Arithmetic Returns for Investment Performance Measurement

23 Pages Posted: 10 Jun 2012 Last revised: 23 Apr 2014

See all articles by Carlo Alberto Magni

Carlo Alberto Magni

Università degli studi di Modena e Reggio Emilia (UNIMORE) - School of Doctorate E4E (Engineering for Economics-Economics for Engineering)

Abstract

This paper introduces new money-weighted metrics for investment performance analysis, based on arithmetic means of holding period rates weighted by the investment’s market values. This approach generates rates of return which measure a fund’s or portfolio’s performance and a fund manager’s performance. It also enables to show that the Internal Rate of Return (IRR) is a weighted mean of holding period rates associated with interim values which differ from market values, so that value additivity is violated. The manager’s Arithmetic Internal Rate of Return (AIRR) is shown to be the true period equivalent of the cumulative Time Weighted Rate of Return (TWRR), whereas the period TWRR (a geometric return) provides a different ranking. The method is easily generalized for coping with varying benchmark rates. We also cope with the practical problem of estimating interim values whenever they are not available.

Keywords: performance measurement, AIRR, value added, internal rate of return, time-weighted rate of return

JEL Classification: G00, G10, G11, G12, G31

Suggested Citation

Magni, Carlo Alberto, Arithmetic Returns for Investment Performance Measurement. Insurance: Mathematics and Economics, 2014, 55, 291-300., Available at SSRN: https://ssrn.com/abstract=2080775 or http://dx.doi.org/10.2139/ssrn.2080775

Carlo Alberto Magni (Contact Author)

Università degli studi di Modena e Reggio Emilia (UNIMORE) - School of Doctorate E4E (Engineering for Economics-Economics for Engineering) ( email )

Italy

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