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Exact properties of measures of optimal investment for benchmarked portfolios

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  • J. Knight
  • S. E. Satchell

Abstract

We revisit the problem of calculating the exact distribution of optimal investments in a mean variance world under multivariate normality. The context we consider is where problems in optimisation are addressed through the use of Monte-Carlo simulation. Our findings give clear insight as to when Monte-Carlo simulation will, and will not work. Whilst a number of authors have considered aspects of this exact problem before, we extend the problem by considering the problem of an investor who wishes to maximise quadratic utility defined in terms of alpha and tracking errors. The results derived allow some exact and numerical analysis. Furthermore, they allow us to also derive results for the more traditional non-benchmarked portfolio problem.

Suggested Citation

  • J. Knight & S. E. Satchell, 2010. "Exact properties of measures of optimal investment for benchmarked portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 495-502.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:5:p:495-502
    DOI: 10.1080/14697680903061412
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    References listed on IDEAS

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    1. Frahm, Gabriel, 2007. "Linear statistical inference for global and local minimum variance portfolios," Discussion Papers in Econometrics and Statistics 1/07, University of Cologne, Institute of Econometrics and Statistics.
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    Cited by:

    1. Zura Kakushadze, 2014. "Mean-Reversion and Optimization," Papers 1408.2217, arXiv.org, revised Feb 2016.
    2. A. D. Hall & S. E. Satchell & P. J. Spence, 2015. "Evaluating the impact of inequality constraints and parameter uncertainty on optimal portfolio choice," Applied Economics, Taylor & Francis Journals, vol. 47(45), pages 4801-4813, September.
    3. Begoña Font, 2016. "Bootstrap estimation of the efficient frontier," Computational Management Science, Springer, vol. 13(4), pages 541-570, October.
    4. Bodnar Taras & Schmid Wolfgang & Zabolotskyy Tara, 2012. "Minimum VaR and minimum CVaR optimal portfolios: Estimators, confidence regions, and tests," Statistics & Risk Modeling, De Gruyter, vol. 29(4), pages 281-314, November.

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