening weights or a stated timing rule; mutually consistent classifications; explicit treatment of corporate actions, cash, derivatives and hedges; cost, fee and tax treatment; reconciled transactions and valuations; and independently verified total returns.

If the benchmark is wrong, a perfectly balanced attribution explains a difference to an unsuitable reference. If portfolio and index classifications do not align, allocation and selection can contain mapping residuals.

One-period Brinson model

For segment i, let wᵢ and Wᵢ be portfolio and benchmark weights, rᵢ and bᵢ their segment returns, and B total benchmark return. One Brinson–Hood–Beebower (BHB) formulation is:

Allocationᵢ = (wᵢ − Wᵢ) × bᵢ
Selectionᵢ = Wᵢ × (rᵢ − bᵢ)
Interactionᵢ = (wᵢ − Wᵢ) × (rᵢ − bᵢ)

Brinson–Fachler changes allocation to:

Allocation_BF,ᵢ = (wᵢ − Wᵢ) × (bᵢ − B)

The variants are not mistakes; they distribute return around different references. A report must name BHB or Brinson–Fachler and explain how interaction is treated.

Interpreting the effects

Allocation compares segment weights with the benchmark. Under BF, overweighting a segment that beats the total benchmark contributes positively, all else equal. Selection compares portfolio and benchmark return within a segment under the displayed benchmark-weight convention. Interaction is the joint effect of active weight and relative segment return. Some reports show it separately; others combine it with allocation or selection.

Not every process makes sector–security decisions. Fixed-income portfolios may need curve and spread effects, quantitative portfolios factor models, option portfolios delta and volatility effects, and global mandates currency overlays. Applying BHB to arbitrary categories can produce readable numbers that do not represent actual decisions.

BHB example

One segment has portfolio weight 60%, benchmark weight 50%, portfolio return 8% and benchmark segment return 6%:

Allocation = (0.60−0.50)×0.06 = 0.60%
Selection = 0.50×(0.08−0.06) = 1.00%
Interaction = (0.60−0.50)×(0.08−0.06) = 0.20%

The segment contributes 1.80% under this convention. Full reconciliation requires every segment, including cash, on the same return basis. BF would also require total benchmark return B and produce a different allocation effect.

Multiple periods and linking

One-period arithmetic effects do not simply add across periods when returns compound. Multi-period attribution selects a linking or smoothing method that reconciles compound return, preserves signs and proportions where possible, handles extreme periods and documents residuals and chronology.

No method should be implicit. Summing monthly effects need not equal annual active return; geometrically linking each component need not remain additive. Attribution frequency and performance-measurement frequency must be coherent.

Returns, holdings or transactions

CFA Institute distinguishes returns-based attribution, which infers drivers from return series; holdings-based attribution, which uses position snapshots; and transactions-based attribution, which incorporates positions and trades. The first needs less data but may infer an average exposure that never existed. The second can miss activity between snapshots. The third can better explain timing and cost but requires complete reconciled data.

A trading journal may decompose P&L by setup, regime, time of day, execution and plan adherence. This process attribution can support governance, but it is not BHB unless it actually uses the model's weights and benchmark.

Costs and residuals

Gross attribution can show apparent value that disappears after commissions, spread, impact, slippage, funding, borrow, management and performance fees, tax, FX differences, errors and transition cost. Costs can be a separate category or embedded in returns, but the choice must prevent double counting.

A residual should not be silently allocated away. It may reveal timing, rounding, classification, missing-data or formula mismatches.

What attribution does not prove

Positive selection can come from an omitted factor; favourable allocation can be luck; interaction depends on convention. Skill claims require stability, predefined hypotheses, risk taken, cost, significance, out-of-sample evidence and an understood process.

The Brinson pension-fund research has often been overgeneralised. A result about time-series variation in specific samples is not the universal claim that asset allocation determines one fixed percentage of return.

Common error — Reading a positive selection effect as causal proof of stock-picking skill. The model allocates an accounting difference under its chosen benchmark and classification; omitted factors and luck remain possible.

Publication checklist

State the model and variant; complete benchmark; classification and mapping; weights and timing; total/price basis, currency and FX; gross/net treatment; frequency and multi-period linking; cash, derivatives and residual handling; reconciliation to total return; and separation from appraisal.

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