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Geometric Mean Approximations

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  • Jean, William H.
  • Helms, Billy P.

Abstract

In 1959, Henry Lataná [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the Latané approximation, as well as a set of other approximations to the geometric mean based on moments, and concluded that the Latane formula yielded a quite accurate approximation to the geometric mean. In Jean's 1980 paper [1] relating the geometric mean model to stochastic dominance models, the infinite series representation of the geometric mean used suggests a more accurate approximation with moments of the geometric mean than that contained in the earlier papers may be possible. Various forms of that series expressed in alternate-origin moments are tested empirically below, and the results confirm that this later series does yield the greatest accuracy of the three approaches.

Suggested Citation

  • Jean, William H. & Helms, Billy P., 1983. "Geometric Mean Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(3), pages 287-293, September.
    • Handle: RePEc:cup:jfinqa:v:18:y:1983:i:03:p:287-293_01
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    Cited by:

    1. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    2. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.

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