An alternative to portfolio selection problem beyond Markowitz’s: Log Optimal Growth Portfolio
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.
|Date of creation:||Oct 2010|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- James Tobin, 1956.
"Liquidity Preference as Behavior Towards Risk,"
Cowles Foundation Discussion Papers
14, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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.
- Truc Le & Eckhard Platen, 2006.
"Approximating the Growth Optimal Portfolio with a Diversified World Stock Index,"
Research Paper Series
180, Quantitative Finance Research Centre, University of Technology, Sydney.
- Truc Le & Eckhard Platen, 2006. "Approximating the growth optimal portfolio with a diversified world stock index," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 559-574, November.
- 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.
- 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.
- 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.
- Roll, Richard, 1973. "Evidence on the "Growth-Optimum" Model," Journal of Finance, American Finance Association, vol. 28(3), pages 551-66, June.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:50240. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.