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Exact Properties of Measures of Optimal Investment for Institutional Investors

Author

Listed:
  • 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: https://eprints.bbk.ac.uk/id/eprint/27040
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. 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 1651-1683, August.
    2. Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(2), pages 185-204, June.
    3. 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.
    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.
    5. Scowcroft, Alan & Satchell, Stephen (ed.), 2003. "Advances in Portfolio Construction and Implementation," Elsevier Monographs, Elsevier, edition 1, number 9780750654487.
    6. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
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    More about this item

    Keywords

    alpha; tracking error; mean-variance; Monte-Carlo;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

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