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The Variance Drain and Jensen's Inequality

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  • Robert Becker

    () (Indiana University)

Abstract

The well-known approximation of the difference between the arithmetic average and geometric average returns as one-half of the variance of the underlying returns is reexamined using Jensen’s Inequality. The ”defect” in Jensen’s Inequality, is given an exlicit formula in terms of the variance following some ideas put forward by Holder. A new form of the AM-GM Inequality follows and is is applied to financial returns. Both exact, and approximate relations between the arithmetic average, geometric average, and variance of returns are discussed. The mathematical formulation of these relations are free of distributional assumptions governing the underlying returns process.

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File URL: http://www.iub.edu/~caepr/RePEc/PDF/2012/CAEPR2012-004.pdf
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Bibliographic Info

Paper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2012-004.

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Length: 14 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:inu:caeprp:2012-004

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  1. Hirshleifer,Jack & Riley,John G., 1992. "The Analytics of Uncertainty and Information," Cambridge Books, Cambridge University Press, number 9780521283694.
  2. Goetzmann, William N. & Ibbotson, Roger G., 2006. "The Equity Risk Premium: Essays and Explorations," OUP Catalogue, Oxford University Press, number 9780195148145, September.
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