On the Exact Solution of the Multi-Period Portfolio Choice Problem for an Exponential Utility under Return Predictability
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable variables follow a vector autoregressive process. We prove that the optimal portfolio weights depend on the covariance matrices of the next two periods and the conditional mean vector of the next period. The case without predictable variables and the case of independent asset returns are partial cases of our solution. Furthermore, we provide an empirical study where the cumulative empirical distribution function of the investor's wealth is calculated using the exact solution. It is compared with the investment strategy obtained under the additional assumption that the asset returns are independently distributed.
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.:
- 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.
- 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.
- Campbell, John, 1996.
"Understanding Risk and Return,"
3153293, Harvard University Department of Economics.
- John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
- John Y. Campbell, 1993. "Understanding Risk and Return," NBER Working Papers 4554, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Suleyman Basak & Georgy Chabakauri, 2010.
"Dynamic Mean-Variance Asset Allocation,"
Review of Financial Studies,
Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
- Campbell, John Y, 1991.
"A Variance Decomposition for Stock Returns,"
Royal Economic Society, vol. 101(405), pages 157-79, March.
- Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
- Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, 02.
- 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.
- Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2013.
"On the equivalence of quadratic optimization problems commonly used in portfolio theory,"
European Journal of Operational Research,
Elsevier, vol. 229(3), pages 637-644.
- Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2012. "On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory," Papers 1207.1029, arXiv.org, revised Apr 2013.
- 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.
- John Y. Campbell & Yeung Lewis Chan & Luis M. Viceira, 2001.
"A Multivariate Model of Strategic Asset Allocation,"
NBER Working Papers
8566, National Bureau of Economic Research, Inc.
- Campbell, John Y. & Chan, Yeung Lewis & Viceira, Luis M., 2003. "A multivariate model of strategic asset allocation," Journal of Financial Economics, Elsevier, vol. 67(1), pages 41-80, January.
- Chan, Yeung Lewis & Viceira, Luis & Campbell, John, 2003. "A Multivariate Model of Strategic Asset Allocation," Scholarly Articles 3163263, Harvard University Department of Economics.
- Campbell, John Y & Chan, Yeung Lewis & Viceira, Luis M, 2001. "A Multivariate Model of Strategic Asset Allocation," CEPR Discussion Papers 3070, C.E.P.R. Discussion Papers.
- Ping Li & Jianming Xia & Jia-an Yan, 2001. "Martingale Measure Method for Expected Utility Maximization in Discrete-Time Incomplete Markets," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 445-465, November.
- 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.
- Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
- Lynch, Anthony W. & Tan, Sinan, 2010. "Multiple Risky Assets, Transaction Costs, and Return Predictability: Allocation Rules and Implications for U.S. Investors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(04), pages 1015-1053, August.
- Elton, Edwin J & Gruber, Martin J, 1974. "On the Optimality of Some Multiperiod Portfolio Selection Criteria," The Journal of Business, University of Chicago Press, vol. 47(2), pages 231-43, April.
- Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
- 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.
- Soyer, Refik & Tanyeri, Kadir, 2006. "Bayesian portfolio selection with multi-variate random variance models," European Journal of Operational Research, Elsevier, vol. 171(3), pages 977-990, June.
- 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.
- Zhu, Min, 2013. "Return distribution predictability and its implications for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 209-223.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1207.1037. 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.