Value-based Performance Measurement with the Attribution Matrix and the Finite Change Sensitivity Index

We present a model of performance measurement and attribution for delegated investments that summarizes the manager effect and the client effect on value creation. In particular, we introduce an innovative two-dimensional approach that, on one hand, detects the (manager and client) decision effects, measuring the impact of manager/investor choices on the overall investment performance and, on the other hand, detects the (manager and client) period effects, measuring the impact of all the (manager and client) decisions on the investment performance in a given assessment interval. As for the decision effects, the value added of an active investment portfolio is broken down in terms of the value generated by the decisions made by the manager (manager decision effect) and the value generated by the client/investor (client decision effect). As for the period effects, we quantify the impact of all the decisions made in the assessment interval on the value creation generated in a single period by the manager (manager period effect) and the client (client period effect), so that the sum of the periods' attribution values is the investment's value added. In order to accomplish the task, we employ the Finite Change Sensitivity Index (FCSI), which enables one to quantify the impact of the most influential decisions made by manager and investor, and a truncation approach which is equivalent to the well-known residual-income approach. We then combine the two attribution dimensions into an Attribution Matrix (AM). Each element of the AM provides the amount of value added generated in a given period by the decisions made by the manager or by the investor in (the same or) another period.