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