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New light on the portfolio allocation problem

Author

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  • R. A. Maller
  • D. A. Turkington

Abstract

The basics of the mean-variance portfolio optimisation procedure have been well understood since the seminal work of Markowitz in the 1950's. A vector x of asset weights, restricted only by requiring its components to add to 1, is to be chosen so that the linear combination μ p =x ′ μ of the expected asset returns μ (or, expected excess returns), which represents the expected return on a portfolio, is maximised for a specified level of “risk”, σ p , the standard deviation of the portfolio. The efficient frontier is the curve traced out in (μ p , σ p ) space by portfolios whose return/risk tradeoff is optimal in this sense. The portfolio with the maximum Sharpe ratio is the portfolio with the highest return/risk tradeoff achievable from the assets, and under some conditions can be obtained as the point of tangency of a line from the origin to the efficient frontier, as is well known. But when the tangency approach fails, which it commonly can, the question arises as to the maximum Sharpe ratio achievable from the assets. This problem, which has not been dealt with before, is solved explicitly in this paper, and the corresponding optimal portfolio found. The suggested procedure is easily implemented when the usual inputs – estimates of mean excess returns and their covariance matrix – are available. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • R. A. Maller & D. A. Turkington, 2003. "New light on the portfolio allocation problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(3), pages 501-511, January.
    • Handle: RePEc:spr:mathme:v:56:y:2003:i:3:p:501-511
    DOI: 10.1007/s001860200211
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    Citations

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    Cited by:

    1. Yuanyao Ding & Bo Zhang, 2009. "Risky asset pricing based on safety first fund management," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 353-361.
    2. Zhihui Lv & Amanda M. Y. Chu & Wing Keung Wong & Thomas C. Chiang, 2021. "The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio," Risk Management, Palgrave Macmillan, vol. 23(1), pages 97-122, June.
    3. Ekaterina Seregina, 2020. "A Basket Half Full: Sparse Portfolios," Papers 2011.04278, arXiv.org, revised Apr 2021.

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