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The Variance Drain and Jensen's Inequality

Robert A. Becker

Indiana University Bloomington - Department of Economics

March 19, 2012

CAEPR Working Paper No. 2012-004

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.

Number of Pages in PDF File: 14

Keywords: AM-GM Inequality, variance, Jensen's Inequality, Holder's Defect

JEL Classification: G00, G10, C80

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Date posted: March 24, 2012 ; Last revised: December 18, 2015

Suggested Citation

Becker, Robert A., The Variance Drain and Jensen's Inequality (March 19, 2012). CAEPR Working Paper No. 2012-004. Available at SSRN: http://ssrn.com/abstract=2027471 or http://dx.doi.org/10.2139/ssrn.2027471

Contact Information

Robert A. Becker (Contact Author)
Indiana University Bloomington - Department of Economics ( email )
Wylie Hall
Bloomington, IN 47405-6620
United States
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