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Markowitz Portfolio Construction at Seventy

Author

Listed:
  • Stephen Boyd
  • Kasper Johansson
  • Ronald Kahn
  • Philipp Schiele
  • Thomas Schmelzer

Abstract

More than seventy years ago Harry Markowitz formulated portfolio construction as an optimization problem that trades off expected return and risk, defined as the standard deviation of the portfolio returns. Since then the method has been extended to include many practical constraints and objective terms, such as transaction cost or leverage limits. Despite several criticisms of Markowitz's method, for example its sensitivity to poor forecasts of the return statistics, it has become the dominant quantitative method for portfolio construction in practice. In this article we describe an extension of Markowitz's method that addresses many practical effects and gracefully handles the uncertainty inherent in return statistics forecasting. Like Markowitz's original formulation, the extension is also a convex optimization problem, which can be solved with high reliability and speed.

Suggested Citation

  • Stephen Boyd & Kasper Johansson & Ronald Kahn & Philipp Schiele & Thomas Schmelzer, 2024. "Markowitz Portfolio Construction at Seventy," Papers 2401.05080, arXiv.org.
    • Handle: RePEc:arx:papers:2401.05080
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    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. Michaud, Richard O. & Michaud, Robert O., 2008. "Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation," OUP Catalogue, Oxford University Press, edition 2, number 9780195331912.
    4. Kasper Johansson & Mehmet Giray Ogut & Markus Pelger & Thomas Schmelzer & Stephen Boyd, 2023. "A Simple Method for Predicting Covariance Matrices of Financial Returns," Papers 2305.19484, arXiv.org, revised Nov 2023.
    5. repec:dau:papers:123456789/4688 is not listed on IDEAS
    6. Markus Pelger & Ruoxuan Xiong, 2022. "State-Varying Factor Models of Large Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1315-1333, June.
    7. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    8. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    9. Martin Lettau & Markus Pelger & Stijn Van Nieuwerburgh, 2020. "Factors That Fit the Time Series and Cross-Section of Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 33(5), pages 2274-2325.
    10. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    11. Nicholas Moehle & Jack Gindi & Stephen Boyd & Mykel Kochenderfer, 2021. "Portfolio Construction as Linearly Constrained Separable Optimization," Papers 2103.05455, arXiv.org, revised Jul 2022.
    12. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    13. Markus Pelger & Ruoxuan Xiong, 2022. "Interpretable Sparse Proximate Factors for Large Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1642-1664, October.
    14. Lettau, Martin & Pelger, Markus, 2020. "Estimating latent asset-pricing factors," Journal of Econometrics, Elsevier, vol. 218(1), pages 1-31.
    15. Elissaios Sarmas & Panos Xidonas & Haris Doukas, 2020. "Multicriteria Portfolio Construction with Python," Springer Optimization and Its Applications, Springer, number 978-3-030-53743-2, September.
    16. Li, Xiaoyue & Uysal, A. Sinem & Mulvey, John M., 2022. "Multi-period portfolio optimization using model predictive control with mean-variance and risk parity frameworks," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1158-1176.
    17. Jiaqin Chen & Ming Yuan, 2016. "Efficient Portfolio Selection in a Large Market," Journal of Financial Econometrics, Oxford University Press, vol. 14(3), pages 496-524.
    18. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    19. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    20. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    21. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    22. Martin Lettau & Markus Pelger, 2020. "Factors That Fit the Time Series and Cross-Section of Stock Returns," Review of Finance, European Finance Association, vol. 33(5), pages 2274-2325.
    23. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    24. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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