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Arithmetic returns for investment performance measurement

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  • Magni, Carlo Alberto

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.

Suggested Citation

  • Magni, Carlo Alberto, 2014. "Arithmetic returns for investment performance measurement," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 291-300.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:291-300
    DOI: 10.1016/j.insmatheco.2014.02.005
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    References listed on IDEAS

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    1. Kenneth B. Gray, Jr. & Robert B. K. Dewar, 1971. "Axiomatic Characterization of the Time-Weighted Rate of Return," Management Science, INFORMS, vol. 18(2), pages 32-35, October.
    2. Magni, Carlo Alberto, 2013. "Generalized Makeham’s formula and economic profitability," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 747-756.
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    Citations

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    Cited by:

    1. Magni, Carlo Alberto, 2016. "Capital depreciation and the underdetermination of rate of return: A unifying perspective," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 54-79.
    2. Magni, Carlo Alberto & Marchioni, Andrea, 2019. "Performance measurement and decomposition of value added," MPRA Paper 95258, University Library of Munich, Germany.
    3. Magni, Carlo Alberto & Marchioni, Andrea & Baschieri, Davide, 2023. "The Attribution Matrix and the joint use of Finite Change Sensitivity Index and Residual Income for value-based performance measurement," European Journal of Operational Research, Elsevier, vol. 306(2), pages 872-892.
    4. Carlo Alberto Magni & Andrea Marchioni, 2022. "Performance attribution, time-weighted rate of return, and clean finite change sensitivity index," Journal of Asset Management, Palgrave Macmillan, vol. 23(1), pages 62-72, February.
    5. Carbajal-De-Nova, Carolina & Venegas-Martínez, Francisco, 2019. "On the paradigm shift of asset pricing models, before and after the global financial crisis: a literature review," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 15(29), pages 7-38, Primer se.
    6. Guzzetti, Marco, 2020. "Approximating the time-weighted return: The case of flows at unknown time," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 25-34.

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    1. Carlo Alberto Magni & Andrea Marchioni, 2022. "Performance attribution, time-weighted rate of return, and clean finite change sensitivity index," Journal of Asset Management, Palgrave Macmillan, vol. 23(1), pages 62-72, February.
    2. Magni, Carlo Alberto, 2016. "Capital depreciation and the underdetermination of rate of return: A unifying perspective," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 54-79.
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    9. Guzzetti, Marco, 2020. "Approximating the time-weighted return: The case of flows at unknown time," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 25-34.
    10. Magni, Carlo Alberto & Veronese, Piero & Graziani, Rebecca, 2017. "Chisini means and rational decision making: Equivalence of investment criteria," MPRA Paper 81532, University Library of Munich, Germany.

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