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Sensitivity Analysis for Mean-Variance Portfolio Problems

Author

Listed:
  • Michael J. Best

    (Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada)

  • Robert R. Grauer

    (Department of Economics, Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 Canada)

Abstract

This paper shows how to perform sensitivity analysis for Mean-Variance (MV) portfolio problems using a general form of parametric quadratic programming. The analysis allows an investor to examine how parametric changes in either the means or the right-hand side of the constraints affect the composition, mean, and variance of the optimal portfolio. The optimal portfolio and associated multipliers are piecewise linear functions of the changes in either the means or the right-hand side of the constraints. The parametric parts of the solution show the rates of substitution of securities in the optimal portfolio, while the parametric parts of the multipliers show the rates at which constraints are either tightening or loosening. Furthermore, the parametric parts of the solution and multipliers change in different intervals when constraints become active or inactive. The optimal MV paths for sensitivity analyses are piecewise parabolic, as in traditional MV analysis. However, the optimal paths may contain negatively sloping segments and are characterized by types of kinks, i.e., points of nondifferentiability, not found in MV analysis.

Suggested Citation

  • Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
  • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:8:p:980-989
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    File URL: http://dx.doi.org/10.1287/mnsc.37.8.980
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    Citations

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    Cited by:

    1. Fletcher, Jonathan, 2011. "Do optimal diversification strategies outperform the 1/N strategy in U.K. stock returns?," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 375-385.
    2. repec:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500492 is not listed on IDEAS
    3. Bouaddi, Mohammed & Taamouti, Abderrahim, 2013. "Portfolio selection in a data-rich environment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2943-2962.
    4. Becker, Franziska & Gürtler, Marc & Hibbeln, Martin, 2009. "Markowitz versus Michaud: Portfolio optimization strategies reconsidered," Working Papers IF30V3, Technische Universität Braunschweig, Institute of Finance.
    5. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    6. LECLUYSE, C. & VAN WOENSEL, Tom & PEREMANS, Herbert, 2007. "Vehicle routing with stochastic time-dependent travel times," Working Papers 2007018, University of Antwerp, Faculty of Applied Economics.
    7. Pınar, Mustafa Ç., 2014. "Equilibrium in an ambiguity-averse mean–variance investors market," European Journal of Operational Research, Elsevier, vol. 237(3), pages 957-965.
    8. Mourad Mroua & Fathi Abid, 2014. "Portfolio revision and optimal diversification strategy choices," International Journal of Managerial Finance, Emerald Group Publishing, vol. 10(4), pages 537-564, August.
    9. repec:pal:jorsoc:v:68:y:2017:i:12:d:10.1057_s41274-016-0164-5 is not listed on IDEAS
    10. James DiLellio, 2015. "A Kalman filter control technique in mean-variance portfolio management," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(2), pages 235-261, April.
    11. Kim, Jang Ho & Kim, Woo Chang & Fabozzi, Frank J., 2013. "Composition of robust equity portfolios," Finance Research Letters, Elsevier, vol. 10(2), pages 72-81.
    12. Alejandro Corvalán, 2005. "Well Diversified Efficient Portfolios," Working Papers Central Bank of Chile 336, Central Bank of Chile.
    13. A. Paç & Mustafa Pınar, 2014. "Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 875-891, October.
    14. repec:spr:annopr:v:256:y:2017:i:1:d:10.1007_s10479-016-2176-6 is not listed on IDEAS
    15. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    16. Annalisa Fabretti & Stefano Herzel & Mustafa C. Pinar, 2014. "Delegated Portfolio Management under Ambiguity Aversion," CEIS Research Paper 304, Tor Vergata University, CEIS, revised 06 Feb 2014.
    17. Bastien Drut, 2009. "Nice but cautious guys: The cost of responsible investing in the bond markets," Working Papers CEB 09-034.RS, ULB -- Universite Libre de Bruxelles.
    18. 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.
    19. Kim, Woo Chang & Kim, Jang Ho & Fabozzi, Frank J., 2014. "Deciphering robust portfolios," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 1-8.

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