Introducing Aggregate Return on Investment as a Solution to the Contradiction Between Some PME Metrics and IRR

The Index Comparison Method (ICM) is a well-known approach for measuring a Private Equity Investment's (PEI) performance. It is based on the construction of a benchmark portfolio that, each period, earns the index return. This generates a time series of interim net asset values that leads to a terminal NAV, from which an Internal Rate of Return is computed. However, the IRR is itself necessarily associated with its own time series of built-in NAVs, to which the IRR is applied. And, unfortunately, this series of values will be different from the aforementioned benchmark portfolio's NAVs. As a result, the ICM approach rests on two contradictory sets of values, thereby rendering it illegitimate. Furthermore, the ICM approach does not preserve additivity of the rates of return, and, in principle, might even generate multiple IRRs. This paper presents the Aggregate Return on Investment (AROI), a metric which (i) uses one consistent time series of NAVs (the benchmark portfolio's true values) (ii) preserves additivity, and (iii) does not incur the problem of multiple solutions