The Attribution Matrix and the joint use of Finite Change Sensitivity Index and Residual Income for value-based performance measurement

Abstract

We present a model of performance measurement and attribution for delegated investments. We introduce an innovative two-dimensional approach that, on one hand, detects the (manager and client) decision effects, measuring the impact on the overall investment performance of the choices made by manager and client in a given period and, on the other hand, detects the (manager and client) period effects, measuring the impact on the period investment performance generated by the entire set of decisions made by manager and client. To accomplish the task, we employ two techniques of analysis and a three-step procedure: we first use the Finite Change Sensitivity Index (FCSI) for measuring the decision effects (step 1); then, we use the Residual Income (RI) approach for measuring the period effects (step 2); finally, we combine the two attribution dimensions into an Attribution Matrix (AM) (step 3) which contains the attribution values. An attribution value 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. We apply the AM to an Italian fund, “Anima Italia A”, between 2013 and 2020.