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On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies

Author

Listed:
  • Robert R. Grauer

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

  • Nils H. Hakansson

    (Haas School of Business, University of California, Berkeley, 350 Barrows Hall, Berkeley, California 94720)

Abstract

This paper compares two approximation schemes for calculating the optimal portfolios in the discrete-time dynamic investment model, specifically, the mean-variance (MV) and the quadratic approximations, to the exact power function method. Future returns are estimated via the empirical probability assessment approach. The results show that (i) with quarterly revision, the MV model approximates the dynamic model very well; (ii) with annual revision, there are often sharp differences between the power function model and the MV approximation; and (iii) these differences become even larger when the quadratic approximation is used.

Suggested Citation

  • Robert R. Grauer & Nils H. Hakansson, 1993. "On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies," Management Science, INFORMS, vol. 39(7), pages 856-871, July.
  • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:7:p:856-871
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    File URL: http://dx.doi.org/10.1287/mnsc.39.7.856
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    Citations

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    Cited by:

    1. Michael J. Best & Jaroslava Hlouskova, 2005. "An Algorithm for Portfolio Optimization with Transaction Costs," Management Science, INFORMS, vol. 51(11), pages 1676-1688, November.
    2. Glensk, Barbara & Madlener, Reinhard, 2011. "Dynamic Portfolio Selection Methods for Power Generation Assets," FCN Working Papers 16/2011, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    3. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    4. Stambaugh, Robert F., 1997. "Analyzing investments whose histories differ in length," Journal of Financial Economics, Elsevier, vol. 45(3), pages 285-331, September.
    5. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    6. Alexandra Rodkina & Nikolai Dokuchaev, 2014. "On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market," Papers 1403.4329, arXiv.org, revised Nov 2014.
    7. 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.
    8. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    9. Fletcher, Jonathan & Hillier, Joe, 2002. "On the usefulness of linear factor models in predicting expected returns in mean-variance analysis," International Review of Financial Analysis, Elsevier, vol. 11(4), pages 449-466.
    10. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    11. Mark Broadie & Weiwei Shen, 2017. "Numerical solutions to dynamic portfolio problems with upper bounds," Computational Management Science, Springer, vol. 14(2), pages 215-227, April.
    12. repec:wsi:qjfxxx:v:07:y:2017:i:02:n:s201013921750001x is not listed on IDEAS
    13. Jianfeng Liang & Shuzhong Zhang & Duan Li, 2008. "Optioned Portfolio Selection: Models And Analysis," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 569-593.
    14. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    15. repec:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9266-z is not listed on IDEAS
    16. repec:gam:jrisks:v:6:y:2018:i:1:p:12-:d:132609 is not listed on IDEAS
    17. Dokuchaev, Nikolai, 2007. "Discrete time market with serial correlations and optimal myopic strategies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1090-1104, March.
    18. repec:eee:finana:v:55:y:2018:i:c:p:23-34 is not listed on IDEAS
    19. Zhang, Wei-Guo & Liu, Yong-Jun & Xu, Wei-Jun, 2012. "A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 222(2), pages 341-349.
    20. Chamberlain, Trevor W., 1996. "The investment decisions of individuals and firms," International Review of Financial Analysis, Elsevier, vol. 5(2), pages 87-97.
    21. Yu, Mei & Takahashi, Satoru & Inoue, Hiroshi & Wang, Shouyang, 2010. "Dynamic portfolio optimization with risk control for absolute deviation model," European Journal of Operational Research, Elsevier, vol. 201(2), pages 349-364, March.
    22. Grauer, Robert R. & Hakansson, Nils H., 1995. "Stein and CAPM estimators of the means in asset allocation," International Review of Financial Analysis, Elsevier, vol. 4(1), pages 35-66.

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