Performance Attribution: the Harsanyi Method

We introduce a general principle-based approach to performance attribution. Our framework defines a performance attribution problem by incorporating decision makers, feasible actions capturing ex-post realizations, benchmarks, and a general return function. We propose the Harsanyi attribution function, rooted in cooperative game theory, to allocate excess returns among all possible teams of decision makers. Attributions to coalitions provide a full description of attributions to single decision makers as well as team interaction effects resulting from the joint effects of multiple decision makers, thereby breaking down performance into a full chart of mutual interactions. We characterize the Harsanyi attribution function axiomatically and prove that it is the unique coalition attribution method satisfying efficiency, outsider independence, and null contribution. Efficiency requires that the full excess return should be attributed. Outsider independence means that a team's attribution remains unaffected by the actions of any external decision maker. Null contribution ensures that a team containing a decision maker who selects the benchmark action gets zero attribution. To enhance computational efficiency, we establish three key theorems that significantly reduce computational complexity and improve practical implementation. Finally, we prove that the Harsanyi method is compatible with respect to aggregation of decisions, in the sense that if the decisions of a team are transferred to a single decision maker, this will inherit exactly the sum of the attributions related to the team's members.