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Risk-Return Analysis: The Theory and Practice of Rational Investing (Volume One) by Kenneth Blay, Harry Markowitz

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3MEAN-VARIANCE APPROXIMATIONS TO THE GEOMETRIC MEAN

INTRODUCTION

Summaries of return series typically report their “geometric mean” return as well as their arithmetic mean. In general, if A1, …, An are n nonnegative numbers, their geometric mean is defined as the nth root of their product,

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This is to be distinguished from their arithmetic mean, or ordinary average,

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The so-called geometric mean return in financial summaries is not literally the geometric mean of the return series r1, r2, …, rT. (It couldn’t be, since returns are sometimes negative.) ...

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