Six manuscripts on the arithmetic linking problem: single-period attribution effects add up, but compounded returns don't. The work moves from production methods that make reconciliation a hard constraint to axiomatic results on what any linking method can and cannot do.
For twenty-five years the industry has answered the linking problem with competing formulas: Cariño, Menchero, Frongello and their variants. This program asks a different question. Which properties does a reporting system actually need, and what do those properties force a linking method to be?
Reconciliation to cumulative active return should be a hard constraint, never a by-product. Preserving the economic story (signs, the dominant driver, the top contributors) belongs in an explicit, auditable objective that a performance team can tune and defend.
Aggregation consistency forces every admissible linker into one common-coefficient form. Temporal associativity is exactly a coefficient factorization law. These axioms place Cariño and both Frongello directions on one parameter line and show what symmetry selects.
Whether a system can safely compress a closed period depends on the method. Some linkers are exact with a small fixed state; others need state that grows with the horizon. Under the usual common-coefficient design, no linker has every desirable property at once.
The practical question is not which formula to adopt. It is what information your attribution architecture must retain, and on what principle the remaining freedom is resolved.
For performance and reporting teams, the LD and HLD frameworks provide convex-optimization linking that reconciles exactly at every level of a reporting hierarchy, keeps parent–child sums coherent by construction, and makes the trade-off between reconciliation and interpretation visible to reviewers and auditors.
For methodologists, the axiomatic papers characterize the space of linkers. Reduced-form methods that see only aggregate effects cannot be defined everywhere. Keeping the return path removes that obstruction, and the Aumann–Shapley value of the compounding function emerges as the principled resolution, backed by the cost-sharing literature.
For system architects, associativity turns out to be an information-sufficiency condition. That gives a concrete test of whether storing period summaries and discarding raw history is safe for a given method, under appends and under restatements.
Each entry shows page one of the manuscript, an executive overview, and the findings in the order the paper develops them. Full manuscripts are shared on request.
Adam B. Soto works at the intersection of investment performance measurement and the platforms that produce it. His career has centered on BlackRock Aladdin implementations and performance transformation for asset managers.
This research grew out of a recurring production problem: linked attribution reports that reconcile on paper but lose the story, or tell the story but fail to tie out. The program pairs methods built for production with proofs of what is and isn't possible.
Previews show page one only. For a full manuscript, a reference implementation conversation, speaking or collaboration, reach out directly.