The Variance Drain and Jensen's Inequality

Robert Becker

No 2012-004, CAEPR Working Papers from Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington

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.

Pages: 14 pages
Date: 2012-03
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