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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.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp180.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 180.

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Length: 20
Date of creation: 01 Aug 2006
Date of revision:
Handle: RePEc:uts:rpaper:180

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Keywords: world stock index; growth optimal portfolio; diversification; mean-variance portfolio selection; enhanced index fund;

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References

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  1. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
  3. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  5. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  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. Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88.
  8. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  9. Kevin Fergusson & Eckhard Platen, 2005. "On the Distributional Characterization of Log-returns of a World Stock Index," Research Paper Series 153, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. 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.
  11. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095, September.
  13. 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.
  14. 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.
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Citations

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Cited by:
  1. Katja Ignatieva & Eckhard Platen, 2009. "Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae," Research Paper Series 265, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. 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.
  3. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. 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.
  5. 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.
  6. 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.
  7. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. 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.
  9. 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.
  10. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
  11. 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.
  12. 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.
  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.

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