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Sensitivity Analysis for Mean-Variance Portfolio Problems

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  • 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)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.37.8.980
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 37 (1991)
    Issue (Month): 8 (August)
    Pages: 980-989

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    Handle: RePEc:inm:ormnsc:v:37:y:1991:i:8:p:980-989

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    Keywords: sensitivity analysis; parametric quadratic programming; mean-variance portfolio selection;

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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Becker, Franziska & Gürtler, Marc & Hibbeln, Martin, 2009. "Markowitz versus Michaud: Portfolio optimization strategies reconsidered," Working Papers IF30V3, Technische Universität Braunschweig, Institute of Finance.
    8. 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.
    9. Alejandro Corvalán, 2005. "Well Diversified Efficient Portfolios," Working Papers Central Bank of Chile 336, Central Bank of Chile.

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