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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
    DOI: 10.1287/mnsc.13.7.499
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    Cited by:

    1. Christian Walter, 2005. "La gestion indicielle et la théorie des moyennes," Revue d'Économie Financière, Programme National Persée, vol. 79(2), pages 113-136.
    2. 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.
    3. Fuentes, Patricia Contzen & Daza, Rigoberto Parada, 1996. "A decision model in investment according to price/earning ratio," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 50(1), January.
    4. Musdalifah Azis & Maryam Nadir & dan Ike Purnamasari, 2017. "Optimazed Mutual Funds Investment Portfolio Through Good Corporate Governance And Financial Banking Performance," International Journal of Economics and Financial Issues, Econjournals, vol. 7(5), pages 189-197.
    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. Amritansu Ray & Sanat Kumar Majumder, 2018. "Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 107-133, March.
    7. 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.
    8. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    9. Cinzia Colapinto & Davide Torre & Belaid Aouni, 2019. "Goal programming for financial portfolio management: a state-of-the-art review," Operational Research, Springer, vol. 19(3), pages 717-736, September.
    10. 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.
    11. Cenedese, Gino & Elard, Ilaf, 2021. "Unconventional monetary policy and the portfolio choice of international mutual funds," Journal of International Money and Finance, Elsevier, vol. 115(C).
    12. 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.
    13. 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.
    14. Jyotirmayee Behera & Pankaj Kumar, 2024. "Implementation of machine learning in $$\ell _{\infty }$$ ℓ ∞ -based sparse Sharpe ratio portfolio optimization: a case study on Indian stock market," Operational Research, Springer, vol. 24(4), pages 1-26, December.
    15. Lynda S. Livingston, 2013. "Intraportfolio Correlation: An Application For Investments Students," Business Education and Accreditation, The Institute for Business and Finance Research, vol. 5(1), pages 91-105.
    16. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    17. Javad Koushki & Kaisa Miettinen & Majid Soleimani-damaneh, 2022. "LR-NIMBUS: an interactive algorithm for uncertain multiobjective optimization with lightly robust efficient solutions," Journal of Global Optimization, Springer, vol. 83(4), pages 843-863, August.
    18. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    19. 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.
    20. 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.

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