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Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

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  • Michal Dvořák

Abstract

The choice of averaging method has considerable impact on the average yield of a financial variable. Usually, geometric average is preferred, though dissenting opinions exist. Here it is shown that the problem has a consistent solution, which is called the horizon-consistent average. It is shown why geometric and arithmetic average calculations are almost always biased. When using company valuation's most common SP500 dataset by Ibbotson Associates for 1928-2012 and the recommended 10-year forecasting horizon, consistent with the 10-year government securities in a CAPM model, the arithmetic average is severely flawed. On the other hand, the geometric average for similar horizons does not deviate much from the horizon-consistent average.

Suggested Citation

  • Michal Dvořák, 2016. "Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average," Prague Economic Papers, Prague University of Economics and Business, vol. 2016(3), pages 335-353.
    • Handle: RePEc:prg:jnlpep:v:2016:y:2016:i:3:id:563:p:335-353
    DOI: 10.18267/j.pep.563
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    References listed on IDEAS

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    1. Dawit Alemu Bemerew, 1999. "Cointegration between stock market indices: the case of the slovak and czech stock price indices," Prague Economic Papers, Prague University of Economics and Business, vol. 1999(1).
    2. Daniel C. Indro & Wayne Y. Lee, 1997. "Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia," Financial Management, Financial Management Association, vol. 26(4), Winter.
    3. Alenka KAVKLER & Mejra FESTIC, 2011. "A Tree-Based Approach to Modelling Stock Exchange Index Returns in EU Countries," Ege Academic Review, Ege University Faculty of Economics and Administrative Sciences, vol. 11(Special I), pages 1-8.
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    More about this item

    Keywords

    yield; risk premium; historical yield; geometric average; arithmetic average;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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