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Mean-Variance Approximations To The Geometric Mean



    () (Rady School of Management, University of California, San Diego, USA)


This paper uses two databases to test the ability of six functions of arithmetic mean and variance to approximate geometric mean return or, equivalently, Bernoulli's expected log utility. The two databases are: (1) a database of returns on frequently used asset classes, and (2) that of real returns on the equity markets of sixteen countries, 1900–2000. Three of the functions of arithmetic mean and variance do quite well, even for return series with large losses. The other three do less well.

Suggested Citation

  • Harry Markowitz, 2012. "Mean-Variance Approximations To The Geometric Mean," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-30.
  • Handle: RePEc:wsi:afexxx:v:07:y:2012:i:01:n:s2010495212500017
    DOI: 10.1142/S2010495212500017

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    1. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0201-0 is not listed on IDEAS
    2. repec:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2447-x is not listed on IDEAS

    More about this item


    Mean-variance analysis; geometric mean; expected utility; logarithmic utility; mean-variance approximations; asset class returns; twentieth century equity returns; JEL Classification: G11;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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