Sensitivity, Precision, and Linear Aggregation of Signals for Performance Evaluation

Several accounting and other signals generally are available for the construction of a managerial performance evaluation measure on which an optimal compensation contract is based. A focus on performance measures that are linear aggregated enables the determination of the relative weights on the individual signals in the optimal linear aggregate, since these weights are invariant for all realizations of the signals. The weights are interpreted in terms of statistical characteristics of the joint distribution of the signals. The performance evaluation measure based on basic signals is distinguished from the compensation schedule based on the evaluation measure. An implication of this analysis is that evaluating the performance of a profit center manager on the basis of a pure profit number will be optimal only if the sensitivity times precision of revenue and costs is equal. In addition, it is optimal to include noncontrollable corporate overhead expenses in the construction of the performance evaluation measure if the corporate overheads are correlated with controllable divisional profits.