Prague Economic Papers 2016, 25(3):335-353 | DOI: 10.18267/j.pep.563

Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

Michal Dvořák
Faculty of Finance and Accounting, University of Economics, Prague, Department of Monetary Theory and Policy, and Czech National Bank, Czech Republic (michal@michaldvorak.eu).

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.

Keywords: yield, risk premium, historical yield, geometric average, arithmetic average
JEL classification: G1, G32

Published: January 1, 2016  Show citation

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Dvořák, M. (2016). Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average. Prague Economic Papers25(3), 335-353. doi: 10.18267/j.pep.563
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References

  1. Bemerew, D. A. (1999), "Cointegration between Stock Market Indices: The Case of the Slovak and Czech Stock Price Indices." Prague Economic Papers, No. 1.
  2. Damodaran, A. (2013), "Annual Returns on Stock, T. Bonds and T. Bills: 1928 - Current." Stern School of Business. New York University. Available from: http://people.stern.nyu.edu/adamodar/New_Home_Page/datafile/histretSP.html
  3. Damodaran. A. (2013a), "Estimating Risk Parameters." Stern School of Business. New York University. Available from: http://people.stern.nyu.edu/adamodar/pdfiles/papers/beta.pdf.
  4. Damodaran. A. (2013b), "Equity Risk Premiums (ERP): Determinants. Estimation and Implications - The 2013 Edition." Stern School of Business. New York University. Available from: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2238064 Go to original source...
  5. Damodaran. A. (2008), "What Is the Riskfree Rate? A Search for the Basic Building Block." Stern School of Business. New York University. Available from: http://people.stern.nyu.edu/adamodar/pdfiles/papers/riskfreerate.pdf Go to original source...
  6. Dariusz, F. (2013), "Returns and Persistence of Investment Fund Performance in the Czech Republic." Prague Economic Papers, Vol. 22, No. 3, pp. 324-342. Go to original source...
  7. Fama, E. F., French, K. R. (1988), "Permanent and Transitory Components of Stock Prices." Journal of Political Economy, Vol. 96, pp. 246-273. Go to original source...
  8. Indro, D. C., Lee, W. Y. (1997), "Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia." Financial Management, Vol. 26, No. 4, pp. 81-90, http://dx.doi.org/10.2307/3666130 Go to original source...
  9. Kavker, A., Festic, M. (2011), "Modelling Stock Exchange Index Returns in Different GDP Growth Regimes." Prague Economic Papers, Vol. 20, No. 1, pp. 3-22. Go to original source...
  10. Mařík, M., et al. (2011), Metody oceňování podniku pro pokročilé: Hlubší pohled na vybrané problémy. Prague: Ekopress.
  11. Trešl, J. (1999), "Prague Stock Exchange: Sectorial Indices Development in 1997." Prague Economic Papers, Vol. 8, No. 1. Go to original source...
  12. Trešl, J., Blatná, D. (2007), "Dynamic Analysis of Selected European Stock Markets." Prague Economic Papers, Vol. 16, No. 4, pp. 291-302. Go to original source...
  13. Veselý, J. (2004), Základy matematické analýzy. První díl. Prague: Matfyzpress.

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