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.
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- 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.
- Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
- Liu, Jun & Pan, Jun, 2003. "Dynamic Derivative Strategies," Working papers 4334-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Hanno Lustig & Stijn Van Nieuwerburgh & Adrien Verdelhan, 2008. "The Wealth-Consumption Ratio," NBER Working Papers 13896, National Bureau of Economic Research, Inc.
- Lustig, Hanno & van Nieuwerburgh, Stijn & Verdelhan, Adrien, 2012. "The Wealth-Consumption Ratio," CEPR Discussion Papers 9022, C.E.P.R. Discussion Papers.
- 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.
- 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.
- 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.
- 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.
- Heaton, John & Lucas, Deborah, 1997. "Market Frictions, Savings Behavior, And Portfolio Choice," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 76-101, January.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
- 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.
- 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.
- 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.
- 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.
- 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.
- repec:spr:compst:v:50:y:1999:i:2:p:219-243 is not listed on IDEAS
- Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161. Full references (including those not matched with items on IDEAS)