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A Linear Programming Algorithm for Mutual Fund Portfolio Selection

Author

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  • William F. Sharpe

    (University of Washington, Seattle)

Abstract

The portfolio selection problem faced by a mutual fund manager can be formulated following the Markowitz approach: find those portfolios that are efficient in terms of predicted expected return and standard deviation of return, subject to legal constraints in the form of upper bounds on the proportion of the fund invested in any single security. This paper suggests that such problems be re-formulated as parametric linear-programming problems, utilizing a linear approximation to the true (quadratic) formula for a portfolio's risk. Limited empirical evidence suggests that the approximation is acceptable. Moreover, it allows the use of an extremely simple and efficient special-purpose solution algorithm. With appropriate modifications, this algorithm may prove useful to the managers of mutual funds with a wide variety of objectives.

Suggested Citation

  • William F. Sharpe, 1967. "A Linear Programming Algorithm for Mutual Fund Portfolio Selection," Management Science, INFORMS, vol. 13(7), pages 499-510, March.
  • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:7:p:499-510
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    File URL: http://dx.doi.org/10.1287/mnsc.13.7.499
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    Cited by:

    1. Abdelaziz, Fouad Ben & Aouni, Belaid & Fayedh, Rimeh El, 2007. "Multi-objective stochastic programming for portfolio selection," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1811-1823, March.
    2. Fuentes, Patricia Contzen & Daza, Rigoberto Parada, 1996. "A decision model in investment according to price/earning ratio," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 50(1), January.
    3. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
    4. repec:eco:journ1:2017-05-23 is not listed on IDEAS
    5. Polak, George G. & Rogers, David F. & Sweeney, Dennis J., 2010. "Risk management strategies via minimax portfolio optimization," European Journal of Operational Research, Elsevier, vol. 207(1), pages 409-419, November.
    6. repec:spr:opsear:v:55:y:2018:i:1:d:10.1007_s12597-017-0311-z is not listed on IDEAS
    7. Spronk, Jaap & Hallerbach, Winfried, 1997. "Financial modelling: Where to go? With an illustration for portfolio management," European Journal of Operational Research, Elsevier, vol. 99(1), pages 113-125, May.
    8. repec:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0289-y is not listed on IDEAS
    9. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    10. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    11. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    12. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.

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