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Portfolio theory: mean-variance

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Encyclopedia of Operations Research and Management Science

PORTFOLIO SELECTION PROBLEM

The heart of the portfolio problem is the selection of an optimal set of investment assets by rational economic agents. Although elements of portfolio problems were discussed in the 1930s and 1950s by Allais, De Finetti, Hicks, Marschak and others, the first formal specification of such a selection model was by Markowitz (1952, 1959) who defined a mean-variance model for calculating optimal portfolios. Following Tobin (1958, 1965), Sharpe (1970) and Roll (1977), this portfolio selection model may be stated as

(1)

where xv is a column vector of investment proportions in each of the risky assets, Vv is a positive semi-definite variance-covariance matrix of asset returns, rv is a column vector of expected asset returns, r p is the investor's target rate of return and ev is a column unit vector. An explicit solution for the problem can be found using the procedures described in Merton (1972), Ziemba and Vickson (1975), or Roll (1977).

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Author information

Authors and Affiliations

  1. London School of Economics, London, England

    John L. G. Board

  2. University of Southampton, Southampton, England

    Charles M. S. Sutcliffe

  3. University of British Columbia, Vancouver, Canada

    William T. Ziemba

Authors
  1. John L. G. Board
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  2. Charles M. S. Sutcliffe
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  3. William T. Ziemba
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Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

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© 2001 Kluwer Academic Publishers

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Board, J.L.G., Sutcliffe, C.M.S., Ziemba, W.T. (2001). Portfolio theory: mean-variance . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_775

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  • DOI: https://doi.org/10.1007/1-4020-0611-X_775

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