Simulation of Diversified Portfolios in a Continuous Financial Market

Quantitative Finance Research Centre, University of Technology, Sydney, Research Paper Number 282

29 Pages Posted: 3 Nov 2012

See all articles by Eckhard Platen

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Renatak Rendek

affiliation not provided to SSRN

Date Written: August 1, 2010

Abstract

The paper analyzes the simulated long-term behavior of well diversified portfolios in continuous financial markets. It focuses on the equi-weighted index and the market portfolio. The paper illustrates that the equally weighted portfolio constitutes a good proxy of the growth optimal portfolio, which maximizes expected logarithmic utility. 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 a multi-asset version of the minimal market model. All these models are simulated exactly or almost exactly over an extremely long period of time to analyze the long term growth of the respective portfolios. The paper illustrates the robustness of the diversification phenomenon when approximating the growth optimal portfolio by the equi-weighted index. Significant outperformance in the long run of the market capitalization weighted portfolio by the equi-weighted index is documented for different market models. Under the multi-asset minimal market model the equi-weighted index outperforms remarkably the market portfolio. In this case the benchmarked market portfolio is a strict supermartingale, whereas the benchmarked equi-weighted index is a martingale. Equal value weighting overcomes the strict supermartingale property that the benchmarked market portfolio inherits from its strict supermartingale constituents under this model.

Keywords: growth optimal portfolio, diversification theorem, diversified portfolios, market portfolio, equi-weighted index, almost exact simulation, minimal market model

Suggested Citation

Platen, Eckhard and Rendek, Renatak, Simulation of Diversified Portfolios in a Continuous Financial Market (August 1, 2010). Quantitative Finance Research Centre, University of Technology, Sydney, Research Paper Number 282. Available at SSRN: https://ssrn.com/abstract=2170212 or http://dx.doi.org/10.2139/ssrn.2170212

Eckhard Platen (Contact Author)

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Renatak Rendek

affiliation not provided to SSRN ( email )

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