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Simulation of Diversified Portfolios in a Continuous Financial Market

In this paper we analyze the simulated behavior of diversified portfolios in a continuous financial market. In particular, we focus on equally weighted portfolios. We illustrate that these well diversified portfolios constitute good proxies of the growth optimal portfolio. The multi-asset market models considered include the Black-Scholes model, the Heston model, the ARCH diffusion model, the geometric Ornstein-Uhlenbeck volatility model and the multi-currency minimal market model. The choice of these models was motivated by the fact that they can be simulated almost exactly and, therefore, very accurately also over longer periods of time. Finally, we provide examples, which demonstrate the robustness of the diversification phenomenon when approximating the growth optimal portfolio of a market by an equal value weighted portfolio. Significant out performance of the market capitalization weighted portfolio by the equal value weighted portfolio can be observed for models.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp264.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 264.

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Length: 32
Date of creation: 01 Dec 2009
Date of revision:
Handle: RePEc:uts:rpaper:264
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Web page: http://www.qfrc.uts.edu.au/

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  1. 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.
  2. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88.
  4. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  5. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
  6. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. 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.
  9. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. Frey, RĂ¼diger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
  11. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
  13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  14. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  15. Eckhard Platen & Renata Rendek, 2010. "Approximating the Numeraire Portfolio by Naive Diversification," Research Paper Series 281, Quantitative Finance Research Centre, University of Technology, Sydney.
  16. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
  17. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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