Factor return and risk attribution

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portfolio_backtester.factor_attribution provides two calculation helpers: attribute_factor_return() decomposes active return, and attribute_factor_risk() decomposes active variance. Both use caller-supplied weights, exposures, and factor inputs. They do not estimate those inputs.

Return attribution

Let w be portfolio weights, b benchmark weights, X asset exposures, and f factor returns:

active_weights       = w - b
active_exposures     = X' active_weights
factor_contributions = active_exposures * f
active_return        = portfolio_return - benchmark_return
cost_contribution    = -transaction_cost
specific_return      = active_return - sum(factor_contributions) - cost_contribution

portfolio_return is the portfolio return after transaction costs; benchmark_return must cover the same period. Pass transaction_cost as a nonnegative return amount in the same units, such as 0.0005 for 5 bps. The helper does not convert basis points or calculate returns and costs. The specific return is the residual needed to reconcile the supplied net active return with factor contributions and the separately reported cost drag.

The factor_return_attribution.v1 receipt includes active exposures, factor contributions, specific return, cost contribution, active return, and the reconciled active return. The components sum to the supplied active return.

Risk attribution

Let F be factor-return covariance and s the per-asset specific risk:

factor_variance_contribution_i = e_i * (F e)_i
specific_variance              = sum((active_weight_j * s_j)^2)
active_variance                 = sum(factor_variance_contribution) + specific_variance

The helper requires F to be symmetric and positive semidefinite. It assumes specific returns are independent across assets. Factor covariance and specific risk must use compatible periods and units. The factor_risk_attribution.v1 receipt reports factor contributions, specific variance contribution, active exposures, and active variance. It reports variance, not annualized risk.

Input and scope limits

Portfolio weights, benchmark weights, and exposure rows must contain exactly the same assets. Factor returns and both axes of the factor covariance must match the exposure columns. Inputs must be finite; specific risk cannot be negative. The helpers reject mismatched labels rather than aligning or filling missing assets and factors silently.

These functions do not estimate exposures, factor returns, covariance, or specific risk. They do not calculate Brinson allocation or selection effects. Results are arithmetic decompositions of the supplied model inputs, not causal claims about why a portfolio performed as it did.