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Approximating the Growth Optimal Portfolio with a Diversified World Stock Index

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Abstract

This paper constructs and compares various total return world stock indices based on daily data. Due to diversification these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio. The paper constructs a diversified world stock index that outperforms a number of other indices and argues that it is a good proxy for the growth optimal portfolio. This has applications to derivative pricing and investment management.

Suggested Citation

  • 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.
    • Handle: RePEc:uts:rpaper:184
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    1. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
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    4. Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88, January.
    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. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095, Decembrie.
    7. Eckhard Platen, 2004. "Modeling The Volatility And Expected Value Of A Diversified World Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 511-529.
    8. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    9. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    10. Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.
    11. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    13. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    14. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    15. Aitken, Michael J. & Berkman, Henk & Mak, Derek, 2001. "The use of undisclosed limit orders on the Australian Stock Exchange," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1589-1603, August.
    16. Oecd, 2002. "Access for Business," OECD Digital Economy Papers 67, OECD Publishing.
    17. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Citations

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    Cited by:

    1. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    2. Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Katja Ignatieva & Eckhard Platen, 2010. "Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(3), pages 261-302, September.
    4. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Katja Ignatieva & Eckhard Platen & Renata Rendek, 2010. "Using Dynamic Copulae for Modeling Dependency in Currency Denominations of a Diversifed World Stock Index," Research Paper Series 284, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    8. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2007. "Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models," Research Paper Series 198, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2012. "Alternative Term Structure Models for Reviewing Expectations Puzzles," Research Paper Series 305, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    12. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. 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.
    14. Ignatieva, Katja & Platen, Eckhard, 2012. "Estimating the diffusion coefficient function for a diversified world stock index," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1333-1349.
    15. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.

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    More about this item

    Keywords

    world stock index; growth optimal portfolio; diversification; mean-variance portfolio selection; enhanced index fund;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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    This paper has been announced in the following NEP Reports:

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