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Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios

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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
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    File URL: http://dx.doi.org/10.1287/mnsc.18.2.B1
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    Cited by:

    1. Giloni, Avi & Simonoff, Jeffrey S. & Sengupta, Bhaskar, 2006. "Robust weighted LAD regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3124-3140, July.
    2. Trzpiot Gra┼╝yna, 2012. "Selected Robust Methods for Camp Model Estimation," Folia Oeconomica Stetinensia, Sciendo, vol. 12(2), pages 58-71, December.
    3. W. Michalowski & W. Ogryczak, 1998. "Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion," Working Papers ir98041, International Institute for Applied Systems Analysis.
    4. 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.
    5. repec:col:000442:015652 is not listed on IDEAS
    6. repec:spr:joptap:v:175:y:2017:i:1:d:10.1007_s10957-017-1165-5 is not listed on IDEAS

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