Performance attribution, time-weighted rate of return, and clean finite change sensitivity index

We propose an innovative methodology for decomposing the value added generated by a money manager within a given assessment interval into the contributions of the manager’s investment decisions made in the various periods, in order to identify the most (and the least) impactful period decisions. To this end, we benchmark an actively-managed investment against a reference portfolio replicating the client’s contributions and distributions and earning the benchmark returns. We apply the Clean Finite Change Sensitivity Index method (Borgonovo in Eur J Oper Res 200:127–138, 2010a, Risk Anal 30(3):385–399, 2010b; Magni et al. in J Oper Res Soc 71(12):1940–1958, 2020) to the investment’s value added in order to obtain a complete decomposition of it into the contributions of the investment decisions made in the various periods; we rank the period decisions according to their contributions and 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, which testifies of the interaction between the manager’s decisions and the client’s decisions, the former affecting the financial efficiency and latter affecting the investment scale. In particular, neutralizing the contributions and distributions (and, therefore, the investment scale), we show that the Time-Weighted Rate of Return (TWRR) can be arithmetically obtained from the value added and can be decomposed into the same period contributions of the value added, thereby providing a reconciliation between the value added notion and the TWRR.