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Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios

Author

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  • William F. Sharpe

    (Stanford University)

Abstract

The characteristic line of a security or portfolio relates its rate of return to that of a "market portfolio." Several investigators have suggested the desirability of obtaining such a line by minimizing the sum of the absolute deviations rather than the sum of the squared deviations around the line. This paper presents a new algorithm for such a regression problem. The procedure has at least two virtues: it is simple, and it produces useful information as a byproduct of the solution process. Empirical evidence is also presented on the differences in the values obtained with the two regression methods (i.e., mean-absolute-deviation and least-squares). The differences appear to be relatively slight, at least for well-diversified portfolios.

Suggested Citation

  • William F. Sharpe, 1971. "Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios," Management Science, INFORMS, vol. 18(2), pages 1-13, October.
    • Handle: RePEc:inm:ormnsc:v:18:y:1971:i:2:p:b1-b13
    DOI: 10.1287/mnsc.18.2.B1
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    Cited by:

    1. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    2. Giloni, Avi & Simonoff, Jeffrey S. & Sengupta, Bhaskar, 2006. "Robust weighted LAD regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3124-3140, July.
    3. Renata Mansini & Włodzimierz Ogryczak & M. Speranza, 2007. "Conditional value at risk and related linear programming models for portfolio optimization," Annals of Operations Research, Springer, vol. 152(1), pages 227-256, July.
    4. Richard W. Cottle, 2017. "On “Pre-historic” Linear Programming and the Figure of the Earth," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 255-277, October.
    5. R. Douglas Martin & Daniel Z. Xia, 2022. "Efficient bias robust regression for time series factor models," Journal of Asset Management, Palgrave Macmillan, vol. 23(3), pages 215-234, May.
    6. Pan, Yubin & Hong, Rongjing & Chen, Jie & Wu, Weiwei, 2020. "A hybrid DBN-SOM-PF-based prognostic approach of remaining useful life for wind turbine gearbox," Renewable Energy, Elsevier, vol. 152(C), pages 138-154.
    7. Iddo Eliazar, 2024. "Beautiful Gini," METRON, Springer;Sapienza Università di Roma, vol. 82(3), pages 293-313, December.
    8. Garud Iyengar & Alfred Ma, 2013. "Fast gradient descent method for Mean-CVaR optimization," Annals of Operations Research, Springer, vol. 205(1), pages 203-212, May.
    9. Joe Hirschberg & Jenny Lye, 2021. "Estimating risk premiums for regulated firms when accounting for reference-day variation and high-order moments of return volatility," Environment Systems and Decisions, Springer, vol. 41(3), pages 455-467, September.
    10. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    11. Trzpiot Grażyna, 2012. "Selected Robust Methods for Camp Model Estimation," Folia Oeconomica Stetinensia, Sciendo, vol. 12(2), pages 58-71, December.
    12. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
    13. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    14. Juan Carlos Gutierrez Betancur, 2017. "Robust Estimation of beta and the hedging ratio in Stock Index Futures In the Integrated Latin American Market," Revista Ecos de Economía, Universidad EAFIT, vol. 21(44), pages 37-71, June.
    15. Jen-Peng Huang & Genesis Sembiring Depari & Srivandayuli Riorini & Pai-Chouwang, 2018. "Leveraging Social Media Metrics In Improving Social Media Performances Through Organic Reach: A Data Mining Approach," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 22, pages 33-48, December.

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