On the Exact Solution of the Multi-Period Portfolio Choice Problem for an Exponential Utility under Return Predictability
AbstractIn 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.
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Date of creation: Jul 2012
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- John Y. Campbell, 1993.
"Understanding Risk and Return,"
NBER Working Papers
4554, National Bureau of Economic Research, Inc.
- John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
- Campbell, John, 1996. "Understanding Risk and Return," Scholarly Articles 3153293, Harvard University Department of Economics.
- 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.
- 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.
- 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.
- Chan, Yeung Lewis & Viceira, Luis & Campbell, John, 2003. "A Multivariate Model of Strategic Asset Allocation," Scholarly Articles 3163263, Harvard University Department of Economics.
- Basak, Suleyman & Chabakauri, Georgy, 2009.
"Dynamic Mean-Variance Asset Allocation,"
CEPR Discussion Papers
7256, C.E.P.R. Discussion Papers.
- John Y. Campbell, 1991.
"A Variance Decomposition for Stock Returns,"
NBER Working Papers
3246, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- 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.
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