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Performance Measurement and Decomposition of Value Added

In this paper, we benchmark an investment actively managed (e.g., fund, portfolio) against a reference portfolio passively managed replicating the investment's cash flows in order to measure the value added by the active investment and decompose it according to the influence of the investment choices (i.e., selection and allocation of assets) made in the various periods. The active investment choices are reflected in the investment's returns as opposed to the benchmark returns earned by the passive strategy. We precisely quantify the impact of the holding period rates on the value added and rank them accordingly, in order to identify the most (and the least) influential ones. The analysis is performed by applying the Finite Change Sensitivity Index (FCSI) method (Borgonovo 2010a, 2010b), a recently-conceived technique of sensitivity analysis, which we refine by means of a duplication-clearing procedure which allows a perfect (i.e., with no residue) decomposition of the value added. We conduct the analysis for a given contribution-and-distribution policy, characterized by a fixed sequence of deposits and withdrawals. We show that, if the contribution-and-distribution policy changes, the effect of the investment choices made in the various periods on the value added changes as well.