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Exact Properties of Measures of Optimal Investment for Institutional Investors

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  • John Knight
  • Stephen 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 nonbenchmarked portfolio problem.

Suggested Citation

  • John Knight & Stephen Satchell, 2005. "Exact Properties of Measures of Optimal Investment for Institutional Investors," Birkbeck Working Papers in Economics and Finance 0513, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:0513
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    File URL: http://www.bbk.ac.uk/ems/research/wp/PDF/BWPEF0513.pdf
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. Scowcroft, Alan & Satchell, Stephen (ed.), 2003. "Advances in Portfolio Construction and Implementation," Elsevier Monographs, Elsevier, edition 1, number 9780750654487.
    2. Green, Richard C & Hollifield, Burton, 1992. " When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    4. Mark Britten-Jones, 1999. "The Sampling Error in Estimates of Mean-Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    alpha; tracking error; mean-variance; Monte-Carlo;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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