On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean-variance efficient. The conditions for the mean-variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean-variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.
|Date of creation:||Jul 2012|
|Date of revision:||Apr 2013|
|Publication status:||Published in European Journal of Operational Research, Volume 229, Issue 3, 2013, pp. 637-644|
|Contact details of provider:|| Web page: http://arxiv.org/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
- Yarema Okhrin & Wolfgang Schmid, 2007. "Comparison of different estimation techniques for portfolio selection," AStA Advances in Statistical Analysis, Springer, vol. 91(2), pages 109-127, August.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 673-705.
- Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2011. "Portfolio selection problems in practice: a comparison between linear and quadratic optimization models," Papers 1105.3594, arXiv.org.
- Markus LEIPPOLD & Fabio TROJANI & Paolo VANINI, 2002.
"A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities,"
FAME Research Paper Series
rp48, International Center for Financial Asset Management and Engineering.
- Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
- Gabriel Frahm & Christoph Memmel, 2010.
"Dominating Estimators for Minimum-Variance Portfolios,"
- Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
- Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
- Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
- Taras Bodnar & Wolfgang Schmid, 2008. "A test for the weights of the global minimum variance portfolio in an elliptical model," Metrika, Springer, vol. 67(2), pages 127-143, March.
- Taras Bodnar & Wolfgang Schmid, 2009. "Econometrical analysis of the sample efficient frontier," The European Journal of Finance, Taylor & Francis Journals, vol. 15(3), pages 317-335.
- Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
- Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. " Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
- repec:hal:journl:peer-00741629 is not listed on IDEAS
- Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
- Mark Britten-Jones, 1999. "The Sampling Error in Estimates of Mean-Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, 04.
- Yarema Okhrin & Wolfgang Schmid, 2008. "Estimation Of Optimal Portfolio Weights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 249-276.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
- Gopal K. Basak & Ravi Jagannathan & Tongshu Ma, 2009. "Jackknife Estimator for Tracking Error Variance of Optimal Portfolios," Management Science, INFORMS, vol. 55(6), pages 990-1002, June.
- Tu, Jun & Zhou, Guofu, 2004. "Data-generating process uncertainty: What difference does it make in portfolio decisions?," Journal of Financial Economics, Elsevier, vol. 72(2), pages 385-421, May.
- Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
- Yu, Bosco Wing-Tong & Pang, Wan Kai & Troutt, Marvin D. & Hou, Shui Hung, 2009. "Objective comparisons of the optimal portfolios corresponding to different utility functions," European Journal of Operational Research, Elsevier, vol. 199(2), pages 604-610, December.
- Michael W. Brandt & Pedro Santa-Clara, 2006. "Dynamic Portfolio Selection by Augmentingthe Asset Space," Journal of Finance, American Finance Association, vol. 61(5), pages 2187-2217, October.
- J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
- Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(02), pages 185-204, June.
- White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1207.1029. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.