Time diversification: Definitions and some closed-form solutions
We establish general conditions under which younger investors should invest a larger proportion of their wealth in risky assets than older ones. In the finite horizon dynamic setting, we show that such phenomenon, known as ''time diversification," can occur in the presence of human wealth, guaranteed consumption, or mean-reverting stock returns. We formalize two alternative notions of time diversification commonly confounded in the literature. Analytic solutions are provided for both time-series and cross-sectional forms of time diversification. To our best knowledge, this paper is the first to solve in closed-form the hedging demand for a CARA investor with inter-temporal consumption and a finite horizon, facing mean-reverting expected returns. Our results indicate that horizon can have a significant effect on the portfolio demand of a CARA investor due to inter-temporal hedging.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2007.
"Portfolio Choice over the Life-Cycle when the Stock and Labor Markets Are Cointegrated,"
Journal of Finance,
American Finance Association, vol. 62(5), pages 2123-2167, October.
- Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2007. "Portfolio choice over the life-cycle when the stock and labor markets are cointegrated," Working Paper Series WP-07-11, Federal Reserve Bank of Chicago.
- Hanno Lustig & Stijn Van Nieuwerburgh & Adrien Verdelhan, 2008.
"The Wealth-Consumption Ratio,"
NBER Working Papers
13896, National Bureau of Economic Research, Inc.
- Ravi Jagannathan & Narayana R. Kocherlakota, 1996. "Why should older people invest less in stock than younger people?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Sum, pages 11-23.
- Valery Polkovnichenko, 2007. "Life-Cycle Portfolio Choice with Additive Habit Formation Preferences and Uninsurable Labor Income Risk," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 83-124, January.
- 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.
- Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
- Normandin, Michel & St-Amour, Pascal, 2008. "An empirical analysis of aggregate household portfolios," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1583-1597, August.
- Zvi Bodie & Robert C. Merton & William F. Samuelson, 1992.
"Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model,"
NBER Working Papers
3954, National Bureau of Economic Research, Inc.
- Bodie, Zvi & Merton, Robert C. & Samuelson, William F., 1992. "Labor supply flexibility and portfolio choice in a life cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 427-449.
- repec:spr:compst:v:50:y:1999:i:2:p:219-243 is not listed on IDEAS
- Liu, Jun & Pan, Jun, 2003.
"Dynamic derivative strategies,"
Journal of Financial Economics,
Elsevier, vol. 69(3), pages 401-430, September.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Ackert, Lucy F. & Church, Bryan K. & Englis, Basil, 2002. "The asset allocation decision and investor heterogeneity: a puzzle?," Journal of Economic Behavior & Organization, Elsevier, vol. 47(4), pages 423-433, April.
- Luis M. Viceira, 2001.
"Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income,"
Journal of Finance,
American Finance Association, vol. 56(2), pages 433-470, 04.
- Luis M. Viceira, 1999. "Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income," NBER Working Papers 7409, National Bureau of Economic Research, Inc.
- Gollier, Christian, 2002. "Time diversification, liquidity constraints, and decreasing aversion to risk on wealth," Journal of Monetary Economics, Elsevier, vol. 49(7), pages 1439-1459, October.
- Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March.
- Branger, Nicole & Schlag, Christian & Schneider, Eva, 2008. "Optimal portfolios when volatility can jump," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1087-1097, June.
- Paul A. Samuelson, 2011.
"Lifetime Portfolio Selection by Dynamic Stochastic Programming,"
World Scientific Book Chapters,
in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472
World Scientific Publishing Co. Pte. Ltd..
- Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-246, August.
- Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
- Heaton, John & Lucas, Deborah, 1997. "Market Frictions, Savings Behavior, And Portfolio Choice," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 76-101, January.
- Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim, 2008. "Nonlinear mean reversion in stock prices," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 767-782, May.
- Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
- Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:33:y:2009:i:6:p:1101-1111. 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: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.