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

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  • Muteba Mwamba, John
  • Suteni, Mwambi

Abstract

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

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    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.
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    More about this item

    Keywords

    Portfolio selection; Kelly criteria; mean variance; optimization;
    All these keywords.

    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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