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Note--On the Maximization of the Geometric Mean with Lognormal Return Distribution

Author

Listed:
  • Edwin J. Elton

    (New York University)

  • Martin J. Gruber

    (New York University)

Abstract

In this paper we discuss the relevancy of the geometric mean as a portfolio selection criteria. A procedure for finding that portfolio with the highest geometric mean when returns on portfolios are lognormally distributed is presented. The development of this algorithm involves a proof that the portfolio with maximum geometric mean lies on the efficient frontier in arithmetic mean variance space. This finding has major implications for the relevancy of much of portfolio and general equilibrium theory. These implications are explored.

Suggested Citation

  • Edwin J. Elton & Martin J. Gruber, 1974. "Note--On the Maximization of the Geometric Mean with Lognormal Return Distribution," Management Science, INFORMS, vol. 21(4), pages 483-488, December.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:4:p:483-488
    DOI: 10.1287/mnsc.21.4.483
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    Cited by:

    1. Jerome L Kreuser & Didier Sornette, 2017. "Super-Exponential RE Bubble Model with Efficient Crashes," Swiss Finance Institute Research Paper Series 17-33, Swiss Finance Institute.
    2. David J Johnstone, 2023. "Capital budgeting and Kelly betting," Australian Journal of Management, Australian School of Business, vol. 48(3), pages 625-651, August.
    3. Renée Kidson & Brent Haddad & Hui Zheng & Steven Kasower & Robert Raucher, 2013. "Optimising Reliability: Portfolio Modeling of Contract Types for Retail Water Providers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(9), pages 3209-3225, July.
    4. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    5. Muteba Mwamba, John & Suteni, Mwambi, 2010. "An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio," MPRA Paper 50240, University Library of Munich, Germany.
    6. Jimmy E. Hilliard & Jitka Hilliard, 2018. "Rebalancing versus buy and hold: theory, simulation and empirical analysis," Review of Quantitative Finance and Accounting, Springer, vol. 50(1), pages 1-32, January.

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