A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function
In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.
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.:
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003.
"Multivariate GARCH models: a survey,"
CORE Discussion Papers
2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Frahm, Gabriel & Memmel, Christoph, 2010.
"Dominating estimators for minimum-variance portfolios,"
Journal of Econometrics,
Elsevier, vol. 159(2), pages 289-302, December.
- Gabriel Frahm & Christoph Memmel, 2010. "Dominating Estimators for Minimum-Variance Portfolios," Post-Print hal-00741629, HAL.
- Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
- 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.
- Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan Storud, 2004. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," NBER Working Papers 10934, National Bureau of Economic Research, Inc.
- Eric Jondeau & Michael Rockinger, 2006.
"Optimal Portfolio Allocation under Higher Moments,"
European Financial Management,
European Financial Management Association, vol. 12(1), pages 29-55.
- Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Society for Computational Economics, vol. 29(3), pages 355-367, May.
- Enrique Sentana & Javier Mencía, 2008.
"Multivariate Location-Scale Mixtures Of Normals And Mean-Variance-Skwness Portfolio Allocation,"
- Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
- Javier Mencía & Enrique Sentana, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Working Papers 0909, Banco de España;Working Papers Homepage.
- Shiqing Ling & Michael McAleer, 2001.
"Asymptotic Theory for a Vector ARMA-GARCH Model,"
ISER Discussion Paper
0549, Institute of Social and Economic Research, Osaka University.
- Basak, Suleyman & Chabakauri, Georgy, 2009.
"Dynamic Mean-Variance Asset Allocation,"
CEPR Discussion Papers
7256, C.E.P.R. Discussion Papers.
- Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
- Amengual, Dante & Sentana, Enrique, 2010.
"A comparison of mean-variance efficiency tests,"
Journal of Econometrics,
Elsevier, vol. 154(1), pages 16-34, January.
- 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.
- 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.
- Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
- James Tobin, 1956.
"Liquidity Preference as Behavior Towards Risk,"
Cowles Foundation Discussion Papers
14, Cowles Foundation for Research in Economics, Yale University.
- Brandt, Michael W. & Santa-Clara, Pedro, 2004.
"Dynamic Portfolio Selection by Augmenting the Asset Space,"
University of California at Los Angeles, Anderson Graduate School of Management
qt632436gt, Anderson Graduate School of Management, UCLA.
- 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.
- Michael W. Brandt & Pedro Santa-Clara, 2004. "Dynamic Portfolio Selection by Augmenting the Asset Space," NBER Working Papers 10372, National Bureau of Economic Research, Inc.
- 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.
- Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
- Olha Bodnar, 2009. "Sequential Surveillance Of The Tangency Portfolio Weights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 797-810.
- Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
- Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
- Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
- Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1207.1003. 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.