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Generalized Makeham’s formula and economic profitability

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  • Magni, Carlo Alberto

Abstract

This paper generalizes Makeham’s formula, allowing for varying interest rates and for a non-flat structure of valuation rates. An average interest rate (AIR) is introduced, as well as an average valuation rate (AVR), both of which exist and are unique for any asset. They can be computed either as principal-weighted arithmetic means or as interest-weighted harmonic means of period rates. Economic profitability of an asset or a portfolio of assets is captured by the spread between AIR and AVR, which has the same sign as the Net Present Value. This makes (i) AIR a more reliable tool for valuation and decision than the venerable Internal Rate of Return, and (ii) AVR a natural generalization of the cost-of-capital notion.

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  • Magni, Carlo Alberto, 2013. "Generalized Makeham’s formula and economic profitability," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 747-756.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:747-756
    DOI: 10.1016/j.insmatheco.2013.09.014
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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, 2014. "Arithmetic returns for investment performance measurement," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 291-300.
    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.

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    More about this item

    Keywords

    Makeham’s formula; Net present value; Average interest rate;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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