Optimum Consumption and Portfolio Allocations under Incomplete Information
We solve in closed form the optimal consumption / portfolio choice problem for the class of isoelastic utility functions under incomplete information about the mean return of the stock price. Our approach consists in converting the original investor's problem into an equivalent program where the agent's utility function is state dependent and for which standard martingale techniques can be easily implemented. Upon observing the realizations of the stock and possibly outside market information, the investor can revise her beliefs about the true value of the mean return, which induces optimal allocations that can be significantly different from those of a myopic agent. We find that the fraction of wealth invested into the risky asset is always increasing in the investor's assessment of the conditional mean return whereas the consumption-wealth is increasing (decreasing) in the latter if the intertemporal elasticity of substitution (I.E.S.) is below (above) unity. When the investor has access to outside market information, the more informative the signal, the higher (lower) the fraction of wealth invested into the risky asset and the lower (higher) the consumption-wealth ratio exactly when the I.E.S. is greater (smaller) than one. The reason is that the agent understands that when she receives better quality information, she can update her beliefs more quickly which in turn can lead to larger changes in her optimal consumption and portfolio allocations. She devotes more of her wealth into the risky asset only if she is willing to tolerate changes in her consumption pattern. Finally, as far as the hedging demand for the risky security is concerned, it is positive (negative) and rises (falls) with more accurate information and the investor horizon, exactly when the I.E.S. if above (below) unity. Hence, the conventional advice according to which long horizon investors should allocate aggressively their wealth to equity is founded only for agents whose intertemporal elasticity of substitution is above unity
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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.:
- Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
- 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.
- Zapatero, Fernando, 1998. "Effects of financial innovations on market volatility when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 597-626, April.
- Gady Zohar, 2001. "A Generalized Cameron-Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 475-494.
- Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
- 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.
- Detemple Jerome & Murthy Shashidhar, 1994. "Intertemporal Asset Pricing with Heterogeneous Beliefs," Journal of Economic Theory, Elsevier, vol. 62(2), pages 294-320, April.
- Philip H. Dybvig, Chi-fu Huang, 1988.
"Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans,"
Review of Financial Studies,
Society for Financial Studies, vol. 1(4), pages 377-401.
- Philip H. Dybvig & Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," Cowles Foundation Discussion Papers 860, Cowles Foundation for Research in Economics, Yale University.
- Detemple, Jerome B, 1986. " Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-91, June.
- Pietro Veronesi, . "How Does Information Quality Affect Stock Returns?," CRSP working papers 462, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- Pietro Veronesi, 2000. "How Does Information Quality Affect Stock Returns?," Journal of Finance, American Finance Association, vol. 55(2), pages 807-837, 04.
- Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
- Pietro Veronesi, . "How Does Information Quality Affect Stock Returns?," CRSP working papers 361, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
- Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
When requesting a correction, please mention this item's handle: RePEc:ecm:latm04:79. 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: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.