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An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio


  • Muteba Mwamba, John
  • Suteni, Mwambi


This paper constructs an alternative investment strategy to portfolio optimization model in the framework of the Mean–Variance portfolio selection model. To differentiate it from the ubiquitously applied Mean–Variance model, which is constructed on an assumption that returns are normally distributed, our model makes two assumptions: Firstly, that asset prices follow a Geometric Brownian Motion and that secondly asset prices are Log-normally distributed meaning that continuously compounded returns are normally distributed. The traditional Mean–Variance optimization approach has only one objective, which fails to capture the stochastic nature of asset returns and their correlations. This paper presents an alternative approach to the portfolio selection problem. The proposed optimization model which is an optimal portfolio strategy is produced for investors of various risk tolerance, taking into account the stochastic nature of the returns. Detailed analysis based on log– optimal growth optimization and the application of the model are provided and compared to the standard Mean–Variance approach.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:50240

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    References listed on IDEAS

    1. James H. Vander Weide & David W. Peterson & Steven F. Maier, 1977. "A Strategy Which Maximizes the Geometric Mean Return on Portfolio Investments," Management Science, INFORMS, vol. 23(10), pages 1117-1123, June.
    2. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508 World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    5. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    6. Fernholz, Robert & Shay, Brian, 1982. " Stochastic Portfolio Theory and Stock Market Equilibrium," Journal of Finance, American Finance Association, vol. 37(2), pages 615-624, May.
    7. Benjamin Francis Hunt, 2002. "Growth Optimal Investment Strategy Efficacy: An Application on Long Run Australian Equity Data," Research Paper Series 86, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Hakansson, Nils H, 1971. "Multi-Period Mean-Variance Analysis: Toward A General Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 26(4), pages 857-884, September.
    10. Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-566, June.
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    More about this item


    Portfolio selection; Kelly criteria; mean variance; optimization;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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