By Arizmic LLC4 min readPublished 2026-08-10Last reviewed 2026-07-28

Portfolio attribution, correlation, and risk

Explain a portfolio result through contribution, interaction, concentration, and changing dependence.

A portfolio result is a set of interacting contributors

Portfolio attribution explains where return and risk came from. It separates the combined headline into component contributions, allocation effects, interactions, costs, and dependence.

A strategy with the highest standalone return may contribute little because it received a small weight. A low-return hedge may be valuable because it gains during portfolio drawdowns. A component with equal capital can dominate risk if its volatility and correlation are high.

Attribution is not one universal formula. The method must match the portfolio construction and the question being asked.

Return contribution starts with weight and component return

For a simple period with beginning weights $w_i$ and component returns $r_i$ , portfolio return is approximately:

r_p = \sum_i w_i r_i

The term $w_i r_i$ is the component’s arithmetic contribution for that period under the stated convention. Rebalancing, cash flows, derivatives, currency, and nonlinear payoffs can require more detailed treatment.

Contribution answers “how many return points came from this component?” It does not answer whether the component was efficient or diversified risk.

Illustrative example. Suppose Strategy A begins the period at a 60% weight and returns 3%, while Strategy B begins at a 40% weight and returns −1%. Their arithmetic contributions are:

Sleeve	Beginning weight	Period return	Return contribution
Strategy A	60%	3%	+1.8 percentage points
Strategy B	40%	−1%	−0.4 percentage points
Portfolio	100%	—	+1.4%

Strategy A contributed more because both its weight and return were larger. This one-period arithmetic decomposition is additive; it does not by itself describe risk contribution, compounding across periods, or what would happen if either sleeve were removed.

Allocation and selection are contextual

Traditional performance attribution often separates:

allocation — the effect of weighting categories differently from a benchmark;
selection — the effect of choosing components that performed differently within categories;
interaction — the combined effect of both decisions.

For a multi-strategy portfolio, more useful categories may be strategy family, asset class, market, direction, or risk bucket. The taxonomy should reflect actual decisions. Calling every difference “alpha” prevents diagnosis.

Risk contribution includes covariance

A component’s standalone volatility is not its portfolio risk contribution. Risk depends on how it co-moves with everything else.

A volatile strategy with low or negative covariance can reduce total portfolio variance. A modest-volatility strategy that moves with the largest sleeve can add substantial risk. Marginal and component risk contribution use the covariance matrix and current weights to describe this interaction.

Because covariance is estimated, risk contribution is also uncertain. Read it across windows and stress assumptions, not as a permanent property.

Capital weight and risk contribution can disagree

Illustrative example. Consider this portfolio:

Sleeve	Capital weight	Standalone volatility	Relationship to others
Equity trend	40%	12%	Positively related to equity factor
Equity factor	40%	10%	Positively related to equity trend
Rates trend	20%	14%	Low ordinary correlation

The rates sleeve has the smallest capital weight and highest standalone volatility. It may still reduce total risk if it offsets the equity sleeves. The two 40% equity sleeves can dominate drawdown because their mechanisms and markets overlap.

Equal capital is therefore not equal risk, and a low full-sample correlation does not guarantee protection during a common deleveraging event.

Read attribution through time

Full-sample totals can hide regime changes. Inspect:

contribution by month, quarter, or regime;
contribution during the largest portfolio drawdowns;
cumulative component contribution;
weight and exposure history;
turnover and cost by component;
correlation and covariance changes;
concentration in one instrument, factor, or event.

A component that contributes positively overall but worsens every major drawdown may not provide the diversification its label suggests.

Counterfactuals answer a different question

Attribution describes what happened under the realized portfolio. A counterfactual asks what would have happened under another declared allocation or without one component.

Removing a sleeve changes weights, shared capital, rebalancing, and sometimes strategy behavior. A valid counterfactual recomputes those interactions rather than merely subtracting the sleeve’s profit and loss (P&L) from the final line.

Costs and capacity belong to the contributor

Portfolio-level net return can hide a sleeve whose gross contribution is consumed by turnover or impact. Attribute costs to the decisions that caused them where the data permits.

Shared instruments create additional interaction. Two strategies trading the same market in opposite directions may net exposure and turnover. Trading together may increase impact. The portfolio result should not assume component costs add independently when execution is shared.

Common attribution mistakes

Calling capital weight risk contribution.
Reporting only full-sample contribution.
Ignoring covariance and drawdown overlap.
Using categories that do not correspond to portfolio decisions.
Treating a low-return hedge as useless without examining stress periods.
Subtracting a sleeve’s P&L as if removal would leave everything else unchanged.
Allocating all costs at the portfolio level and losing the source.
Treating an estimated covariance matrix as fixed.