Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Portfolio Theory: Mean-Variance Model

  • John L. G. Board
  • Charles M. S. Sutcliffe
  • William T. Ziemba
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_775


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 ( 1972), this portfolio selection model may be stated as
$$ \eqalign{\mathrm{ Minimize}\;\ & \boldsymbol{ x}^\prime \boldsymbol{ Vx} \cr \mathrm{ subject}\;\mathrm{ to}\;\ & \boldsymbol{ x}^\prime \boldsymbol{ r}={r_p} \cr & \boldsymbol{ x}^\prime \boldsymbol{ e}=1 \cr} $$
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • John L. G. Board
    • 1
  • Charles M. S. Sutcliffe
    • 2
  • William T. Ziemba
    • 3
    • 4
  1. 1.The ICMA CentreHenley Business School, University of ReadingReadingUK
  2. 2.The ICMA Centre, Henley Business SchoolUniversity of ReadingReadingUK
  3. 3.Sauder School of BusinessUniversity of British ColumbiaVancouverCanada
  4. 4.Oxford UniversityOxfordUK