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Mean-Variance Approximations To The Geometric Mean

Author

Listed:
  • HARRY MARKOWITZ

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

Abstract

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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    Cited by:

    1. Andreas Renard Widarto & Harjum Muharam & Sugeng Wahyudi & Irene Rini Demi Pangestuti, 2022. "ASEAN-5 and Crypto Hedge Fund: Dynamic Portfolio Approach," SAGE Open, , vol. 12(2), pages 21582440221, April.
    2. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    3. Nasim Dehghan Hardoroudi & Abolfazl Keshvari & Markku Kallio & Pekka Korhonen, 2017. "Solving cardinality constrained mean-variance portfolio problems via MILP," Annals of Operations Research, Springer, vol. 254(1), pages 47-59, July.

    More about this item

    Keywords

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

    JEL classification:

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

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