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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 50240.

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Date of creation: Oct 2010
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Handle: RePEc:pra:mprapa:50240

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Related research

Keywords: Portfolio selection; Kelly criteria; mean variance; optimization;

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References

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  1. Fernholz, Robert & Shay, Brian, 1982. " Stochastic Portfolio Theory and Stock Market Equilibrium," Journal of Finance, American Finance Association, vol. 37(2), pages 615-24, May.
  2. 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.
  3. Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-66, June.
  4. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. 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.
  6. 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.
  7. 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 637-54, May-June.
  8. 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 857-84, September.
  9. Markowitz, Harry M, 1976. "Investment for the Long Run: New Evidence for an Old Rule," Journal of Finance, American Finance Association, vol. 31(5), pages 1273-86, December.
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