Introducing Excess Return on Time-scaled Contributions : An Intuitive Return Measure and New Solution to The IRR and PME Problem

While the internal rate of return (IRR) remains to be widely used despite its well-documented flaws, considerable progress has been made in the literature on the search for a proper measure of performance of illiquid investments. Most recently, two general approaches have been proposed, namely the Average Internal Rate of Return (AIRR) approach and the Aggregate Return on Investment (AROI) approach, and the following cash flow based metrics have appeared in the literature: the economic AIRR, the Index Comparison Method (ICM) based AROI and the Direct Alpha method. Motivated by the AIRR approach, we present a new cash flow based metric, Excess Return on Time-scaled Contributions (ERTC), that is free from all of the IRR flaws and represents a solution to the public market equivalent (PME) problem. ERTC is intuitively defined as the ratio of Net Present Value to the aggregate discounted net contributions scaled by the length of time the net contribution is relevant to the investment. We show that ERTC can be obtained as a special case of the continuous version of AIRR with a ICM based assumption on capital growth. Moreover, as part of the definition of ERTC, we introduce a decomposition procedure that can also be adapted to help ensure value consistency (ie, value additivity and consistency with known market values) for all cash flow based AIRR or AROI metrics